[Top][All Lists]
[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
[Texi2html-cvs] texi2html ChangeLog T2h_l2h.pm TODO texi2html.i...
|
From: |
Patrice Dumas |
|
Subject: |
[Texi2html-cvs] texi2html ChangeLog T2h_l2h.pm TODO texi2html.i... |
|
Date: |
Thu, 22 Oct 2009 20:23:25 +0000 |
CVSROOT: /cvsroot/texi2html
Module name: texi2html
Changes by: Patrice Dumas <pertusus> 09/10/22 20:23:24
Modified files:
. : ChangeLog T2h_l2h.pm TODO texi2html.init
texi2html.pl
examples : mediawiki.init
formats : html.init
maintained_extra: tex4ht.init
test : README run_test_all.sh
test/formatting: tests.txt
test/formatting/res/tex: tex_l2h.tex
test/formatting/res/tex_httex: tex_tex4ht_math.texi
tex_tex4ht_tex.tex
test/formatting/res/texi_tex: tex_l2h.tex
test/invalid/res/math_not_closed: math_not_closed_l2h.tex
test/invalid/res/tex_in_copying: tex_in_copying_l2h.tex
test/invalid/res/tex_not_closed: tex_not_closed_l2h.tex
test/invalid/res/texi_math_not_closed: math_not_closed_l2h.tex
test/invalid/res/texi_tex_in_copying: tex_in_copying_l2h.tex
test/invalid/res/texi_tex_not_closed: tex_not_closed_l2h.tex
test/manuals/res/mini_ker: 1D-gridded-model.html
Controlling-the-run.html
Feedback-gain.html Kalman-filter.html
Linearization-and-discretization.html
Sensitivities.html
mini_ker_tex4ht_math.html
mini_ker_tex4ht_math.texi
mini_ker_tex4ht_tex.tex
test/manuals/res_all/mini_ker: 1D-gridded-model.html
Controlling-the-run.html
Feedback-gain.html
Kalman-filter.html
Linearization-and-discretization.html
Sensitivities.html
mini_ker_tex4ht_math.html
mini_ker_tex4ht_math.texi
mini_ker_tex4ht_tex.tex
test/manuals/res_info/mini_ker: mini_ker_1.2.html
mini_ker_2.4.html
mini_ker_3.3.html
mini_ker_4.1.html
mini_ker_4.3.html
mini_ker_4.4.html
mini_ker_tex4ht_math.html
mini_ker_tex4ht_math.texi
mini_ker_tex4ht_tex.tex
test/many_input_files/tex_l2h_res: mini_ker_l2h.tex tex_l2h.tex
test/many_input_files/tex_t4ht_res: mini_ker.html
mini_ker_tex4ht_math.html
mini_ker_tex4ht_math.texi
mini_ker_tex4ht_tex.tex
tex_tex4ht_math.texi
tex_tex4ht_tex.tex
test/misc/res/mini_ker_httex: mini_ker.html
mini_ker_tex4ht_math.html
mini_ker_tex4ht_math.texi
mini_ker_tex4ht_tex.tex
test/misc/res/mini_ker_l2h: mini_ker_l2h.tex
test/singular_manual/res/singular: sing_l2h.tex
test/singular_manual/res/singular_httex: sing_tex4ht_tex.tex
Added files:
test/formatting/res/tex_httex_mediawiki: tex tex.2
tex_tex4ht_math.texi
tex_tex4ht_tex.4ct
tex_tex4ht_tex.4tc
tex_tex4ht_tex.css
tex_tex4ht_tex.lg
tex_tex4ht_tex.tex
tex_tex4ht_tex.tmp
tex_tex4ht_tex.xref
test/formatting/res/tex_l2h_mediawiki: tex tex-l2h_cache.pm
tex.2 tex_l2h.html
tex_l2h.tex
tex_l2h_images.pl
tex_l2h_images.tex
tex_l2h_labels.pl
test/formatting/res_all/tex_httex_mediawiki: tex tex.2
tex_tex4ht_math.texi
tex_tex4ht_tex.4ct
tex_tex4ht_tex.4tc
tex_tex4ht_tex.css
tex_tex4ht_tex.lg
tex_tex4ht_tex.tex
tex_tex4ht_tex.tmp
tex_tex4ht_tex.xref
test/formatting/res_all/tex_l2h_mediawiki: tex tex-l2h_cache.pm
tex.2 tex_l2h.html
tex_l2h.tex
tex_l2h_images.pl
tex_l2h_images.tex
tex_l2h_labels.pl
test/formatting/res_info/tex_httex_mediawiki: tex tex.2
tex_tex4ht_math.texi
tex_tex4ht_tex.4ct
tex_tex4ht_tex.4tc
tex_tex4ht_tex.css
tex_tex4ht_tex.lg
tex_tex4ht_tex.tex
tex_tex4ht_tex.tmp
tex_tex4ht_tex.xref
test/formatting/res_info/tex_l2h_mediawiki: tex tex.2
Log message:
* texi2html.init, texi2html.pl, T2h_l2h.pm,
maintained_extra/tex4ht.init:
split tex handling further, with html extraction done in
@command_handler_output such that it is possible to modify the
resulting files after 'process' and before 'output'.
Add newlines between TeX fragments.
If L2H_SKIP is 0, cache is not used.
* examples/mediawiki.init: use html2wiki between 'process' and
before 'output' to translate the html produced by tex4ht or
latex2html to wiki.
CVSWeb URLs:
http://cvs.savannah.gnu.org/viewcvs/texi2html/ChangeLog?cvsroot=texi2html&r1=1.447&r2=1.448
http://cvs.savannah.gnu.org/viewcvs/texi2html/T2h_l2h.pm?cvsroot=texi2html&r1=1.12&r2=1.13
http://cvs.savannah.gnu.org/viewcvs/texi2html/TODO?cvsroot=texi2html&r1=1.153&r2=1.154
http://cvs.savannah.gnu.org/viewcvs/texi2html/texi2html.init?cvsroot=texi2html&r1=1.243&r2=1.244
http://cvs.savannah.gnu.org/viewcvs/texi2html/texi2html.pl?cvsroot=texi2html&r1=1.345&r2=1.346
http://cvs.savannah.gnu.org/viewcvs/texi2html/examples/mediawiki.init?cvsroot=texi2html&r1=1.29&r2=1.30
http://cvs.savannah.gnu.org/viewcvs/texi2html/formats/html.init?cvsroot=texi2html&r1=1.33&r2=1.34
http://cvs.savannah.gnu.org/viewcvs/texi2html/maintained_extra/tex4ht.init?cvsroot=texi2html&r1=1.2&r2=1.3
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/README?cvsroot=texi2html&r1=1.4&r2=1.5
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/run_test_all.sh?cvsroot=texi2html&r1=1.11&r2=1.12
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/tests.txt?cvsroot=texi2html&r1=1.34&r2=1.35
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res/tex/tex_l2h.tex?cvsroot=texi2html&r1=1.1&r2=1.2
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res/tex_httex/tex_tex4ht_math.texi?cvsroot=texi2html&r1=1.1&r2=1.2
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res/tex_httex/tex_tex4ht_tex.tex?cvsroot=texi2html&r1=1.1&r2=1.2
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res/tex_httex_mediawiki/tex?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res/tex_httex_mediawiki/tex.2?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res/tex_httex_mediawiki/tex_tex4ht_math.texi?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res/tex_httex_mediawiki/tex_tex4ht_tex.4ct?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res/tex_httex_mediawiki/tex_tex4ht_tex.4tc?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res/tex_httex_mediawiki/tex_tex4ht_tex.css?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res/tex_httex_mediawiki/tex_tex4ht_tex.lg?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res/tex_httex_mediawiki/tex_tex4ht_tex.tex?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res/tex_httex_mediawiki/tex_tex4ht_tex.tmp?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res/tex_httex_mediawiki/tex_tex4ht_tex.xref?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res/tex_l2h_mediawiki/tex?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res/tex_l2h_mediawiki/tex-l2h_cache.pm?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res/tex_l2h_mediawiki/tex.2?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res/tex_l2h_mediawiki/tex_l2h.html?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res/tex_l2h_mediawiki/tex_l2h.tex?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res/tex_l2h_mediawiki/tex_l2h_images.pl?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res/tex_l2h_mediawiki/tex_l2h_images.tex?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res/tex_l2h_mediawiki/tex_l2h_labels.pl?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res/texi_tex/tex_l2h.tex?cvsroot=texi2html&r1=1.1&r2=1.2
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res_all/tex_httex_mediawiki/tex?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res_all/tex_httex_mediawiki/tex.2?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res_all/tex_httex_mediawiki/tex_tex4ht_math.texi?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res_all/tex_httex_mediawiki/tex_tex4ht_tex.4ct?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res_all/tex_httex_mediawiki/tex_tex4ht_tex.4tc?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res_all/tex_httex_mediawiki/tex_tex4ht_tex.css?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res_all/tex_httex_mediawiki/tex_tex4ht_tex.lg?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res_all/tex_httex_mediawiki/tex_tex4ht_tex.tex?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res_all/tex_httex_mediawiki/tex_tex4ht_tex.tmp?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res_all/tex_httex_mediawiki/tex_tex4ht_tex.xref?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res_all/tex_l2h_mediawiki/tex?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res_all/tex_l2h_mediawiki/tex-l2h_cache.pm?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res_all/tex_l2h_mediawiki/tex.2?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res_all/tex_l2h_mediawiki/tex_l2h.html?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res_all/tex_l2h_mediawiki/tex_l2h.tex?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res_all/tex_l2h_mediawiki/tex_l2h_images.pl?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res_all/tex_l2h_mediawiki/tex_l2h_images.tex?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res_all/tex_l2h_mediawiki/tex_l2h_labels.pl?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res_info/tex_httex_mediawiki/tex?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res_info/tex_httex_mediawiki/tex.2?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res_info/tex_httex_mediawiki/tex_tex4ht_math.texi?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res_info/tex_httex_mediawiki/tex_tex4ht_tex.4ct?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res_info/tex_httex_mediawiki/tex_tex4ht_tex.4tc?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res_info/tex_httex_mediawiki/tex_tex4ht_tex.css?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res_info/tex_httex_mediawiki/tex_tex4ht_tex.lg?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res_info/tex_httex_mediawiki/tex_tex4ht_tex.tex?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res_info/tex_httex_mediawiki/tex_tex4ht_tex.tmp?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res_info/tex_httex_mediawiki/tex_tex4ht_tex.xref?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res_info/tex_l2h_mediawiki/tex?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/formatting/res_info/tex_l2h_mediawiki/tex.2?cvsroot=texi2html&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/invalid/res/math_not_closed/math_not_closed_l2h.tex?cvsroot=texi2html&r1=1.1&r2=1.2
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/invalid/res/tex_in_copying/tex_in_copying_l2h.tex?cvsroot=texi2html&r1=1.1&r2=1.2
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/invalid/res/tex_not_closed/tex_not_closed_l2h.tex?cvsroot=texi2html&r1=1.1&r2=1.2
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/invalid/res/texi_math_not_closed/math_not_closed_l2h.tex?cvsroot=texi2html&r1=1.1&r2=1.2
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/invalid/res/texi_tex_in_copying/tex_in_copying_l2h.tex?cvsroot=texi2html&r1=1.1&r2=1.2
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/invalid/res/texi_tex_not_closed/tex_not_closed_l2h.tex?cvsroot=texi2html&r1=1.1&r2=1.2
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/manuals/res/mini_ker/1D-gridded-model.html?cvsroot=texi2html&r1=1.14&r2=1.15
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/manuals/res/mini_ker/Controlling-the-run.html?cvsroot=texi2html&r1=1.15&r2=1.16
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/manuals/res/mini_ker/Feedback-gain.html?cvsroot=texi2html&r1=1.16&r2=1.17
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/manuals/res/mini_ker/Kalman-filter.html?cvsroot=texi2html&r1=1.16&r2=1.17
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/manuals/res/mini_ker/Linearization-and-discretization.html?cvsroot=texi2html&r1=1.13&r2=1.14
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/manuals/res/mini_ker/Sensitivities.html?cvsroot=texi2html&r1=1.15&r2=1.16
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/manuals/res/mini_ker/mini_ker_tex4ht_math.html?cvsroot=texi2html&r1=1.1&r2=1.2
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/manuals/res/mini_ker/mini_ker_tex4ht_math.texi?cvsroot=texi2html&r1=1.1&r2=1.2
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/manuals/res/mini_ker/mini_ker_tex4ht_tex.tex?cvsroot=texi2html&r1=1.1&r2=1.2
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/manuals/res_all/mini_ker/1D-gridded-model.html?cvsroot=texi2html&r1=1.5&r2=1.6
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/manuals/res_all/mini_ker/Controlling-the-run.html?cvsroot=texi2html&r1=1.5&r2=1.6
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/manuals/res_all/mini_ker/Feedback-gain.html?cvsroot=texi2html&r1=1.5&r2=1.6
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/manuals/res_all/mini_ker/Kalman-filter.html?cvsroot=texi2html&r1=1.5&r2=1.6
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/manuals/res_all/mini_ker/Linearization-and-discretization.html?cvsroot=texi2html&r1=1.5&r2=1.6
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/manuals/res_all/mini_ker/Sensitivities.html?cvsroot=texi2html&r1=1.5&r2=1.6
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/manuals/res_all/mini_ker/mini_ker_tex4ht_math.html?cvsroot=texi2html&r1=1.1&r2=1.2
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/manuals/res_all/mini_ker/mini_ker_tex4ht_math.texi?cvsroot=texi2html&r1=1.1&r2=1.2
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/manuals/res_all/mini_ker/mini_ker_tex4ht_tex.tex?cvsroot=texi2html&r1=1.1&r2=1.2
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/manuals/res_info/mini_ker/mini_ker_1.2.html?cvsroot=texi2html&r1=1.5&r2=1.6
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/manuals/res_info/mini_ker/mini_ker_2.4.html?cvsroot=texi2html&r1=1.5&r2=1.6
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/manuals/res_info/mini_ker/mini_ker_3.3.html?cvsroot=texi2html&r1=1.5&r2=1.6
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/manuals/res_info/mini_ker/mini_ker_4.1.html?cvsroot=texi2html&r1=1.5&r2=1.6
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/manuals/res_info/mini_ker/mini_ker_4.3.html?cvsroot=texi2html&r1=1.5&r2=1.6
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/manuals/res_info/mini_ker/mini_ker_4.4.html?cvsroot=texi2html&r1=1.5&r2=1.6
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/manuals/res_info/mini_ker/mini_ker_tex4ht_math.html?cvsroot=texi2html&r1=1.1&r2=1.2
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/manuals/res_info/mini_ker/mini_ker_tex4ht_math.texi?cvsroot=texi2html&r1=1.1&r2=1.2
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/manuals/res_info/mini_ker/mini_ker_tex4ht_tex.tex?cvsroot=texi2html&r1=1.1&r2=1.2
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/many_input_files/tex_l2h_res/mini_ker_l2h.tex?cvsroot=texi2html&r1=1.1&r2=1.2
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/many_input_files/tex_l2h_res/tex_l2h.tex?cvsroot=texi2html&r1=1.1&r2=1.2
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/many_input_files/tex_t4ht_res/mini_ker.html?cvsroot=texi2html&r1=1.23&r2=1.24
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/many_input_files/tex_t4ht_res/mini_ker_tex4ht_math.html?cvsroot=texi2html&r1=1.1&r2=1.2
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/many_input_files/tex_t4ht_res/mini_ker_tex4ht_math.texi?cvsroot=texi2html&r1=1.1&r2=1.2
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/many_input_files/tex_t4ht_res/mini_ker_tex4ht_tex.tex?cvsroot=texi2html&r1=1.1&r2=1.2
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/many_input_files/tex_t4ht_res/tex_tex4ht_math.texi?cvsroot=texi2html&r1=1.1&r2=1.2
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/many_input_files/tex_t4ht_res/tex_tex4ht_tex.tex?cvsroot=texi2html&r1=1.1&r2=1.2
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/misc/res/mini_ker_httex/mini_ker.html?cvsroot=texi2html&r1=1.23&r2=1.24
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/misc/res/mini_ker_httex/mini_ker_tex4ht_math.html?cvsroot=texi2html&r1=1.1&r2=1.2
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/misc/res/mini_ker_httex/mini_ker_tex4ht_math.texi?cvsroot=texi2html&r1=1.1&r2=1.2
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/misc/res/mini_ker_httex/mini_ker_tex4ht_tex.tex?cvsroot=texi2html&r1=1.1&r2=1.2
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/misc/res/mini_ker_l2h/mini_ker_l2h.tex?cvsroot=texi2html&r1=1.1&r2=1.2
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/singular_manual/res/singular/sing_l2h.tex?cvsroot=texi2html&r1=1.1&r2=1.2
http://cvs.savannah.gnu.org/viewcvs/texi2html/test/singular_manual/res/singular_httex/sing_tex4ht_tex.tex?cvsroot=texi2html&r1=1.1&r2=1.2
Patches:
Index: ChangeLog
===================================================================
RCS file: /cvsroot/texi2html/texi2html/ChangeLog,v
retrieving revision 1.447
retrieving revision 1.448
diff -u -b -r1.447 -r1.448
--- ChangeLog 19 Oct 2009 13:40:50 -0000 1.447
+++ ChangeLog 22 Oct 2009 20:23:18 -0000 1.448
@@ -1,3 +1,15 @@
+2009-10-20 Patrice Dumas <address@hidden>
+
+ * texi2html.init, texi2html.pl, T2h_l2h.pm,
maintained_extra/tex4ht.init:
+ split tex handling further, with html extraction done in
+ @command_handler_output such that it is possible to modify the
+ resulting files after 'process' and before 'output'.
+ Add newlines between TeX fragments.
+ If L2H_SKIP is 0, cache is not used.
+ * examples/mediawiki.init: use html2wiki between 'process' and
+ before 'output' to translate the html produced by tex4ht or
+ latex2html to wiki.
+
2009-10-19 Patrice Dumas <address@hidden>
* formats/*.init: don't strip {} in @math in html, docbook and
Index: T2h_l2h.pm
===================================================================
RCS file: /cvsroot/texi2html/texi2html/T2h_l2h.pm,v
retrieving revision 1.12
retrieving revision 1.13
diff -u -b -r1.12 -r1.13
--- T2h_l2h.pm 19 Oct 2009 13:40:50 -0000 1.12
+++ T2h_l2h.pm 22 Oct 2009 20:23:18 -0000 1.13
@@ -57,7 +57,6 @@
my $verbose;
my $docu_rdir;
my $docu_name;
-my $docu_ext;
# init_from_html
my $extract_error_count;
@@ -139,7 +138,6 @@
$docu_name = $Texi2HTML::THISDOC{'file_base_name'};
$docu_rdir = $Texi2HTML::THISDOC{'destination_directory'};
$docu_rdir = '' if (!defined($docu_rdir));
- $docu_ext = $Texi2HTML::THISDOC{'extension'};
$l2h_name = "${docu_name}_l2h";
$l2h_latex_file = "$docu_rdir${l2h_name}.tex";
$l2h_cache_file = "${docu_rdir}${docu_name}-l2h_cache.pm";
@@ -162,7 +160,7 @@
print L2H_LATEX $l2h_latex_preamble;
}
# open the database that holds cached text
- init_cache();
+ init_cache() if (!defined($Texi2HTML::Config::L2H_SKIP) or
$Texi2HTML::Config::L2H_SKIP);
$status = 1;
}
@@ -205,14 +203,14 @@
$latex_converted_count++;
unless ($Texi2HTML::Config::L2H_SKIP)
{
- print L2H_LATEX "\\begin{rawhtml}\n";
+ print L2H_LATEX "\\begin{rawhtml}\n\n";
print L2H_LATEX "<!-- l2h_begin $l2h_name $count -->\n";
print L2H_LATEX "\\end{rawhtml}\n";
print L2H_LATEX "$text\n";
print L2H_LATEX "\\begin{rawhtml}\n";
- print L2H_LATEX "<!-- l2h_end $l2h_name $count -->\n";
+ print L2H_LATEX "<!-- l2h_end $l2h_name $count -->\n\n";
print L2H_LATEX "\\end{rawhtml}\n";
}
}
@@ -320,9 +318,14 @@
# Finish with: finish
# closes $l2h_html_dir/$l2h_name.".$docu_ext"
+
# the images generated by latex2html have names like ${docu_name}_l2h_img?.png
# they are copied to ${docu_name}_?.png, and html is changed accordingly.
+# FIXME is it really necessary to bother doing that? Looks like an unneeded
+# complication to me (pertusus, 2009), and it could go bad if there is some
+# SRC="(.*?)" in the text (though the regexp could be made more specific).
+
# %l2h_img; # associate src file to destination file
# such that files are not copied twice
sub change_image_file_names($)
@@ -337,12 +340,15 @@
unless ($dest)
{
my $ext = '';
- if ($src =~ /.*\.(.*)$/ && $1 ne $docu_ext)
+ if ($src =~ /.*\.(.*)$/ and
(!defined($Texi2HTML::THISDOC{'extension'}) or $1 ne
$Texi2HTML::THISDOC{'extension'}))
{
$ext = ".$1";
}
else
- { # FIXME what is that check about?
+ { # A warning when the image extension is the same than the
+ # document extension. copying the file could result in
+ # overwriting an output file (almost surely if the default
+ # texi2html file names are used).
main::document_warn ("L2h image $src has invalid extension");
next;
}
@@ -351,11 +357,18 @@
$image_count++;
}
$dest = "${docu_name}_${image_count}$ext";
-# FIXME this isn't portable. + error condition not checked.
+ if ($debug)
+ {
+ # not portable, but only used with debug.
system("cp -f $docu_rdir$src $docu_rdir$dest");
+ }
+ else
+ {
+ # FIXME error condition not checked.
+ rename ("$docu_rdir$src", "$docu_rdir$dest");
+ }
$l2h_img{$src} = $dest;
-# FIXME error condition not checked
- unlink "$docu_rdir$src" unless ($debug);
+ #unlink "$docu_rdir$src" unless ($debug);
}
$content =~ s/SRC="$src"/SRC="$dest"/g;
}
@@ -385,14 +398,14 @@
my ($count, $h_line);
while ($h_line = <L2H_HTML>)
{
- if ($h_line =~ /^<!-- l2h_begin $l2h_name ([0-9]+) -->/)
+ if ($h_line =~ /!-- l2h_begin $l2h_name ([0-9]+) --/)
{
$count = $1;
my $h_content = '';
my $h_end_found = 0;
while ($h_line = <L2H_HTML>)
{
- if ($h_line =~ /^<!-- l2h_end $l2h_name $count -->/)
+ if ($h_line =~ /!-- l2h_end $l2h_name $count --/)
{
$h_end_found = 1;
chomp $h_content;
@@ -469,8 +482,9 @@
{
$html_output_count++;
# maybe we could also have something if simple_format
- # with Texi2HTML::Config::protect_text, once simple_format
- # may happen for anything else than lines
+ # with Texi2HTML::Config::protect_text in case there
+ # was some @math on a line passed through simple_format.
+ # This would certainly be illegal texinfo, however.
if ($state->{'remove_texi'})
{# don't protect anything
$result .= $l2h_to_latex[$count];
@@ -530,20 +544,21 @@
return 1;
}
-# the driver of end of first pass, second pass and beginning of third pass
+# the driver of end of first pass and second pass
#
sub latex2html()
{
return unless($status);
return unless ($status = finish_to_latex());
return unless ($status = to_html());
- return unless ($status = init_from_html());
}
##############################
# stuff for l2h caching
#
+# FIXME it is clear that l2h stuff takes very long compared with texi2html
+# which is already quite long. However this also adds some complexity
# I tried doing this with a dbm data base, but it did not store all
# keys/values. Hence, I did as latex2html does it
Index: TODO
===================================================================
RCS file: /cvsroot/texi2html/texi2html/TODO,v
retrieving revision 1.153
retrieving revision 1.154
diff -u -b -r1.153 -r1.154
--- TODO 19 Oct 2009 13:40:50 -0000 1.153
+++ TODO 22 Oct 2009 20:23:18 -0000 1.154
@@ -95,20 +95,14 @@
* do a translation to TeX/LaTeX to be used in @math,
for example @equiv->\equiv. t2h_default_protect_text should be used
- such as not too do anything in that context.
+ such that there is no change in text in this context.
-* to use html2wiki, could use --preserve-nowiki or the same. Output
- in tex_l2h.html
-<nowiki>!-- l2h_end tex_l2h 1 --</nowiki>
- and change regexp in T2h_l2h.pm ro be like tex4ht, only match !-- --.
- Add %Texi2HTML::Config::append_enclosed_converted_text {'math'}, {'tex'}
- Texi2HTML::Config::prepend_enclosed_converted_text
- to be able to use '<' (default) or '<nowiki>'.
-
- Then it becomes possible, after the regular call to latex2html and
- before extraction. To make this possible the calls to latex2html
- should be split into command_handler_process and command_handler_output,
- similar with tex4ht.
+* in LaTeX, @example and the like could be implemented as \fancyvrb
+ with fontfamily=helvetica, fontsize=\small commandchars=\\\{\}
+
+* use libintl as a gettext implementation?
+
+* %f$x (index in printf) appeared in perl 5.8.0, 18 jul 2002
* document the new $image arguments/API
Index: texi2html.init
===================================================================
RCS file: /cvsroot/texi2html/texi2html/texi2html.init,v
retrieving revision 1.243
retrieving revision 1.244
diff -u -b -r1.243 -r1.244
--- texi2html.init 19 Oct 2009 13:40:50 -0000 1.243
+++ texi2html.init 22 Oct 2009 20:23:18 -0000 1.244
@@ -13,7 +13,7 @@
# Afterwards, load the file with command-line
# option --init-file <your_init_file>
#
-# $Id: texi2html.init,v 1.243 2009/10/19 13:40:50 pertusus Exp $
+# $Id: texi2html.init,v 1.244 2009/10/22 20:23:18 pertusus Exp $
######################################################################
# The following variables can also be set by command-line options
@@ -308,7 +308,10 @@
# --l2h-skip
# If this is set the actual call to latex2html is skipped. The previously
# generated content is reused, instead.
-$L2H_SKIP = '';
+# If set to 0, the cache is not used.
+# If undef the cache is used for as many tex fragments as possible
+# and for the remaining the command is run.
+$L2H_SKIP = undef;
# --l2h-tmp
# If this is set l2h uses the specified directory for temporary files. The path
Index: texi2html.pl
===================================================================
RCS file: /cvsroot/texi2html/texi2html/texi2html.pl,v
retrieving revision 1.345
retrieving revision 1.346
diff -u -b -r1.345 -r1.346
--- texi2html.pl 18 Oct 2009 21:52:34 -0000 1.345
+++ texi2html.pl 22 Oct 2009 20:23:18 -0000 1.346
@@ -86,7 +86,7 @@
}
# CVS version:
-# $Id: texi2html.pl,v 1.345 2009/10/18 21:52:34 pertusus Exp $
+# $Id: texi2html.pl,v 1.346 2009/10/22 20:23:18 pertusus Exp $
# Homepage:
my $T2H_HOMEPAGE = "http://www.nongnu.org/texi2html/";;
@@ -3898,6 +3898,7 @@
{
push @Texi2HTML::Config::command_handler_init,
\&Texi2HTML::LaTeX2HTML::init;
push @Texi2HTML::Config::command_handler_process,
\&Texi2HTML::LaTeX2HTML::latex2html;
+ push @Texi2HTML::Config::command_handler_output,
\&Texi2HTML::LaTeX2HTML::init_from_html;
push @Texi2HTML::Config::command_handler_finish,
\&Texi2HTML::LaTeX2HTML::finish;
$Texi2HTML::Config::command_handler{'math'} =
{ 'init' => \&Texi2HTML::LaTeX2HTML::to_latex,
Index: examples/mediawiki.init
===================================================================
RCS file: /cvsroot/texi2html/texi2html/examples/mediawiki.init,v
retrieving revision 1.29
retrieving revision 1.30
diff -u -b -r1.29 -r1.30
--- examples/mediawiki.init 18 Oct 2009 21:52:34 -0000 1.29
+++ examples/mediawiki.init 22 Oct 2009 20:23:19 -0000 1.30
@@ -8,7 +8,7 @@
# Load the file with command-line
# option -init-file mediawiki.init
#
-# $Id: mediawiki.init,v 1.29 2009/10/18 21:52:34 pertusus Exp $
+# $Id: mediawiki.init,v 1.30 2009/10/22 20:23:19 pertusus Exp $
use strict;
@@ -166,18 +166,135 @@
# no acronym nor abbr allowed in wikitext.
$acronym_like = \&t2h_default_acronym_like;
-push @command_handler_setup, \&mediawiki_initialize_variables;
+push @command_handler_setup, \&mediawiki_default_initialize_variables;
my %mediawiki_doc_nr_to_file; # File name cache based on file index.
my %mediawiki_target_to_name;
my %mediawiki_special_file_name;
-sub mediawiki_initialize_variables()
+sub mediawiki_default_initialize_variables()
{
%mediawiki_doc_nr_to_file = (); # File name cache based on file index.
%mediawiki_target_to_name = ();
%mediawiki_special_file_name = ();
}
+my @html_files_from_tex;
+my $mediawiki_out_dir;
+my $tex_extension;
+
+push @command_handler_init, \&mediawiki_default_init_html_to_wiki;
+
+sub mediawiki_default_init_html_to_wiki
+{
+ # This must be done here, because the latex2html handler is added
+ # after command line scanning, so after the mediawiki.init parsing
+ push @command_handler_process, \&mediawiki_default_html_to_wiki;
+
+ $command_handler{'math'}->{'init'} = undef;
+ $command_handler{'math'}->{'expand'} = undef;
+ $command_handler{'math'} = undef;
+ $mediawiki_out_dir = "$Texi2HTML::THISDOC{'destination_directory'}";
+ $mediawiki_out_dir = './' if (!defined($mediawiki_out_dir) or
$mediawiki_out_dir =~ /^\s*$/);
+ @html_files_from_tex = ();
+ $tex_extension = undef;
+ if ($Texi2HTML::THISDOC{'extensions'}->{'tex4ht'})
+ {
+ push @html_files_from_tex,
"$Texi2HTML::THISDOC{'file_base_name'}_tex4ht_tex.html";
+ $tex_extension = 'tex4ht';
+ }
+ elsif ($L2H)
+ {
+ push @html_files_from_tex,
"$Texi2HTML::THISDOC{'file_base_name'}_l2h.html";
+ $tex_extension = 'l2h';
+ # avoid use of the cache
+ $Texi2HTML::Config::L2H_SKIP = 0;
+ }
+}
+
+# could be in texi2html.init...
+sub mediawiki_default_readd_end_of_lines($$$$;$)
+{
+ my $from_file = shift;
+ my $to_file = shift;
+ my $tex_extension = shift;
+ my $basename = shift;
+ my $before_wiki = shift;
+ # html2wiki removes end of lines, they are readded here
+ unless (open (ORIG, $from_file))
+ {
+ print STDERR "open $from_file error: $!\n";
+ return 0;
+ }
+ unless (open (FINAL, ">$to_file"))
+ {
+ print STDERR "open $to_file error: $!\n";
+ return 0;
+ }
+ my $line;
+ while ($line = <ORIG>)
+ {
+ if ($before_wiki)
+ {
+ $line =~ s/(<!-- ${tex_extension}_end $basename ((\w+ |)(\d+)) -->)
*$/$1\n\n<p>intersticiae<\/p>\n/;
+ $line = Texi2HTML::LaTeX2HTML::change_image_file_names($line) if
($tex_extension eq 'l2h');
+ }
+ else
+ {
+ $line =~ s/^(<!-- ${tex_extension}_begin $basename ((\w+ |)(\d+))
-->)(.+)/$1\n$5/;
+ $line =~ s/(.+)(<!-- ${tex_extension}_end $basename ((\w+ |)(\d+))
-->) *$/$1\n$2/;
+ }
+ print FINAL "$line";
+ }
+ close ORIG;
+ close FINAL;
+ return 1;
+}
+
+sub mediawiki_default_html_to_wiki
+{
+ foreach my $file (@html_files_from_tex)
+ {
+ if (-f $mediawiki_out_dir.$file)
+ {
+ my $html_file = $mediawiki_out_dir.$file;
+ my $tmp_file = $mediawiki_out_dir.$file.".tmp";
+ my $tmp_file2 = $mediawiki_out_dir.$file.".tmp2";
+ my $tmp_file3 = $mediawiki_out_dir.$file.".tmp3";
+ my $basename = $file;
+ $basename =~ s/\.html$//;
+ if (!rename ($html_file, $tmp_file))
+ {
+ print STDERR "rename $html_file $tmp_file error: $!\n";
+ return;
+ }
+ #system ("cp $tmp_file $tmp_file.save");
+ # Add a paragraph between the end and begin comments to force
+ # html2wiki to leave them appart.
+ return unless (mediawiki_default_readd_end_of_lines($tmp_file,
$tmp_file3, $tex_extension, $basename, 1));
+ if (!rename ($tmp_file3, $tmp_file))
+ {
+ print STDERR "rename $tmp_file3 $tmp_file error: $!\n";
+ return;
+ }
+ #system ("cp $tmp_file $tmp_file3.save");
+ my $cmd = "html2wiki --dialect MediaWiki --strip-tags '' $tmp_file >
$tmp_file2";
+ print STDERR "Launching(". Cwd::cwd() ."): $cmd\n" if
($Texi2HTML::Config::VERBOSE);
+ if (system ($cmd))
+ {
+ main::document_warn ("mediawiki_tex command failed: $cmd");
+ return;
+ }
+ # this ensures that there is one end of line before the
+ # html comment, and after, even though html2wiki removed them
+ return unless (mediawiki_default_readd_end_of_lines($tmp_file2,
$html_file, $tex_extension, $basename));
+ #system ("cp $html_file $html_file.save");
+ }
+ else
+ { # FIXME error message?
+ }
+ }
+}
+
$heading_text = \&mediawiki_heading_text;
sub mediawiki_heading_text($$$)
Index: formats/html.init
===================================================================
RCS file: /cvsroot/texi2html/texi2html/formats/html.init,v
retrieving revision 1.33
retrieving revision 1.34
diff -u -b -r1.33 -r1.34
--- formats/html.init 19 Oct 2009 13:40:51 -0000 1.33
+++ formats/html.init 22 Oct 2009 20:23:19 -0000 1.34
@@ -6,7 +6,7 @@
# A copy of this file is pasted into the beginning of texi2html by
# running './configure'.
#
-# $Id: html.init,v 1.33 2009/10/19 13:40:51 pertusus Exp $
+# $Id: html.init,v 1.34 2009/10/22 20:23:19 pertusus Exp $
use strict;
@@ -68,31 +68,6 @@
# file name used for Top node when NODE_FILES is true
$TOP_NODE_FILE = 'index';
-# if this is set, latex2html is used for generation of math content.
-$L2H = '';
-
-######################
-# The following options are only relevant if $L2H is set
-#
-# name/location of latex2html program
-$L2H_L2H = "latex2html";
-
-# If this is set the actual call to latex2html is skipped. The previously
-# generated content is reused, instead.
-$L2H_SKIP = '';
-
-# If this is set l2h uses the specified directory for temporary files. The path
-# leading to this directory may not contain a dot (i.e., a ".");
-# otherwise, l2h will fail.
-$L2H_TMP = '';
-
-# If set, l2h uses the file as latex2html init file
-$L2H_FILE = 'l2h.init';
-
-# if this is set the intermediate files generated by texi2html in relation with
-# latex2html are cleaned (they all have the prefix <document name>_l2h_).
-$L2H_CLEAN = 1;
-
##############################################################################
#
# The following can only be set in the init file
Index: maintained_extra/tex4ht.init
===================================================================
RCS file: /cvsroot/texi2html/texi2html/maintained_extra/tex4ht.init,v
retrieving revision 1.2
retrieving revision 1.3
diff -u -b -r1.2 -r1.3
--- maintained_extra/tex4ht.init 19 Oct 2009 13:40:51 -0000 1.2
+++ maintained_extra/tex4ht.init 22 Oct 2009 20:23:19 -0000 1.3
@@ -36,6 +36,7 @@
{
push @command_handler_init, \&Texi2HTML::TeX4HT::tex4ht_init;
push @command_handler_process, \&Texi2HTML::TeX4HT::tex4ht_process;
+push @command_handler_output, \&Texi2HTML::TeX4HT::tex4ht_output;
push @command_handler_finish, \&Texi2HTML::TeX4HT::tex4ht_finish;
$command_handler{'math'} =
@@ -48,11 +49,17 @@
};
}
+
{
use Cwd;
package Texi2HTML::TeX4HT;
+use vars qw(
+$STYLE_MATH
+$STYLE_TEX
+);
+
$STYLE_MATH = 'texi' if (!defined($STYLE_MATH));
$STYLE_TEX = 'tex' if (!defined($STYLE_TEX));
@@ -143,6 +150,7 @@
}
}
}
+ $Texi2HTML::THISDOC{'extensions'}->{'tex4ht'} = 1;
}
sub tex4ht_to_latex
@@ -154,13 +162,21 @@
my $fh = $commands{$command}->{'handle'};
# write to tex file
- my $before_comment = "address@hidden";
- $before_comment = "\\HCode{\\Hnewline " if ($style ne 'texi');
- my $after_comment = "address@hidden verbatim\n";
- $after_comment = "\\Hnewline}\n" if ($style ne 'texi');
+ my $before_comment_open = "address@hidden";
+ my $after_comment_open = "address@hidden verbatim\n";
+ my $before_comment_close = "address@hidden";
+ my $after_comment_close = "address@hidden verbatim\n";
+
+ if ($style ne 'texi')
+ {
+ $before_comment_open = "\\HCode{\\Hnewline \\Hnewline ";
+ $after_comment_open = "\\Hnewline}\n";
+ $before_comment_close = "\\HCode{\\Hnewline ";
+ $after_comment_close = "\\Hnewline \\Hnewline}\n";
+ }
my $begin_comment = "<!-- tex4ht_begin $commands{$command}->{'basename'}
$command $counter -->";
- print $fh "$before_comment$begin_comment$after_comment";
+ print $fh "$before_comment_open$begin_comment$after_comment_open";
if ($command eq 'tex')
{
print $fh $text;
@@ -177,7 +193,7 @@
}
}
my $end_comment = "<!-- tex4ht_end $commands{$command}->{'basename'}
$command $counter -->";
- print $fh "$before_comment$end_comment$after_comment";
+ print $fh "$before_comment_close$end_comment$after_comment_close";
$commands{$command}->{'counter'}++;
return 1;
}
@@ -205,6 +221,21 @@
tex4ht_return_to_dir();
}
+sub tex4ht_output
+{
+ unless (chdir $tex4ht_out_dir)
+ {
+ main::document_warn ("t2h_tex4ht chdir to $tex4ht_out_dir failed");
+ $tex4ht_latex_failed = 1;
+ return;
+ }
+ foreach my $command ('math', 'tex')
+ {
+ tex4ht_output_command($command);
+ }
+ tex4ht_return_to_dir();
+}
+
sub tex4ht_finish_latex
{
#print STDERR "$style $tex4ht_latex_failed $tex4ht_counter\n";
@@ -229,7 +260,7 @@
close ($fh);
}
-sub tex4ht_process_command
+sub tex4ht_process_command($)
{
my $command = shift;
return unless ($commands{$command}->{'counter'});
@@ -248,7 +279,15 @@
$tex4ht_latex_failed = 1;
return;
}
- # FIXME cut here
+ # this have to be done during the 'process' phase, in 'output' it is
+ # too late.
+ push @{$Texi2HTML::THISDOC{'css_import_lines'}}, "address@hidden
\"$commands{$command}->{'basename'}.css\";\n";
+}
+
+sub tex4ht_output_command($)
+{
+ my $command = shift;
+ return unless ($commands{$command}->{'counter'});
# extract the html from the file created by tex4ht
my $html_basefile = $commands{$command}->{'html_file'};
unless (open (TEX4HT_HTMLFILE, $html_basefile))
@@ -262,7 +301,7 @@
my $line;
while ($line = <TEX4HT_HTMLFILE>)
{
- #print STDERR "while $line";
+ #print STDERR "$html_basefile: while $line";
if ($line =~ /!-- tex4ht_begin $commands{$command}->{'basename'} (\w+)
(\d+) --/)
{
my $command = $1;
@@ -297,8 +336,6 @@
}
close (TEX4HT_HTMLFILE);
- push @{$Texi2HTML::THISDOC{'css_import_lines'}}, "address@hidden
\"$commands{$command}->{'basename'}.css\";\n";
-
}
sub tex4ht_return_to_dir
Index: test/README
===================================================================
RCS file: /cvsroot/texi2html/texi2html/test/README,v
retrieving revision 1.4
retrieving revision 1.5
diff -u -b -r1.4 -r1.5
--- test/README 4 Aug 2009 14:30:45 -0000 1.4
+++ test/README 22 Oct 2009 20:23:19 -0000 1.5
@@ -2,12 +2,12 @@
=============
To run this testsuite, sed (with -i), awk, diff, mktemp are used. To
-find the same results, tex4ht, latex2HTML, perl with unicode support and
-the Text::Unidecode perl module have to be installed (with their
-dependencies). It is possible that some test results involving tex4ht and
-latex2HTML depend on the setup and version of these tools, so you may
-get false negative. If tex4ht or latex2HTML are not found, the corresponding
-tests are skipped.
+find the same results, tex4ht, latex2HTML, html2wiki, perl with unicode
+support and the Text::Unidecode perl module have to be installed (with their
+dependencies). It is possible that some test results involving latex2HTML,
+tex4ht or html2wiki depend on the setup and version of these tools, so you may
+get false negative. If tex4ht, latex2HTML or html2wiki are not found, the
+corresponding tests are skipped.
Running the testsuite
Index: test/run_test_all.sh
===================================================================
RCS file: /cvsroot/texi2html/texi2html/test/run_test_all.sh,v
retrieving revision 1.11
retrieving revision 1.12
diff -u -b -r1.11 -r1.12
--- test/run_test_all.sh 10 Sep 2009 20:32:29 -0000 1.11
+++ test/run_test_all.sh 22 Oct 2009 20:23:19 -0000 1.12
@@ -40,6 +40,11 @@
no_tex4ht=no
fi
+no_html2wiki=yes
+if which html2wiki > /dev/null 2>&1; then
+ no_html2wiki=no
+fi
+
one_test=no
if [ z"$1" != 'z' ]; then
one_test=yes
@@ -189,6 +194,7 @@
eval "perl -w -x $command_run $format_option --force --conf-dir
$testdir/$srcdir_test/../../maintained_extra --conf-dir
$testdir/$srcdir_test/../../examples --conf-dir
$testdir/$srcdir_test/../../formats --conf-dir $testdir/$srcdir_test/ --test
--output ${outdir}$dir/ -I $testdir/$srcdir_test/ -I $testdir/$srcdir_test/../
--dump-texi --macro-expand=${outdir}$dir/$basename.texi $remaining_out_dir
$src_file 2>${outdir}$dir/$basename.2"
ret=$?
else
+ one_test_done=yes
use_latex2html=no
use_tex4ht=no
if echo "$remaining" | grep -qs -- '-l2h'; then
@@ -204,7 +210,14 @@
fi
use_tex4ht=yes
fi
- one_test_done=yes
+ if [ $use_tex4ht = 'yes' -o $use_latex2html = 'yes' ]; then
+ if echo "$remaining" | grep -qs -- '-init mediawiki.init'; then
+ if [ "$no_html2wiki" = 'yes' ]; then
+ echo "S: (no html2wiki) $current"
+ continue 2
+ fi
+ fi
+ fi
dir=$current
[ -d "${outdir}$dir" ] && rm -rf "${outdir}$dir"
mkdir "${outdir}$dir"
@@ -215,7 +228,7 @@
ret=$?
rm -f ${outdir}$dir/*_l2h_images.log ${outdir}$dir/*_tex4ht_*.log \
${outdir}$dir/*_tex4ht_*.idv ${outdir}$dir/*_tex4ht_*.dvi \
- ${outdir}$dir/*_tex4ht_tex.html
+ ${outdir}$dir/*_tex4ht_tex.html* ${outdir}$dir/*_l2h.html.*
fi
if [ $ret = 0 ]; then
diff_base="${dir}${dir_suffix}"
Index: test/formatting/tests.txt
===================================================================
RCS file: /cvsroot/texi2html/texi2html/test/formatting/tests.txt,v
retrieving revision 1.34
retrieving revision 1.35
diff -u -b -r1.34 -r1.35
--- test/formatting/tests.txt 18 Oct 2009 21:52:37 -0000 1.34
+++ test/formatting/tests.txt 22 Oct 2009 20:23:19 -0000 1.35
@@ -65,6 +65,8 @@
tex_notex tex.texi
tex_httex tex.texi --init tex4ht.init --iftex
tex_mediawiki tex.texi --init mediawiki.init --iftex
+tex_httex_mediawiki tex.texi --html --init tex4ht.init --init mediawiki.init
--iftex
+tex_l2h_mediawiki tex.texi --html --l2h --iftex --init l2h_tmp_dir.init --init
mediawiki.init
block_EOL block_EOL.texi
detailmenus detailmenus.texi
detailmenus_simple detailmenus.texi --init simple_menu.init
Index: test/formatting/res/tex/tex_l2h.tex
===================================================================
RCS file: /cvsroot/texi2html/texi2html/test/formatting/res/tex/tex_l2h.tex,v
retrieving revision 1.1
retrieving revision 1.2
diff -u -b -r1.1 -r1.2
--- test/formatting/res/tex/tex_l2h.tex 18 Aug 2008 18:03:10 -0000 1.1
+++ test/formatting/res/tex/tex_l2h.tex 22 Oct 2009 20:23:20 -0000 1.2
@@ -4,6 +4,7 @@
\usepackage{html}
\begin{document}
\begin{rawhtml}
+
<!-- l2h_begin tex_l2h 1 -->
\end{rawhtml}
some
@@ -13,8 +14,10 @@
\over \sigma_i\right)^2 $$
\begin{rawhtml}
<!-- l2h_end tex_l2h 1 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin tex_l2h 2 -->
\end{rawhtml}
some
@@ -22,33 +25,42 @@
tex \TeX
\begin{rawhtml}
<!-- l2h_end tex_l2h 2 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin tex_l2h 3 -->
\end{rawhtml}
${x^i}\over{\tan y}$
\begin{rawhtml}
<!-- l2h_end tex_l2h 3 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin tex_l2h 4 -->
\end{rawhtml}
$a @\ b$
\begin{rawhtml}
<!-- l2h_end tex_l2h 4 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin tex_l2h 5 -->
\end{rawhtml}
address@hidden code}$
\begin{rawhtml}
<!-- l2h_end tex_l2h 5 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin tex_l2h 6 -->
\end{rawhtml}
$ address@hidden \hbox{ code }}} \sum_{i}{\underline{f}}$
\begin{rawhtml}
<!-- l2h_end tex_l2h 6 -->
+
\end{rawhtml}
\end{document}
Index: test/formatting/res/tex_httex/tex_tex4ht_math.texi
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/formatting/res/tex_httex/tex_tex4ht_math.texi,v
retrieving revision 1.1
retrieving revision 1.2
diff -u -b -r1.1 -r1.2
--- test/formatting/res/tex_httex/tex_tex4ht_math.texi 18 Aug 2008 18:03:12
-0000 1.1
+++ test/formatting/res/tex_httex/tex_tex4ht_math.texi 22 Oct 2009 20:23:20
-0000 1.2
@@ -2,32 +2,40 @@
@setfilename tex_tex4ht_math.info
@c Automatically generated
@verbatim
+
<!-- tex4ht_begin tex_tex4ht_math math 1 -->
@end verbatim
@math{{x^i}\over{\tan y}}
@verbatim
<!-- tex4ht_end tex_tex4ht_math math 1 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin tex_tex4ht_math math 2 -->
@end verbatim
@math{a @\ b}
@verbatim
<!-- tex4ht_end tex_tex4ht_math math 2 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin tex_tex4ht_math math 3 -->
@end verbatim
@address@hidden code}}
@verbatim
<!-- tex4ht_end tex_tex4ht_math math 3 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin tex_tex4ht_math math 4 -->
@end verbatim
@math{ address@hidden \hbox{ code }}} \sum_{i}{\underline{f}}}
@verbatim
<!-- tex4ht_end tex_tex4ht_math math 4 -->
+
@end verbatim
@bye
Index: test/formatting/res/tex_httex/tex_tex4ht_tex.tex
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/formatting/res/tex_httex/tex_tex4ht_tex.tex,v
retrieving revision 1.1
retrieving revision 1.2
diff -u -b -r1.1 -r1.2
--- test/formatting/res/tex_httex/tex_tex4ht_tex.tex 18 Aug 2008 18:03:12
-0000 1.1
+++ test/formatting/res/tex_httex/tex_tex4ht_tex.tex 22 Oct 2009 20:23:20
-0000 1.2
@@ -1,6 +1,6 @@
% Automatically generated
\csname tex4ht\endcsname
-\HCode{\Hnewline <!-- tex4ht_begin tex_tex4ht_tex tex 1 -->\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin tex_tex4ht_tex tex 1 -->\Hnewline}
some
$$ \chi^2 = \sum_{i=1}^N
@@ -8,11 +8,11 @@
\over \sigma_i\right)^2 $$
-\HCode{\Hnewline <!-- tex4ht_end tex_tex4ht_tex tex 1 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin tex_tex4ht_tex tex 2 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end tex_tex4ht_tex tex 1 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin tex_tex4ht_tex tex 2 -->\Hnewline}
some
tex \TeX
-\HCode{\Hnewline <!-- tex4ht_end tex_tex4ht_tex tex 2 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end tex_tex4ht_tex tex 2 -->\Hnewline \Hnewline}
\bye
Index: test/formatting/res/texi_tex/tex_l2h.tex
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/formatting/res/texi_tex/tex_l2h.tex,v
retrieving revision 1.1
retrieving revision 1.2
diff -u -b -r1.1 -r1.2
--- test/formatting/res/texi_tex/tex_l2h.tex 18 Aug 2008 18:03:24 -0000
1.1
+++ test/formatting/res/texi_tex/tex_l2h.tex 22 Oct 2009 20:23:20 -0000
1.2
@@ -4,6 +4,7 @@
\usepackage{html}
\begin{document}
\begin{rawhtml}
+
<!-- l2h_begin tex_l2h 1 -->
\end{rawhtml}
some
@@ -13,8 +14,10 @@
\over \sigma_i\right)^2 $$
\begin{rawhtml}
<!-- l2h_end tex_l2h 1 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin tex_l2h 2 -->
\end{rawhtml}
some
@@ -22,32 +25,41 @@
tex \TeX
\begin{rawhtml}
<!-- l2h_end tex_l2h 2 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin tex_l2h 3 -->
\end{rawhtml}
${x^i}\over{\tan y}$
\begin{rawhtml}
<!-- l2h_end tex_l2h 3 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin tex_l2h 4 -->
\end{rawhtml}
$a @\ b$
\begin{rawhtml}
<!-- l2h_end tex_l2h 4 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin tex_l2h 5 -->
\end{rawhtml}
address@hidden code}$
\begin{rawhtml}
<!-- l2h_end tex_l2h 5 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin tex_l2h 6 -->
\end{rawhtml}
$ address@hidden \hbox{ code }}} \sum_{i}{\underline{f}}$
\begin{rawhtml}
<!-- l2h_end tex_l2h 6 -->
+
\end{rawhtml}
Index: test/invalid/res/math_not_closed/math_not_closed_l2h.tex
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/invalid/res/math_not_closed/math_not_closed_l2h.tex,v
retrieving revision 1.1
retrieving revision 1.2
diff -u -b -r1.1 -r1.2
--- test/invalid/res/math_not_closed/math_not_closed_l2h.tex 18 Aug 2008
18:03:52 -0000 1.1
+++ test/invalid/res/math_not_closed/math_not_closed_l2h.tex 22 Oct 2009
20:23:21 -0000 1.2
@@ -4,14 +4,17 @@
\usepackage{html}
\begin{document}
\begin{rawhtml}
+
<!-- l2h_begin math_not_closed_l2h 1 -->
\end{rawhtml}
$\delta + 2
$
\begin{rawhtml}
<!-- l2h_end math_not_closed_l2h 1 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin math_not_closed_l2h 2 -->
\end{rawhtml}
$3\delta + 2
@@ -19,5 +22,6 @@
$
\begin{rawhtml}
<!-- l2h_end math_not_closed_l2h 2 -->
+
\end{rawhtml}
\end{document}
Index: test/invalid/res/tex_in_copying/tex_in_copying_l2h.tex
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/invalid/res/tex_in_copying/tex_in_copying_l2h.tex,v
retrieving revision 1.1
retrieving revision 1.2
diff -u -b -r1.1 -r1.2
--- test/invalid/res/tex_in_copying/tex_in_copying_l2h.tex 18 Aug 2008
18:03:54 -0000 1.1
+++ test/invalid/res/tex_in_copying/tex_in_copying_l2h.tex 22 Oct 2009
20:23:21 -0000 1.2
@@ -4,6 +4,7 @@
\usepackage{html}
\begin{document}
\begin{rawhtml}
+
<!-- l2h_begin tex_in_copying_l2h 1 -->
\end{rawhtml}
From @ someone <> !
@@ -12,8 +13,10 @@
$$
\begin{rawhtml}
<!-- l2h_end tex_in_copying_l2h 1 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin tex_in_copying_l2h 2 -->
\end{rawhtml}
$$
@@ -21,5 +24,6 @@
$$
\begin{rawhtml}
<!-- l2h_end tex_in_copying_l2h 2 -->
+
\end{rawhtml}
\end{document}
Index: test/invalid/res/tex_not_closed/tex_not_closed_l2h.tex
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/invalid/res/tex_not_closed/tex_not_closed_l2h.tex,v
retrieving revision 1.1
retrieving revision 1.2
diff -u -b -r1.1 -r1.2
--- test/invalid/res/tex_not_closed/tex_not_closed_l2h.tex 18 Aug 2008
18:03:55 -0000 1.1
+++ test/invalid/res/tex_not_closed/tex_not_closed_l2h.tex 22 Oct 2009
20:23:21 -0000 1.2
@@ -4,11 +4,13 @@
\usepackage{html}
\begin{document}
\begin{rawhtml}
+
<!-- l2h_begin tex_not_closed_l2h 1 -->
\end{rawhtml}
This is some \LaTeX{}
\begin{rawhtml}
<!-- l2h_end tex_not_closed_l2h 1 -->
+
\end{rawhtml}
\end{document}
Index: test/invalid/res/texi_math_not_closed/math_not_closed_l2h.tex
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/invalid/res/texi_math_not_closed/math_not_closed_l2h.tex,v
retrieving revision 1.1
retrieving revision 1.2
diff -u -b -r1.1 -r1.2
--- test/invalid/res/texi_math_not_closed/math_not_closed_l2h.tex 18 Aug
2008 18:04:02 -0000 1.1
+++ test/invalid/res/texi_math_not_closed/math_not_closed_l2h.tex 22 Oct
2009 20:23:21 -0000 1.2
@@ -4,14 +4,17 @@
\usepackage{html}
\begin{document}
\begin{rawhtml}
+
<!-- l2h_begin math_not_closed_l2h 1 -->
\end{rawhtml}
$\delta + 2
$
\begin{rawhtml}
<!-- l2h_end math_not_closed_l2h 1 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin math_not_closed_l2h 2 -->
\end{rawhtml}
$3\delta + 2
@@ -19,4 +22,5 @@
$
\begin{rawhtml}
<!-- l2h_end math_not_closed_l2h 2 -->
+
\end{rawhtml}
Index: test/invalid/res/texi_tex_in_copying/tex_in_copying_l2h.tex
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/invalid/res/texi_tex_in_copying/tex_in_copying_l2h.tex,v
retrieving revision 1.1
retrieving revision 1.2
diff -u -b -r1.1 -r1.2
--- test/invalid/res/texi_tex_in_copying/tex_in_copying_l2h.tex 18 Aug 2008
18:04:04 -0000 1.1
+++ test/invalid/res/texi_tex_in_copying/tex_in_copying_l2h.tex 22 Oct 2009
20:23:22 -0000 1.2
@@ -4,6 +4,7 @@
\usepackage{html}
\begin{document}
\begin{rawhtml}
+
<!-- l2h_begin tex_in_copying_l2h 1 -->
\end{rawhtml}
From @ someone <> !
@@ -12,8 +13,10 @@
$$
\begin{rawhtml}
<!-- l2h_end tex_in_copying_l2h 1 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin tex_in_copying_l2h 2 -->
\end{rawhtml}
$$
@@ -21,4 +24,5 @@
$$
\begin{rawhtml}
<!-- l2h_end tex_in_copying_l2h 2 -->
+
\end{rawhtml}
Index: test/invalid/res/texi_tex_not_closed/tex_not_closed_l2h.tex
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/invalid/res/texi_tex_not_closed/tex_not_closed_l2h.tex,v
retrieving revision 1.1
retrieving revision 1.2
diff -u -b -r1.1 -r1.2
--- test/invalid/res/texi_tex_not_closed/tex_not_closed_l2h.tex 18 Aug 2008
18:04:05 -0000 1.1
+++ test/invalid/res/texi_tex_not_closed/tex_not_closed_l2h.tex 22 Oct 2009
20:23:22 -0000 1.2
@@ -4,10 +4,12 @@
\usepackage{html}
\begin{document}
\begin{rawhtml}
+
<!-- l2h_begin tex_not_closed_l2h 1 -->
\end{rawhtml}
This is some \LaTeX{}
\begin{rawhtml}
<!-- l2h_end tex_not_closed_l2h 1 -->
+
\end{rawhtml}
Index: test/manuals/res/mini_ker/1D-gridded-model.html
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/manuals/res/mini_ker/1D-gridded-model.html,v
retrieving revision 1.14
retrieving revision 1.15
diff -u -b -r1.14 -r1.15
--- test/manuals/res/mini_ker/1D-gridded-model.html 4 Oct 2009 21:51:31
-0000 1.14
+++ test/manuals/res/mini_ker/1D-gridded-model.html 22 Oct 2009 20:23:22
-0000 1.15
@@ -114,8 +114,7 @@
in the grid, from 1 to N, and two nodes outside of the grid,
a limiting node 0, and a limiting node N + 1. The limiting node
corresponding with node 0 is called the <em>down</em> node, while the limiting
-node corresponding with node N + 1
- is called the <em>up</em> node.
+node corresponding with node N + 1 is called the <em>up</em> node.
Other models not part of the 1D grid may be added if any.
</p>
<p>To enable 1D gridded models, one should set the select flag
‘<samp>grid1d</samp>’.
Index: test/manuals/res/mini_ker/Controlling-the-run.html
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/manuals/res/mini_ker/Controlling-the-run.html,v
retrieving revision 1.15
retrieving revision 1.16
diff -u -b -r1.15 -r1.16
--- test/manuals/res/mini_ker/Controlling-the-run.html 4 Oct 2009 21:51:31
-0000 1.15
+++ test/manuals/res/mini_ker/Controlling-the-run.html 22 Oct 2009 20:23:22
-0000 1.16
@@ -112,8 +112,7 @@
on a pseudo relative quadratic residual between
φ = f(η(t - dt) + dφ (<code> ffl</code>), where
dφ
is given by the system resolution in <code>ker</code>,and
- φ = f(η),φ)
-, Fortran variable (<code>ff</code>):
+ φ = f(η),φ), Fortran variable (<code>ff</code>):
</p>
<pre class="verbatim">!
========================================================
! test linearite ffl - ff
Index: test/manuals/res/mini_ker/Feedback-gain.html
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/manuals/res/mini_ker/Feedback-gain.html,v
retrieving revision 1.16
retrieving revision 1.17
diff -u -b -r1.16 -r1.17
--- test/manuals/res/mini_ker/Feedback-gain.html 4 Oct 2009 21:51:32
-0000 1.16
+++ test/manuals/res/mini_ker/Feedback-gain.html 22 Oct 2009 20:23:22
-0000 1.17
@@ -110,8 +110,7 @@
scheme for the time discretisation
symbolically gives the solution of the Borel transform of the system. One can
identify the <code>dt</code> variable with the Borel τ within a
-factor 2
-. Hence, to numerically study the τ dependency of
+factor 2. Hence, to numerically study the τ dependency of
the transform of various coefficients in the system coupling matrix at one
point in time, one can calculate the Borel transform of the TLS solutions
by making a time-step sweep.
Index: test/manuals/res/mini_ker/Kalman-filter.html
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/manuals/res/mini_ker/Kalman-filter.html,v
retrieving revision 1.16
retrieving revision 1.17
diff -u -b -r1.16 -r1.17
--- test/manuals/res/mini_ker/Kalman-filter.html 4 Oct 2009 21:51:32
-0000 1.16
+++ test/manuals/res/mini_ker/Kalman-filter.html 22 Oct 2009 20:23:22
-0000 1.17
@@ -109,8 +109,7 @@
<p>The observations ω are available at discrete time steps
t = si. The
stochastic perturbation on state, μ is characterized by a
-variance-covariance matrix Q
- and the noise on the observation,
+variance-covariance matrix Q and the noise on the observation,
ν has a variance-covariance matrix R. W relates states
with stochastic perturbations. At each time step the Kalman filter recomputes
an estimation of the state and the variance-covariance matrix of the state.
Index: test/manuals/res/mini_ker/Linearization-and-discretization.html
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/manuals/res/mini_ker/Linearization-and-discretization.html,v
retrieving revision 1.13
retrieving revision 1.14
diff -u -b -r1.13 -r1.14
--- test/manuals/res/mini_ker/Linearization-and-discretization.html 4 Oct
2009 21:51:32 -0000 1.13
+++ test/manuals/res/mini_ker/Linearization-and-discretization.html 22 Oct
2009 20:23:22 -0000 1.14
@@ -97,7 +97,6 @@
of f and g, and with δt. From this system the
elimination of δη leads to another formulation giving
the coupling between transfers, and allows for the δφ
-
computation. The δφ value is then substitued in
δη to complete the time-step solving process.
</p>
Index: test/manuals/res/mini_ker/Sensitivities.html
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/manuals/res/mini_ker/Sensitivities.html,v
retrieving revision 1.15
retrieving revision 1.16
diff -u -b -r1.15 -r1.16
--- test/manuals/res/mini_ker/Sensitivities.html 4 Oct 2009 21:51:32
-0000 1.15
+++ test/manuals/res/mini_ker/Sensitivities.html 22 Oct 2009 20:23:22
-0000 1.16
@@ -174,8 +174,7 @@
of the number of predators.
</p>
<p>In the same way, the <var>j+1</var>th column of
‘<tt>sigma.data</tt>’ will be the
-derivative of ϕj(t) with respect to ηi(t = 0)
-. Here:
+derivative of ϕj(t) with respect to ηi(t = 0). Here:
</p><table><tr><td> </td><td><pre class="example"># Sensy_to: eta_pray
eta_pred
# time \\ of: ff_interact ff_interact
0.00000E+00 1.60683E+00 8.47076E-01
Index: test/manuals/res/mini_ker/mini_ker_tex4ht_math.html
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/manuals/res/mini_ker/mini_ker_tex4ht_math.html,v
retrieving revision 1.1
retrieving revision 1.2
diff -u -b -r1.1 -r1.2
--- test/manuals/res/mini_ker/mini_ker_tex4ht_math.html 18 Aug 2008 18:05:11
-0000 1.1
+++ test/manuals/res/mini_ker/mini_ker_tex4ht_math.html 22 Oct 2009 20:23:22
-0000 1.2
@@ -22,6 +22,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 8 -->
φ
<!-- tex4ht_end mini_ker_tex4ht_math math 8 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 9 -->
f
<!-- tex4ht_end mini_ker_tex4ht_math math 9 -->
@@ -36,7 +37,6 @@
<!-- tex4ht_end mini_ker_tex4ht_math math 12 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 13 -->
δφ
-
<!-- tex4ht_end mini_ker_tex4ht_math math 13 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 14 -->
δφ
@@ -47,6 +47,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 16 -->
a
<!-- tex4ht_end mini_ker_tex4ht_math math 16 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 17 -->
c
<!-- tex4ht_end mini_ker_tex4ht_math math 17 -->
@@ -71,12 +72,12 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 24 -->
φ = f(η(t - dt) + dφ
<!-- tex4ht_end mini_ker_tex4ht_math math 24 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 25 -->
dφ
<!-- tex4ht_end mini_ker_tex4ht_math math 25 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 26 -->
φ = f(η),φ)
-
<!-- tex4ht_end mini_ker_tex4ht_math math 26 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 27 -->
10-3
@@ -96,6 +97,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 32 -->
mk
<!-- tex4ht_end mini_ker_tex4ht_math math 32 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 33 -->
k
<!-- tex4ht_end mini_ker_tex4ht_math math 33 -->
@@ -116,11 +118,11 @@
<!-- tex4ht_end mini_ker_tex4ht_math math 38 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 39 -->
N + 1
-
<!-- tex4ht_end mini_ker_tex4ht_math math 39 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 40 -->
k
<!-- tex4ht_end mini_ker_tex4ht_math math 40 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 41 -->
k
<!-- tex4ht_end mini_ker_tex4ht_math math 41 -->
@@ -145,6 +147,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 48 -->
η1(t)
<!-- tex4ht_end mini_ker_tex4ht_math math 48 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 49 -->
η1(t = 0)
<!-- tex4ht_end mini_ker_tex4ht_math math 49 -->
@@ -156,7 +159,6 @@
<!-- tex4ht_end mini_ker_tex4ht_math math 51 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 52 -->
ηi(t = 0)
-
<!-- tex4ht_end mini_ker_tex4ht_math math 52 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 53 -->
h(t)
@@ -170,6 +172,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 56 -->
J
<!-- tex4ht_end mini_ker_tex4ht_math math 56 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 57 -->
ψ
<!-- tex4ht_end mini_ker_tex4ht_math math 57 -->
@@ -194,9 +197,9 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 64 -->
μ
<!-- tex4ht_end mini_ker_tex4ht_math math 64 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 65 -->
Q
-
<!-- tex4ht_end mini_ker_tex4ht_math math 65 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 66 -->
ν
@@ -219,6 +222,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 72 -->
g(τ)
<!-- tex4ht_end mini_ker_tex4ht_math math 72 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 73 -->
τ
<!-- tex4ht_end mini_ker_tex4ht_math math 73 -->
@@ -236,7 +240,6 @@
<!-- tex4ht_end mini_ker_tex4ht_math math 77 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 78 -->
2
-
<!-- tex4ht_end mini_ker_tex4ht_math math 78 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 79 -->
τ
@@ -244,6 +247,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 80 -->
g(τ;t)
<!-- tex4ht_end mini_ker_tex4ht_math math 80 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 81 -->
τ
<!-- tex4ht_end mini_ker_tex4ht_math math 81 -->
@@ -270,13 +274,13 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 88 -->
τ
<!-- tex4ht_end mini_ker_tex4ht_math math 88 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 89 -->
τ
<!-- tex4ht_end mini_ker_tex4ht_math math 89 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 90 -->
τ
<!-- tex4ht_end mini_ker_tex4ht_math math 90 -->
-
<!-- tex4ht_begin mini_ker_tex4ht_math math 91 -->
g(τ)
<!-- tex4ht_end mini_ker_tex4ht_math math 91 -->
@@ -296,6 +300,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 96 -->
Ast
<!-- tex4ht_end mini_ker_tex4ht_math math 96 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 97 -->
U
<!-- tex4ht_end mini_ker_tex4ht_math math 97 -->
@@ -317,11 +322,11 @@
<!-- tex4ht_end mini_ker_tex4ht_math math 102 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 103 -->
w
-
<!-- tex4ht_end mini_ker_tex4ht_math math 103 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 104 -->
Φ
<!-- tex4ht_end mini_ker_tex4ht_math math 104 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 105 -->
t
<!-- tex4ht_end mini_ker_tex4ht_math math 105 -->
@@ -346,6 +351,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 112 -->
Φ
<!-- tex4ht_end mini_ker_tex4ht_math math 112 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 113 -->
Φ(t,0)
<!-- tex4ht_end mini_ker_tex4ht_math math 113 -->
Index: test/manuals/res/mini_ker/mini_ker_tex4ht_math.texi
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/manuals/res/mini_ker/mini_ker_tex4ht_math.texi,v
retrieving revision 1.1
retrieving revision 1.2
diff -u -b -r1.1 -r1.2
--- test/manuals/res/mini_ker/mini_ker_tex4ht_math.texi 18 Aug 2008 18:05:12
-0000 1.1
+++ test/manuals/res/mini_ker/mini_ker_tex4ht_math.texi 22 Oct 2009 20:23:22
-0000 1.2
@@ -2,802 +2,1030 @@
@setfilename mini_ker_tex4ht_math.info
@c Automatically generated
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 1 -->
@end verbatim
@math{\eta}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 1 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 2 -->
@end verbatim
@math{\varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 2 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 3 -->
@end verbatim
@math{t}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 3 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 4 -->
@end verbatim
@math{t + \delta t}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 4 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 5 -->
@end verbatim
@math{\delta \eta}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 5 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 6 -->
@end verbatim
@math{\eta}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 6 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 7 -->
@end verbatim
@math{\delta \varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 7 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 8 -->
@end verbatim
@math{\varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 8 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 9 -->
@end verbatim
@math{f}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 9 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 10 -->
@end verbatim
@math{g}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 10 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 11 -->
@end verbatim
@math{\delta t}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 11 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 12 -->
@end verbatim
@math{\delta \eta}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 12 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 13 -->
@end verbatim
@math{\delta \varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 13 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 14 -->
@end verbatim
@math{\delta \varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 14 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 15 -->
@end verbatim
@math{\delta \eta}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 15 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 16 -->
@end verbatim
@math{a}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 16 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 17 -->
@end verbatim
@math{c}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 17 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 18 -->
@end verbatim
@math{\varphi_{meet}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 18 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 19 -->
@end verbatim
@math{\eta_{prey}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 19 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 20 -->
@end verbatim
@math{\eta_{pred}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 20 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 21 -->
@end verbatim
@math{\varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 21 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 22 -->
@end verbatim
@math{\delta\eta}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 22 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 23 -->
@end verbatim
@math{\varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 23 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 24 -->
@end verbatim
@math{\varphi=f(\eta(t-dt)+d\varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 24 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 25 -->
@end verbatim
@math{d\varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 25 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 26 -->
@end verbatim
@math{\varphi=f(\eta),\varphi)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 26 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 27 -->
@end verbatim
@math{10^{-3}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 27 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 28 -->
@end verbatim
@math{(I-D)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 28 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 29 -->
@end verbatim
@math{(I-D)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 29 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 30 -->
@end verbatim
@math{(I-D)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 30 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 31 -->
@end verbatim
@math{k}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 31 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 32 -->
@end verbatim
@math{m_k}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 32 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 33 -->
@end verbatim
@math{k}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 33 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 34 -->
@end verbatim
@math{r_k}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 34 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 35 -->
@end verbatim
@math{d_k}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 35 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 36 -->
@end verbatim
@math{N}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 36 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 37 -->
@end verbatim
@math{N}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 37 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 38 -->
@end verbatim
@math{N+1}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 38 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 39 -->
@end verbatim
@math{N+1}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 39 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 40 -->
@end verbatim
@math{k}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 40 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 41 -->
@end verbatim
@math{k}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 41 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 42 -->
@end verbatim
@math{x/\Delta}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 42 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 43 -->
@end verbatim
@math{\omega}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 43 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 44 -->
@end verbatim
@math{h}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 44 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 45 -->
@end verbatim
@math{\varphi_{meet}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 45 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 46 -->
@end verbatim
@math{\eta_{prey}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 46 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 47 -->
@end verbatim
@math{\eta_{pred}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 47 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 48 -->
@end verbatim
@math{\eta_1(t)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 48 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 49 -->
@end verbatim
@math{\eta_1(t=0)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 49 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 50 -->
@end verbatim
@math{t=0}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 50 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 51 -->
@end verbatim
@math{\phi_{j}(t)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 51 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 52 -->
@end verbatim
@math{\eta_i(t=0)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 52 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 53 -->
@end verbatim
@math{h(t)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 53 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 54 -->
@end verbatim
@math{J}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 54 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 55 -->
@end verbatim
@math{T}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 55 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 56 -->
@end verbatim
@math{J}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 56 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 57 -->
@end verbatim
@math{\psi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 57 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 58 -->
@end verbatim
@math{l}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 58 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 59 -->
@end verbatim
@math{h}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 59 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 60 -->
@end verbatim
@math{J}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 60 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 61 -->
@end verbatim
@math{t=0}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 61 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 62 -->
@end verbatim
@math{\omega}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 62 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 63 -->
@end verbatim
@math{t=s_i}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 63 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 64 -->
@end verbatim
@math{\mu}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 64 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 65 -->
@end verbatim
@math{Q}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 65 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 66 -->
@end verbatim
@math{\nu}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 66 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 67 -->
@end verbatim
@math{R}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 67 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 68 -->
@end verbatim
@math{W}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 68 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 69 -->
@end verbatim
@math{W}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 69 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 70 -->
@end verbatim
@math{W}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 70 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 71 -->
@end verbatim
@math{g(\tau)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 71 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 72 -->
@end verbatim
@math{g(\tau)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 72 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 73 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 73 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 74 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 74 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 75 -->
@end verbatim
@math{g(\tau;t)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 75 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 76 -->
@end verbatim
@math{t}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 76 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 77 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 77 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 78 -->
@end verbatim
@math{2}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 78 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 79 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 79 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 80 -->
@end verbatim
@math{g(\tau;t)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 80 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 81 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 81 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 82 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 82 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 83 -->
@end verbatim
@math{tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 83 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 84 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 84 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 85 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 85 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 86 -->
@end verbatim
@math{0.2}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 86 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 87 -->
@end verbatim
@math{\sqrt{\sqrt{2}}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 87 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 88 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 88 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 89 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 89 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 90 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 90 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 91 -->
@end verbatim
@math{g(\tau)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 91 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 92 -->
@end verbatim
@math{g(t,\tau)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 92 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 93 -->
@end verbatim
@math{A_{st}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 93 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 94 -->
@end verbatim
@math{A_{st}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 94 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 95 -->
@end verbatim
@math{A_{st} + A_{st}^\dagger}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 95 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 96 -->
@end verbatim
@math{A_{st}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 96 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 97 -->
@end verbatim
@math{U}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 97 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 98 -->
@end verbatim
@math{w}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 98 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 99 -->
@end verbatim
@math{V}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 99 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 100 -->
@end verbatim
@math{A_{st} + A_{st}^\dagger}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 100 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 101 -->
@end verbatim
@math{A_{st}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 101 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 102 -->
@end verbatim
@math{\Phi(t+\delta t,t)=\exp{A_{st} \delta t}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 102 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 103 -->
@end verbatim
@math{w}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 103 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 104 -->
@end verbatim
@math{\Phi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 104 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 105 -->
@end verbatim
@math{t}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 105 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 106 -->
@end verbatim
@math{\Phi(t,0)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 106 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 107 -->
@end verbatim
@math{U}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 107 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 108 -->
@end verbatim
@math{\Phi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 108 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 109 -->
@end verbatim
@math{w}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 109 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 110 -->
@end verbatim
@math{\Phi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 110 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 111 -->
@end verbatim
@math{V}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 111 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 112 -->
@end verbatim
@math{\Phi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 112 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 113 -->
@end verbatim
@math{\Phi(t,0)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 113 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 114 -->
@end verbatim
@math{\Phi(t,0)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 114 -->
+
@end verbatim
@bye
Index: test/manuals/res/mini_ker/mini_ker_tex4ht_tex.tex
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/manuals/res/mini_ker/mini_ker_tex4ht_tex.tex,v
retrieving revision 1.1
retrieving revision 1.2
diff -u -b -r1.1 -r1.2
--- test/manuals/res/mini_ker/mini_ker_tex4ht_tex.tex 18 Aug 2008 18:05:13
-0000 1.1
+++ test/manuals/res/mini_ker/mini_ker_tex4ht_tex.tex 22 Oct 2009 20:23:22
-0000 1.2
@@ -1,48 +1,48 @@
% Automatically generated
\csname tex4ht\endcsname
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 1 -->\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 1
-->\Hnewline}
$$\partial_t \eta (t) = g(\eta(t),\varphi(t))$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 1 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 2 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 1 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 2
-->\Hnewline}
$$
\varphi(t) = f(\eta(t),\varphi(t))
$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 2 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 3 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 2 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 3
-->\Hnewline}
$$\pmatrix{A & B\cr
-C^+ & I-D\cr} \pmatrix{\delta \eta\cr
\delta \varphi\cr} = \pmatrix{\Gamma\cr
\Omega\cr}$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 3 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 4 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 3 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 4
-->\Hnewline}
$$\eqalign{\partial_t \eta (t) &= g(\eta(t),\varphi(t))\cr
\varphi(t) &= f(\eta(t),\varphi(t))\cr
}$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 4 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 5 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 4 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 5
-->\Hnewline}
$$\left\{\eqalign{\partial_t \eta _{prey} &= a \eta _{prey} - a \varphi
_{meet} \cr
\partial_t \eta _{pred} &= -c \eta _{pred} + c \varphi _{meet}\cr}\right.$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 5 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 6 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 5 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 6
-->\Hnewline}
$$\varphi _{meet} = \eta _{prey}\eta _{pred}$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 6 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 7 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 6 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 7
-->\Hnewline}
$$\partial_{\eta} g(\eta(t),\varphi(t));
$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 7 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 8 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 7 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 8
-->\Hnewline}
$$\partial_{\varphi} g(\eta(t),\varphi(t));
$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 8 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 9 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 8 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 9
-->\Hnewline}
$$\partial_{\eta} f(\eta(t),\varphi(t));
$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 9 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 10 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 9 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 10
-->\Hnewline}
$$\partial_{\varphi} f(\eta(t),\varphi(t));
$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 10 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 11 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 10 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 11
-->\Hnewline}
$$\left\{\eqalign{\partial_t \eta _{k} ^{pos} &= \eta _{k} ^{vel} \cr
\partial_t \eta _{k} ^{vel} &= ( \varphi_k ^{spr} -\varphi _{k+1} ^{spr} +
\varphi _{k} ^{dmp}-\varphi _{k+1} ^{dmp})\,/m_k \cr}\right.$$
$$\left\{\eqalign{
@@ -53,29 +53,29 @@
\eta ^{vel}_{0} &= 0\cr
\varphi ^{spr}_{N+1} &= 0\cr
\varphi ^{dmp}_{N+1} &= 0\cr}\right.$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 11 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 12 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 11 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 12
-->\Hnewline}
$$\eqalign{\partial_x f^g &= g f^{g-1}\partial_x f + f^g \log f\partial_x g\cr
&= f^{g-1}(g\partial_x f + f\partial_x g)\cr}$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 12 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 13 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 12 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 13
-->\Hnewline}
$$
\omega = h ( \eta , \varphi)
$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 13 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 14 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 13 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 14
-->\Hnewline}
$$
J = \psi[\eta(T),\varphi(T) ,h(T)] + \int_0 ^T
{l[\eta(\tau),\varphi(\tau),h(\tau)]}\, d\tau
$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 14 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 15 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 14 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 15
-->\Hnewline}
$$\eqalign{
\partial_t \eta (t) &= g(\eta(t),\varphi(t)) + W(t) \mu\cr
\varphi(t) &= f(\eta(t),\varphi(t))\cr
\omega(t) &= h ( \eta(t) , \varphi(t)) + \nu\cr
}$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 15 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 16 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 15 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 16
-->\Hnewline}
$$\left\{\eqalign{
\partial_t \eta_1 &= a_{11} \eta_1 + a_{12} \varphi_2 + a_{13} \varphi_3 +
W_{11} \mu_1 + W_{12} \mu_2\cr
\partial_t \eta_2 &= a_{21} \varphi_1 + a_{22} \eta_2 + a_{23} \varphi_3 +
W_{21} \mu_1 + W_{22} \mu_2\cr
@@ -91,11 +91,11 @@
\omega _2 &= \eta _2 + \nu_2 \cr
\omega _3 &= \eta _3 + \nu_3
}\right.$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 16 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 17 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 16 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 17
-->\Hnewline}
$$
U w V^\dagger
$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 17 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 17 -->\Hnewline
\Hnewline}
\bye
Index: test/manuals/res_all/mini_ker/1D-gridded-model.html
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/manuals/res_all/mini_ker/1D-gridded-model.html,v
retrieving revision 1.5
retrieving revision 1.6
diff -u -b -r1.5 -r1.6
--- test/manuals/res_all/mini_ker/1D-gridded-model.html 4 Oct 2009 21:51:37
-0000 1.5
+++ test/manuals/res_all/mini_ker/1D-gridded-model.html 22 Oct 2009 20:23:22
-0000 1.6
@@ -117,8 +117,7 @@
in the grid, from 1 to N, and two nodes outside of the grid,
a limiting node 0, and a limiting node N + 1. The limiting node
corresponding with node 0 is called the <em>down</em> node, while the limiting
-node corresponding with node N + 1
- is called the <em>up</em> node.
+node corresponding with node N + 1 is called the <em>up</em> node.
Other models not part of the 1D grid may be added if any.
</p>
<p>To enable 1D gridded models, one should set the select flag
‘<samp>grid1d</samp>’.
Index: test/manuals/res_all/mini_ker/Controlling-the-run.html
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/manuals/res_all/mini_ker/Controlling-the-run.html,v
retrieving revision 1.5
retrieving revision 1.6
diff -u -b -r1.5 -r1.6
--- test/manuals/res_all/mini_ker/Controlling-the-run.html 4 Oct 2009
21:51:37 -0000 1.5
+++ test/manuals/res_all/mini_ker/Controlling-the-run.html 22 Oct 2009
20:23:22 -0000 1.6
@@ -111,8 +111,7 @@
on a pseudo relative quadratic residual between
φ = f(η(t - dt) + dφ (<code> ffl</code>), where
dφ
is given by the system resolution in <code>ker</code>,and
- φ = f(η),φ)
-, Fortran variable (<code>ff</code>):
+ φ = f(η),φ), Fortran variable (<code>ff</code>):
</p>
<pre class="verbatim">!
========================================================
! test linearite ffl - ff
Index: test/manuals/res_all/mini_ker/Feedback-gain.html
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/manuals/res_all/mini_ker/Feedback-gain.html,v
retrieving revision 1.5
retrieving revision 1.6
diff -u -b -r1.5 -r1.6
--- test/manuals/res_all/mini_ker/Feedback-gain.html 4 Oct 2009 21:51:37
-0000 1.5
+++ test/manuals/res_all/mini_ker/Feedback-gain.html 22 Oct 2009 20:23:22
-0000 1.6
@@ -113,8 +113,7 @@
scheme for the time discretisation
symbolically gives the solution of the Borel transform of the system. One can
identify the <code>dt</code> variable with the Borel τ within a
-factor 2
-. Hence, to numerically study the τ dependency of
+factor 2. Hence, to numerically study the τ dependency of
the transform of various coefficients in the system coupling matrix at one
point in time, one can calculate the Borel transform of the TLS solutions
by making a time-step sweep.
Index: test/manuals/res_all/mini_ker/Kalman-filter.html
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/manuals/res_all/mini_ker/Kalman-filter.html,v
retrieving revision 1.5
retrieving revision 1.6
diff -u -b -r1.5 -r1.6
--- test/manuals/res_all/mini_ker/Kalman-filter.html 4 Oct 2009 21:51:37
-0000 1.5
+++ test/manuals/res_all/mini_ker/Kalman-filter.html 22 Oct 2009 20:23:22
-0000 1.6
@@ -112,8 +112,7 @@
<p>The observations ω are available at discrete time steps
t = si. The
stochastic perturbation on state, μ is characterized by a
-variance-covariance matrix Q
- and the noise on the observation,
+variance-covariance matrix Q and the noise on the observation,
ν has a variance-covariance matrix R. W relates states
with stochastic perturbations. At each time step the Kalman filter recomputes
an estimation of the state and the variance-covariance matrix of the state.
Index: test/manuals/res_all/mini_ker/Linearization-and-discretization.html
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/manuals/res_all/mini_ker/Linearization-and-discretization.html,v
retrieving revision 1.5
retrieving revision 1.6
diff -u -b -r1.5 -r1.6
--- test/manuals/res_all/mini_ker/Linearization-and-discretization.html 4 Oct
2009 21:51:37 -0000 1.5
+++ test/manuals/res_all/mini_ker/Linearization-and-discretization.html 22 Oct
2009 20:23:22 -0000 1.6
@@ -100,7 +100,6 @@
of f and g, and with δt. From this system the
elimination of δη leads to another formulation giving
the coupling between transfers, and allows for the δφ
-
computation. The δφ value is then substitued in
δη to complete the time-step solving process.
</p>
Index: test/manuals/res_all/mini_ker/Sensitivities.html
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/manuals/res_all/mini_ker/Sensitivities.html,v
retrieving revision 1.5
retrieving revision 1.6
diff -u -b -r1.5 -r1.6
--- test/manuals/res_all/mini_ker/Sensitivities.html 4 Oct 2009 21:51:38
-0000 1.5
+++ test/manuals/res_all/mini_ker/Sensitivities.html 22 Oct 2009 20:23:22
-0000 1.6
@@ -177,8 +177,7 @@
of the number of predators.
</p>
<p>In the same way, the <var>j+1</var>th column of
‘<tt>sigma.data</tt>’ will be the
-derivative of ϕj(t) with respect to ηi(t = 0)
-. Here:
+derivative of ϕj(t) with respect to ηi(t = 0). Here:
</p><table><tr><td> </td><td><pre class="example"># Sensy_to: eta_pray
eta_pred
# time \\ of: ff_interact ff_interact
0.00000E+00 1.60683E+00 8.47076E-01
Index: test/manuals/res_all/mini_ker/mini_ker_tex4ht_math.html
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/manuals/res_all/mini_ker/mini_ker_tex4ht_math.html,v
retrieving revision 1.1
retrieving revision 1.2
diff -u -b -r1.1 -r1.2
--- test/manuals/res_all/mini_ker/mini_ker_tex4ht_math.html 31 Jul 2009
10:16:58 -0000 1.1
+++ test/manuals/res_all/mini_ker/mini_ker_tex4ht_math.html 22 Oct 2009
20:23:22 -0000 1.2
@@ -22,6 +22,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 8 -->
φ
<!-- tex4ht_end mini_ker_tex4ht_math math 8 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 9 -->
f
<!-- tex4ht_end mini_ker_tex4ht_math math 9 -->
@@ -36,7 +37,6 @@
<!-- tex4ht_end mini_ker_tex4ht_math math 12 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 13 -->
δφ
-
<!-- tex4ht_end mini_ker_tex4ht_math math 13 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 14 -->
δφ
@@ -47,6 +47,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 16 -->
a
<!-- tex4ht_end mini_ker_tex4ht_math math 16 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 17 -->
c
<!-- tex4ht_end mini_ker_tex4ht_math math 17 -->
@@ -71,12 +72,12 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 24 -->
φ = f(η(t - dt) + dφ
<!-- tex4ht_end mini_ker_tex4ht_math math 24 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 25 -->
dφ
<!-- tex4ht_end mini_ker_tex4ht_math math 25 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 26 -->
φ = f(η),φ)
-
<!-- tex4ht_end mini_ker_tex4ht_math math 26 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 27 -->
10-3
@@ -96,6 +97,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 32 -->
mk
<!-- tex4ht_end mini_ker_tex4ht_math math 32 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 33 -->
k
<!-- tex4ht_end mini_ker_tex4ht_math math 33 -->
@@ -116,11 +118,11 @@
<!-- tex4ht_end mini_ker_tex4ht_math math 38 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 39 -->
N + 1
-
<!-- tex4ht_end mini_ker_tex4ht_math math 39 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 40 -->
k
<!-- tex4ht_end mini_ker_tex4ht_math math 40 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 41 -->
k
<!-- tex4ht_end mini_ker_tex4ht_math math 41 -->
@@ -145,6 +147,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 48 -->
η1(t)
<!-- tex4ht_end mini_ker_tex4ht_math math 48 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 49 -->
η1(t = 0)
<!-- tex4ht_end mini_ker_tex4ht_math math 49 -->
@@ -156,7 +159,6 @@
<!-- tex4ht_end mini_ker_tex4ht_math math 51 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 52 -->
ηi(t = 0)
-
<!-- tex4ht_end mini_ker_tex4ht_math math 52 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 53 -->
h(t)
@@ -170,6 +172,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 56 -->
J
<!-- tex4ht_end mini_ker_tex4ht_math math 56 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 57 -->
ψ
<!-- tex4ht_end mini_ker_tex4ht_math math 57 -->
@@ -194,9 +197,9 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 64 -->
μ
<!-- tex4ht_end mini_ker_tex4ht_math math 64 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 65 -->
Q
-
<!-- tex4ht_end mini_ker_tex4ht_math math 65 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 66 -->
ν
@@ -219,6 +222,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 72 -->
g(τ)
<!-- tex4ht_end mini_ker_tex4ht_math math 72 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 73 -->
τ
<!-- tex4ht_end mini_ker_tex4ht_math math 73 -->
@@ -236,7 +240,6 @@
<!-- tex4ht_end mini_ker_tex4ht_math math 77 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 78 -->
2
-
<!-- tex4ht_end mini_ker_tex4ht_math math 78 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 79 -->
τ
@@ -244,6 +247,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 80 -->
g(τ;t)
<!-- tex4ht_end mini_ker_tex4ht_math math 80 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 81 -->
τ
<!-- tex4ht_end mini_ker_tex4ht_math math 81 -->
@@ -270,13 +274,13 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 88 -->
τ
<!-- tex4ht_end mini_ker_tex4ht_math math 88 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 89 -->
τ
<!-- tex4ht_end mini_ker_tex4ht_math math 89 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 90 -->
τ
<!-- tex4ht_end mini_ker_tex4ht_math math 90 -->
-
<!-- tex4ht_begin mini_ker_tex4ht_math math 91 -->
g(τ)
<!-- tex4ht_end mini_ker_tex4ht_math math 91 -->
@@ -296,6 +300,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 96 -->
Ast
<!-- tex4ht_end mini_ker_tex4ht_math math 96 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 97 -->
U
<!-- tex4ht_end mini_ker_tex4ht_math math 97 -->
@@ -317,11 +322,11 @@
<!-- tex4ht_end mini_ker_tex4ht_math math 102 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 103 -->
w
-
<!-- tex4ht_end mini_ker_tex4ht_math math 103 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 104 -->
Φ
<!-- tex4ht_end mini_ker_tex4ht_math math 104 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 105 -->
t
<!-- tex4ht_end mini_ker_tex4ht_math math 105 -->
@@ -346,6 +351,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 112 -->
Φ
<!-- tex4ht_end mini_ker_tex4ht_math math 112 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 113 -->
Φ(t,0)
<!-- tex4ht_end mini_ker_tex4ht_math math 113 -->
Index: test/manuals/res_all/mini_ker/mini_ker_tex4ht_math.texi
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/manuals/res_all/mini_ker/mini_ker_tex4ht_math.texi,v
retrieving revision 1.1
retrieving revision 1.2
diff -u -b -r1.1 -r1.2
--- test/manuals/res_all/mini_ker/mini_ker_tex4ht_math.texi 31 Jul 2009
10:16:58 -0000 1.1
+++ test/manuals/res_all/mini_ker/mini_ker_tex4ht_math.texi 22 Oct 2009
20:23:22 -0000 1.2
@@ -2,802 +2,1030 @@
@setfilename mini_ker_tex4ht_math.info
@c Automatically generated
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 1 -->
@end verbatim
@math{\eta}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 1 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 2 -->
@end verbatim
@math{\varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 2 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 3 -->
@end verbatim
@math{t}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 3 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 4 -->
@end verbatim
@math{t + \delta t}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 4 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 5 -->
@end verbatim
@math{\delta \eta}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 5 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 6 -->
@end verbatim
@math{\eta}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 6 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 7 -->
@end verbatim
@math{\delta \varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 7 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 8 -->
@end verbatim
@math{\varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 8 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 9 -->
@end verbatim
@math{f}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 9 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 10 -->
@end verbatim
@math{g}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 10 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 11 -->
@end verbatim
@math{\delta t}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 11 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 12 -->
@end verbatim
@math{\delta \eta}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 12 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 13 -->
@end verbatim
@math{\delta \varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 13 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 14 -->
@end verbatim
@math{\delta \varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 14 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 15 -->
@end verbatim
@math{\delta \eta}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 15 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 16 -->
@end verbatim
@math{a}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 16 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 17 -->
@end verbatim
@math{c}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 17 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 18 -->
@end verbatim
@math{\varphi_{meet}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 18 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 19 -->
@end verbatim
@math{\eta_{prey}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 19 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 20 -->
@end verbatim
@math{\eta_{pred}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 20 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 21 -->
@end verbatim
@math{\varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 21 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 22 -->
@end verbatim
@math{\delta\eta}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 22 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 23 -->
@end verbatim
@math{\varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 23 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 24 -->
@end verbatim
@math{\varphi=f(\eta(t-dt)+d\varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 24 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 25 -->
@end verbatim
@math{d\varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 25 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 26 -->
@end verbatim
@math{\varphi=f(\eta),\varphi)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 26 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 27 -->
@end verbatim
@math{10^{-3}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 27 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 28 -->
@end verbatim
@math{(I-D)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 28 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 29 -->
@end verbatim
@math{(I-D)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 29 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 30 -->
@end verbatim
@math{(I-D)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 30 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 31 -->
@end verbatim
@math{k}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 31 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 32 -->
@end verbatim
@math{m_k}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 32 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 33 -->
@end verbatim
@math{k}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 33 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 34 -->
@end verbatim
@math{r_k}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 34 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 35 -->
@end verbatim
@math{d_k}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 35 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 36 -->
@end verbatim
@math{N}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 36 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 37 -->
@end verbatim
@math{N}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 37 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 38 -->
@end verbatim
@math{N+1}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 38 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 39 -->
@end verbatim
@math{N+1}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 39 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 40 -->
@end verbatim
@math{k}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 40 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 41 -->
@end verbatim
@math{k}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 41 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 42 -->
@end verbatim
@math{x/\Delta}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 42 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 43 -->
@end verbatim
@math{\omega}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 43 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 44 -->
@end verbatim
@math{h}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 44 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 45 -->
@end verbatim
@math{\varphi_{meet}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 45 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 46 -->
@end verbatim
@math{\eta_{prey}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 46 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 47 -->
@end verbatim
@math{\eta_{pred}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 47 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 48 -->
@end verbatim
@math{\eta_1(t)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 48 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 49 -->
@end verbatim
@math{\eta_1(t=0)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 49 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 50 -->
@end verbatim
@math{t=0}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 50 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 51 -->
@end verbatim
@math{\phi_{j}(t)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 51 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 52 -->
@end verbatim
@math{\eta_i(t=0)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 52 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 53 -->
@end verbatim
@math{h(t)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 53 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 54 -->
@end verbatim
@math{J}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 54 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 55 -->
@end verbatim
@math{T}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 55 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 56 -->
@end verbatim
@math{J}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 56 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 57 -->
@end verbatim
@math{\psi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 57 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 58 -->
@end verbatim
@math{l}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 58 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 59 -->
@end verbatim
@math{h}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 59 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 60 -->
@end verbatim
@math{J}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 60 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 61 -->
@end verbatim
@math{t=0}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 61 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 62 -->
@end verbatim
@math{\omega}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 62 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 63 -->
@end verbatim
@math{t=s_i}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 63 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 64 -->
@end verbatim
@math{\mu}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 64 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 65 -->
@end verbatim
@math{Q}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 65 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 66 -->
@end verbatim
@math{\nu}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 66 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 67 -->
@end verbatim
@math{R}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 67 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 68 -->
@end verbatim
@math{W}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 68 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 69 -->
@end verbatim
@math{W}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 69 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 70 -->
@end verbatim
@math{W}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 70 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 71 -->
@end verbatim
@math{g(\tau)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 71 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 72 -->
@end verbatim
@math{g(\tau)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 72 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 73 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 73 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 74 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 74 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 75 -->
@end verbatim
@math{g(\tau;t)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 75 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 76 -->
@end verbatim
@math{t}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 76 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 77 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 77 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 78 -->
@end verbatim
@math{2}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 78 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 79 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 79 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 80 -->
@end verbatim
@math{g(\tau;t)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 80 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 81 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 81 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 82 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 82 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 83 -->
@end verbatim
@math{tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 83 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 84 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 84 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 85 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 85 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 86 -->
@end verbatim
@math{0.2}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 86 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 87 -->
@end verbatim
@math{\sqrt{\sqrt{2}}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 87 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 88 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 88 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 89 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 89 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 90 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 90 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 91 -->
@end verbatim
@math{g(\tau)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 91 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 92 -->
@end verbatim
@math{g(t,\tau)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 92 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 93 -->
@end verbatim
@math{A_{st}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 93 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 94 -->
@end verbatim
@math{A_{st}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 94 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 95 -->
@end verbatim
@math{A_{st} + A_{st}^\dagger}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 95 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 96 -->
@end verbatim
@math{A_{st}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 96 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 97 -->
@end verbatim
@math{U}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 97 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 98 -->
@end verbatim
@math{w}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 98 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 99 -->
@end verbatim
@math{V}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 99 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 100 -->
@end verbatim
@math{A_{st} + A_{st}^\dagger}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 100 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 101 -->
@end verbatim
@math{A_{st}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 101 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 102 -->
@end verbatim
@math{\Phi(t+\delta t,t)=\exp{A_{st} \delta t}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 102 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 103 -->
@end verbatim
@math{w}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 103 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 104 -->
@end verbatim
@math{\Phi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 104 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 105 -->
@end verbatim
@math{t}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 105 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 106 -->
@end verbatim
@math{\Phi(t,0)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 106 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 107 -->
@end verbatim
@math{U}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 107 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 108 -->
@end verbatim
@math{\Phi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 108 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 109 -->
@end verbatim
@math{w}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 109 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 110 -->
@end verbatim
@math{\Phi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 110 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 111 -->
@end verbatim
@math{V}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 111 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 112 -->
@end verbatim
@math{\Phi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 112 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 113 -->
@end verbatim
@math{\Phi(t,0)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 113 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 114 -->
@end verbatim
@math{\Phi(t,0)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 114 -->
+
@end verbatim
@bye
Index: test/manuals/res_all/mini_ker/mini_ker_tex4ht_tex.tex
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/manuals/res_all/mini_ker/mini_ker_tex4ht_tex.tex,v
retrieving revision 1.1
retrieving revision 1.2
diff -u -b -r1.1 -r1.2
--- test/manuals/res_all/mini_ker/mini_ker_tex4ht_tex.tex 31 Jul 2009
10:16:58 -0000 1.1
+++ test/manuals/res_all/mini_ker/mini_ker_tex4ht_tex.tex 22 Oct 2009
20:23:22 -0000 1.2
@@ -1,48 +1,48 @@
% Automatically generated
\csname tex4ht\endcsname
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 1 -->\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 1
-->\Hnewline}
$$\partial_t \eta (t) = g(\eta(t),\varphi(t))$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 1 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 2 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 1 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 2
-->\Hnewline}
$$
\varphi(t) = f(\eta(t),\varphi(t))
$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 2 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 3 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 2 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 3
-->\Hnewline}
$$\pmatrix{A & B\cr
-C^+ & I-D\cr} \pmatrix{\delta \eta\cr
\delta \varphi\cr} = \pmatrix{\Gamma\cr
\Omega\cr}$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 3 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 4 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 3 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 4
-->\Hnewline}
$$\eqalign{\partial_t \eta (t) &= g(\eta(t),\varphi(t))\cr
\varphi(t) &= f(\eta(t),\varphi(t))\cr
}$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 4 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 5 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 4 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 5
-->\Hnewline}
$$\left\{\eqalign{\partial_t \eta _{prey} &= a \eta _{prey} - a \varphi
_{meet} \cr
\partial_t \eta _{pred} &= -c \eta _{pred} + c \varphi _{meet}\cr}\right.$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 5 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 6 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 5 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 6
-->\Hnewline}
$$\varphi _{meet} = \eta _{prey}\eta _{pred}$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 6 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 7 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 6 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 7
-->\Hnewline}
$$\partial_{\eta} g(\eta(t),\varphi(t));
$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 7 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 8 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 7 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 8
-->\Hnewline}
$$\partial_{\varphi} g(\eta(t),\varphi(t));
$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 8 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 9 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 8 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 9
-->\Hnewline}
$$\partial_{\eta} f(\eta(t),\varphi(t));
$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 9 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 10 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 9 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 10
-->\Hnewline}
$$\partial_{\varphi} f(\eta(t),\varphi(t));
$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 10 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 11 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 10 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 11
-->\Hnewline}
$$\left\{\eqalign{\partial_t \eta _{k} ^{pos} &= \eta _{k} ^{vel} \cr
\partial_t \eta _{k} ^{vel} &= ( \varphi_k ^{spr} -\varphi _{k+1} ^{spr} +
\varphi _{k} ^{dmp}-\varphi _{k+1} ^{dmp})\,/m_k \cr}\right.$$
$$\left\{\eqalign{
@@ -53,29 +53,29 @@
\eta ^{vel}_{0} &= 0\cr
\varphi ^{spr}_{N+1} &= 0\cr
\varphi ^{dmp}_{N+1} &= 0\cr}\right.$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 11 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 12 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 11 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 12
-->\Hnewline}
$$\eqalign{\partial_x f^g &= g f^{g-1}\partial_x f + f^g \log f\partial_x g\cr
&= f^{g-1}(g\partial_x f + f\partial_x g)\cr}$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 12 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 13 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 12 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 13
-->\Hnewline}
$$
\omega = h ( \eta , \varphi)
$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 13 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 14 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 13 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 14
-->\Hnewline}
$$
J = \psi[\eta(T),\varphi(T) ,h(T)] + \int_0 ^T
{l[\eta(\tau),\varphi(\tau),h(\tau)]}\, d\tau
$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 14 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 15 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 14 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 15
-->\Hnewline}
$$\eqalign{
\partial_t \eta (t) &= g(\eta(t),\varphi(t)) + W(t) \mu\cr
\varphi(t) &= f(\eta(t),\varphi(t))\cr
\omega(t) &= h ( \eta(t) , \varphi(t)) + \nu\cr
}$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 15 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 16 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 15 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 16
-->\Hnewline}
$$\left\{\eqalign{
\partial_t \eta_1 &= a_{11} \eta_1 + a_{12} \varphi_2 + a_{13} \varphi_3 +
W_{11} \mu_1 + W_{12} \mu_2\cr
\partial_t \eta_2 &= a_{21} \varphi_1 + a_{22} \eta_2 + a_{23} \varphi_3 +
W_{21} \mu_1 + W_{22} \mu_2\cr
@@ -91,11 +91,11 @@
\omega _2 &= \eta _2 + \nu_2 \cr
\omega _3 &= \eta _3 + \nu_3
}\right.$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 16 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 17 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 16 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 17
-->\Hnewline}
$$
U w V^\dagger
$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 17 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 17 -->\Hnewline
\Hnewline}
\bye
Index: test/manuals/res_info/mini_ker/mini_ker_1.2.html
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/manuals/res_info/mini_ker/mini_ker_1.2.html,v
retrieving revision 1.5
retrieving revision 1.6
diff -u -b -r1.5 -r1.6
--- test/manuals/res_info/mini_ker/mini_ker_1.2.html 4 Oct 2009 21:51:43
-0000 1.5
+++ test/manuals/res_info/mini_ker/mini_ker_1.2.html 22 Oct 2009 20:23:22
-0000 1.6
@@ -100,7 +100,6 @@
of f and g, and with δt. From this system the
elimination of δη leads to another formulation giving
the coupling between transfers, and allows for the δφ
-
computation. The δφ value is then substitued in
δη to complete the time-step solving process.
</p>
Index: test/manuals/res_info/mini_ker/mini_ker_2.4.html
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/manuals/res_info/mini_ker/mini_ker_2.4.html,v
retrieving revision 1.5
retrieving revision 1.6
diff -u -b -r1.5 -r1.6
--- test/manuals/res_info/mini_ker/mini_ker_2.4.html 4 Oct 2009 21:51:43
-0000 1.5
+++ test/manuals/res_info/mini_ker/mini_ker_2.4.html 22 Oct 2009 20:23:22
-0000 1.6
@@ -111,8 +111,7 @@
on a pseudo relative quadratic residual between
φ = f(η(t - dt) + dφ (<code> ffl</code>), where
dφ
is given by the system resolution in <code>ker</code>,and
- φ = f(η),φ)
-, Fortran variable (<code>ff</code>):
+ φ = f(η),φ), Fortran variable (<code>ff</code>):
</p>
<pre class="verbatim">!
========================================================
! test linearite ffl - ff
Index: test/manuals/res_info/mini_ker/mini_ker_3.3.html
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/manuals/res_info/mini_ker/mini_ker_3.3.html,v
retrieving revision 1.5
retrieving revision 1.6
diff -u -b -r1.5 -r1.6
--- test/manuals/res_info/mini_ker/mini_ker_3.3.html 4 Oct 2009 21:51:43
-0000 1.5
+++ test/manuals/res_info/mini_ker/mini_ker_3.3.html 22 Oct 2009 20:23:22
-0000 1.6
@@ -117,8 +117,7 @@
in the grid, from 1 to N, and two nodes outside of the grid,
a limiting node 0, and a limiting node N + 1. The limiting node
corresponding with node 0 is called the <em>down</em> node, while the limiting
-node corresponding with node N + 1
- is called the <em>up</em> node.
+node corresponding with node N + 1 is called the <em>up</em> node.
Other models not part of the 1D grid may be added if any.
</p>
<p>To enable 1D gridded models, one should set the select flag
‘<samp>grid1d</samp>’.
Index: test/manuals/res_info/mini_ker/mini_ker_4.1.html
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/manuals/res_info/mini_ker/mini_ker_4.1.html,v
retrieving revision 1.5
retrieving revision 1.6
diff -u -b -r1.5 -r1.6
--- test/manuals/res_info/mini_ker/mini_ker_4.1.html 4 Oct 2009 21:51:43
-0000 1.5
+++ test/manuals/res_info/mini_ker/mini_ker_4.1.html 22 Oct 2009 20:23:23
-0000 1.6
@@ -177,8 +177,7 @@
of the number of predators.
</p>
<p>In the same way, the <var>j+1</var>th column of
‘<tt>sigma.data</tt>’ will be the
-derivative of ϕj(t) with respect to ηi(t = 0)
-. Here:
+derivative of ϕj(t) with respect to ηi(t = 0). Here:
</p><table><tr><td> </td><td><pre class="example"># Sensy_to: eta_pray
eta_pred
# time \\ of: ff_interact ff_interact
0.00000E+00 1.60683E+00 8.47076E-01
Index: test/manuals/res_info/mini_ker/mini_ker_4.3.html
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/manuals/res_info/mini_ker/mini_ker_4.3.html,v
retrieving revision 1.5
retrieving revision 1.6
diff -u -b -r1.5 -r1.6
--- test/manuals/res_info/mini_ker/mini_ker_4.3.html 4 Oct 2009 21:51:43
-0000 1.5
+++ test/manuals/res_info/mini_ker/mini_ker_4.3.html 22 Oct 2009 20:23:23
-0000 1.6
@@ -112,8 +112,7 @@
<p>The observations ω are available at discrete time steps
t = si. The
stochastic perturbation on state, μ is characterized by a
-variance-covariance matrix Q
- and the noise on the observation,
+variance-covariance matrix Q and the noise on the observation,
ν has a variance-covariance matrix R. W relates states
with stochastic perturbations. At each time step the Kalman filter recomputes
an estimation of the state and the variance-covariance matrix of the state.
Index: test/manuals/res_info/mini_ker/mini_ker_4.4.html
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/manuals/res_info/mini_ker/mini_ker_4.4.html,v
retrieving revision 1.5
retrieving revision 1.6
diff -u -b -r1.5 -r1.6
--- test/manuals/res_info/mini_ker/mini_ker_4.4.html 4 Oct 2009 21:51:43
-0000 1.5
+++ test/manuals/res_info/mini_ker/mini_ker_4.4.html 22 Oct 2009 20:23:23
-0000 1.6
@@ -113,8 +113,7 @@
scheme for the time discretisation
symbolically gives the solution of the Borel transform of the system. One can
identify the <code>dt</code> variable with the Borel τ within a
-factor 2
-. Hence, to numerically study the τ dependency of
+factor 2. Hence, to numerically study the τ dependency of
the transform of various coefficients in the system coupling matrix at one
point in time, one can calculate the Borel transform of the TLS solutions
by making a time-step sweep.
Index: test/manuals/res_info/mini_ker/mini_ker_tex4ht_math.html
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/manuals/res_info/mini_ker/mini_ker_tex4ht_math.html,v
retrieving revision 1.1
retrieving revision 1.2
diff -u -b -r1.1 -r1.2
--- test/manuals/res_info/mini_ker/mini_ker_tex4ht_math.html 31 Jul 2009
10:17:19 -0000 1.1
+++ test/manuals/res_info/mini_ker/mini_ker_tex4ht_math.html 22 Oct 2009
20:23:23 -0000 1.2
@@ -22,6 +22,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 8 -->
φ
<!-- tex4ht_end mini_ker_tex4ht_math math 8 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 9 -->
f
<!-- tex4ht_end mini_ker_tex4ht_math math 9 -->
@@ -36,7 +37,6 @@
<!-- tex4ht_end mini_ker_tex4ht_math math 12 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 13 -->
δφ
-
<!-- tex4ht_end mini_ker_tex4ht_math math 13 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 14 -->
δφ
@@ -47,6 +47,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 16 -->
a
<!-- tex4ht_end mini_ker_tex4ht_math math 16 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 17 -->
c
<!-- tex4ht_end mini_ker_tex4ht_math math 17 -->
@@ -71,12 +72,12 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 24 -->
φ = f(η(t - dt) + dφ
<!-- tex4ht_end mini_ker_tex4ht_math math 24 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 25 -->
dφ
<!-- tex4ht_end mini_ker_tex4ht_math math 25 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 26 -->
φ = f(η),φ)
-
<!-- tex4ht_end mini_ker_tex4ht_math math 26 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 27 -->
10-3
@@ -96,6 +97,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 32 -->
mk
<!-- tex4ht_end mini_ker_tex4ht_math math 32 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 33 -->
k
<!-- tex4ht_end mini_ker_tex4ht_math math 33 -->
@@ -116,11 +118,11 @@
<!-- tex4ht_end mini_ker_tex4ht_math math 38 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 39 -->
N + 1
-
<!-- tex4ht_end mini_ker_tex4ht_math math 39 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 40 -->
k
<!-- tex4ht_end mini_ker_tex4ht_math math 40 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 41 -->
k
<!-- tex4ht_end mini_ker_tex4ht_math math 41 -->
@@ -145,6 +147,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 48 -->
η1(t)
<!-- tex4ht_end mini_ker_tex4ht_math math 48 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 49 -->
η1(t = 0)
<!-- tex4ht_end mini_ker_tex4ht_math math 49 -->
@@ -156,7 +159,6 @@
<!-- tex4ht_end mini_ker_tex4ht_math math 51 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 52 -->
ηi(t = 0)
-
<!-- tex4ht_end mini_ker_tex4ht_math math 52 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 53 -->
h(t)
@@ -170,6 +172,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 56 -->
J
<!-- tex4ht_end mini_ker_tex4ht_math math 56 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 57 -->
ψ
<!-- tex4ht_end mini_ker_tex4ht_math math 57 -->
@@ -194,9 +197,9 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 64 -->
μ
<!-- tex4ht_end mini_ker_tex4ht_math math 64 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 65 -->
Q
-
<!-- tex4ht_end mini_ker_tex4ht_math math 65 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 66 -->
ν
@@ -219,6 +222,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 72 -->
g(τ)
<!-- tex4ht_end mini_ker_tex4ht_math math 72 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 73 -->
τ
<!-- tex4ht_end mini_ker_tex4ht_math math 73 -->
@@ -236,7 +240,6 @@
<!-- tex4ht_end mini_ker_tex4ht_math math 77 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 78 -->
2
-
<!-- tex4ht_end mini_ker_tex4ht_math math 78 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 79 -->
τ
@@ -244,6 +247,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 80 -->
g(τ;t)
<!-- tex4ht_end mini_ker_tex4ht_math math 80 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 81 -->
τ
<!-- tex4ht_end mini_ker_tex4ht_math math 81 -->
@@ -270,13 +274,13 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 88 -->
τ
<!-- tex4ht_end mini_ker_tex4ht_math math 88 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 89 -->
τ
<!-- tex4ht_end mini_ker_tex4ht_math math 89 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 90 -->
τ
<!-- tex4ht_end mini_ker_tex4ht_math math 90 -->
-
<!-- tex4ht_begin mini_ker_tex4ht_math math 91 -->
g(τ)
<!-- tex4ht_end mini_ker_tex4ht_math math 91 -->
@@ -296,6 +300,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 96 -->
Ast
<!-- tex4ht_end mini_ker_tex4ht_math math 96 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 97 -->
U
<!-- tex4ht_end mini_ker_tex4ht_math math 97 -->
@@ -317,11 +322,11 @@
<!-- tex4ht_end mini_ker_tex4ht_math math 102 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 103 -->
w
-
<!-- tex4ht_end mini_ker_tex4ht_math math 103 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 104 -->
Φ
<!-- tex4ht_end mini_ker_tex4ht_math math 104 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 105 -->
t
<!-- tex4ht_end mini_ker_tex4ht_math math 105 -->
@@ -346,6 +351,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 112 -->
Φ
<!-- tex4ht_end mini_ker_tex4ht_math math 112 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 113 -->
Φ(t,0)
<!-- tex4ht_end mini_ker_tex4ht_math math 113 -->
Index: test/manuals/res_info/mini_ker/mini_ker_tex4ht_math.texi
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/manuals/res_info/mini_ker/mini_ker_tex4ht_math.texi,v
retrieving revision 1.1
retrieving revision 1.2
diff -u -b -r1.1 -r1.2
--- test/manuals/res_info/mini_ker/mini_ker_tex4ht_math.texi 31 Jul 2009
10:17:19 -0000 1.1
+++ test/manuals/res_info/mini_ker/mini_ker_tex4ht_math.texi 22 Oct 2009
20:23:23 -0000 1.2
@@ -2,802 +2,1030 @@
@setfilename mini_ker_tex4ht_math.info
@c Automatically generated
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 1 -->
@end verbatim
@math{\eta}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 1 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 2 -->
@end verbatim
@math{\varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 2 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 3 -->
@end verbatim
@math{t}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 3 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 4 -->
@end verbatim
@math{t + \delta t}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 4 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 5 -->
@end verbatim
@math{\delta \eta}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 5 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 6 -->
@end verbatim
@math{\eta}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 6 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 7 -->
@end verbatim
@math{\delta \varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 7 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 8 -->
@end verbatim
@math{\varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 8 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 9 -->
@end verbatim
@math{f}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 9 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 10 -->
@end verbatim
@math{g}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 10 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 11 -->
@end verbatim
@math{\delta t}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 11 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 12 -->
@end verbatim
@math{\delta \eta}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 12 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 13 -->
@end verbatim
@math{\delta \varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 13 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 14 -->
@end verbatim
@math{\delta \varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 14 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 15 -->
@end verbatim
@math{\delta \eta}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 15 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 16 -->
@end verbatim
@math{a}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 16 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 17 -->
@end verbatim
@math{c}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 17 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 18 -->
@end verbatim
@math{\varphi_{meet}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 18 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 19 -->
@end verbatim
@math{\eta_{prey}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 19 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 20 -->
@end verbatim
@math{\eta_{pred}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 20 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 21 -->
@end verbatim
@math{\varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 21 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 22 -->
@end verbatim
@math{\delta\eta}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 22 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 23 -->
@end verbatim
@math{\varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 23 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 24 -->
@end verbatim
@math{\varphi=f(\eta(t-dt)+d\varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 24 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 25 -->
@end verbatim
@math{d\varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 25 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 26 -->
@end verbatim
@math{\varphi=f(\eta),\varphi)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 26 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 27 -->
@end verbatim
@math{10^{-3}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 27 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 28 -->
@end verbatim
@math{(I-D)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 28 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 29 -->
@end verbatim
@math{(I-D)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 29 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 30 -->
@end verbatim
@math{(I-D)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 30 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 31 -->
@end verbatim
@math{k}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 31 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 32 -->
@end verbatim
@math{m_k}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 32 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 33 -->
@end verbatim
@math{k}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 33 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 34 -->
@end verbatim
@math{r_k}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 34 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 35 -->
@end verbatim
@math{d_k}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 35 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 36 -->
@end verbatim
@math{N}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 36 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 37 -->
@end verbatim
@math{N}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 37 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 38 -->
@end verbatim
@math{N+1}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 38 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 39 -->
@end verbatim
@math{N+1}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 39 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 40 -->
@end verbatim
@math{k}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 40 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 41 -->
@end verbatim
@math{k}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 41 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 42 -->
@end verbatim
@math{x/\Delta}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 42 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 43 -->
@end verbatim
@math{\omega}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 43 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 44 -->
@end verbatim
@math{h}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 44 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 45 -->
@end verbatim
@math{\varphi_{meet}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 45 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 46 -->
@end verbatim
@math{\eta_{prey}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 46 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 47 -->
@end verbatim
@math{\eta_{pred}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 47 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 48 -->
@end verbatim
@math{\eta_1(t)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 48 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 49 -->
@end verbatim
@math{\eta_1(t=0)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 49 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 50 -->
@end verbatim
@math{t=0}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 50 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 51 -->
@end verbatim
@math{\phi_{j}(t)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 51 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 52 -->
@end verbatim
@math{\eta_i(t=0)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 52 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 53 -->
@end verbatim
@math{h(t)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 53 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 54 -->
@end verbatim
@math{J}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 54 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 55 -->
@end verbatim
@math{T}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 55 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 56 -->
@end verbatim
@math{J}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 56 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 57 -->
@end verbatim
@math{\psi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 57 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 58 -->
@end verbatim
@math{l}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 58 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 59 -->
@end verbatim
@math{h}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 59 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 60 -->
@end verbatim
@math{J}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 60 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 61 -->
@end verbatim
@math{t=0}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 61 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 62 -->
@end verbatim
@math{\omega}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 62 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 63 -->
@end verbatim
@math{t=s_i}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 63 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 64 -->
@end verbatim
@math{\mu}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 64 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 65 -->
@end verbatim
@math{Q}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 65 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 66 -->
@end verbatim
@math{\nu}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 66 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 67 -->
@end verbatim
@math{R}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 67 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 68 -->
@end verbatim
@math{W}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 68 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 69 -->
@end verbatim
@math{W}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 69 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 70 -->
@end verbatim
@math{W}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 70 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 71 -->
@end verbatim
@math{g(\tau)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 71 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 72 -->
@end verbatim
@math{g(\tau)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 72 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 73 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 73 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 74 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 74 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 75 -->
@end verbatim
@math{g(\tau;t)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 75 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 76 -->
@end verbatim
@math{t}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 76 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 77 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 77 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 78 -->
@end verbatim
@math{2}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 78 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 79 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 79 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 80 -->
@end verbatim
@math{g(\tau;t)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 80 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 81 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 81 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 82 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 82 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 83 -->
@end verbatim
@math{tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 83 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 84 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 84 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 85 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 85 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 86 -->
@end verbatim
@math{0.2}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 86 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 87 -->
@end verbatim
@math{\sqrt{\sqrt{2}}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 87 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 88 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 88 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 89 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 89 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 90 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 90 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 91 -->
@end verbatim
@math{g(\tau)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 91 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 92 -->
@end verbatim
@math{g(t,\tau)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 92 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 93 -->
@end verbatim
@math{A_{st}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 93 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 94 -->
@end verbatim
@math{A_{st}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 94 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 95 -->
@end verbatim
@math{A_{st} + A_{st}^\dagger}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 95 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 96 -->
@end verbatim
@math{A_{st}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 96 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 97 -->
@end verbatim
@math{U}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 97 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 98 -->
@end verbatim
@math{w}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 98 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 99 -->
@end verbatim
@math{V}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 99 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 100 -->
@end verbatim
@math{A_{st} + A_{st}^\dagger}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 100 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 101 -->
@end verbatim
@math{A_{st}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 101 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 102 -->
@end verbatim
@math{\Phi(t+\delta t,t)=\exp{A_{st} \delta t}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 102 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 103 -->
@end verbatim
@math{w}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 103 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 104 -->
@end verbatim
@math{\Phi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 104 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 105 -->
@end verbatim
@math{t}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 105 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 106 -->
@end verbatim
@math{\Phi(t,0)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 106 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 107 -->
@end verbatim
@math{U}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 107 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 108 -->
@end verbatim
@math{\Phi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 108 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 109 -->
@end verbatim
@math{w}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 109 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 110 -->
@end verbatim
@math{\Phi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 110 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 111 -->
@end verbatim
@math{V}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 111 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 112 -->
@end verbatim
@math{\Phi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 112 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 113 -->
@end verbatim
@math{\Phi(t,0)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 113 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 114 -->
@end verbatim
@math{\Phi(t,0)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 114 -->
+
@end verbatim
@bye
Index: test/manuals/res_info/mini_ker/mini_ker_tex4ht_tex.tex
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/manuals/res_info/mini_ker/mini_ker_tex4ht_tex.tex,v
retrieving revision 1.1
retrieving revision 1.2
diff -u -b -r1.1 -r1.2
--- test/manuals/res_info/mini_ker/mini_ker_tex4ht_tex.tex 31 Jul 2009
10:17:19 -0000 1.1
+++ test/manuals/res_info/mini_ker/mini_ker_tex4ht_tex.tex 22 Oct 2009
20:23:23 -0000 1.2
@@ -1,48 +1,48 @@
% Automatically generated
\csname tex4ht\endcsname
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 1 -->\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 1
-->\Hnewline}
$$\partial_t \eta (t) = g(\eta(t),\varphi(t))$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 1 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 2 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 1 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 2
-->\Hnewline}
$$
\varphi(t) = f(\eta(t),\varphi(t))
$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 2 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 3 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 2 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 3
-->\Hnewline}
$$\pmatrix{A & B\cr
-C^+ & I-D\cr} \pmatrix{\delta \eta\cr
\delta \varphi\cr} = \pmatrix{\Gamma\cr
\Omega\cr}$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 3 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 4 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 3 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 4
-->\Hnewline}
$$\eqalign{\partial_t \eta (t) &= g(\eta(t),\varphi(t))\cr
\varphi(t) &= f(\eta(t),\varphi(t))\cr
}$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 4 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 5 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 4 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 5
-->\Hnewline}
$$\left\{\eqalign{\partial_t \eta _{prey} &= a \eta _{prey} - a \varphi
_{meet} \cr
\partial_t \eta _{pred} &= -c \eta _{pred} + c \varphi _{meet}\cr}\right.$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 5 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 6 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 5 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 6
-->\Hnewline}
$$\varphi _{meet} = \eta _{prey}\eta _{pred}$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 6 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 7 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 6 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 7
-->\Hnewline}
$$\partial_{\eta} g(\eta(t),\varphi(t));
$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 7 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 8 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 7 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 8
-->\Hnewline}
$$\partial_{\varphi} g(\eta(t),\varphi(t));
$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 8 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 9 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 8 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 9
-->\Hnewline}
$$\partial_{\eta} f(\eta(t),\varphi(t));
$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 9 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 10 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 9 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 10
-->\Hnewline}
$$\partial_{\varphi} f(\eta(t),\varphi(t));
$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 10 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 11 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 10 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 11
-->\Hnewline}
$$\left\{\eqalign{\partial_t \eta _{k} ^{pos} &= \eta _{k} ^{vel} \cr
\partial_t \eta _{k} ^{vel} &= ( \varphi_k ^{spr} -\varphi _{k+1} ^{spr} +
\varphi _{k} ^{dmp}-\varphi _{k+1} ^{dmp})\,/m_k \cr}\right.$$
$$\left\{\eqalign{
@@ -53,29 +53,29 @@
\eta ^{vel}_{0} &= 0\cr
\varphi ^{spr}_{N+1} &= 0\cr
\varphi ^{dmp}_{N+1} &= 0\cr}\right.$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 11 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 12 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 11 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 12
-->\Hnewline}
$$\eqalign{\partial_x f^g &= g f^{g-1}\partial_x f + f^g \log f\partial_x g\cr
&= f^{g-1}(g\partial_x f + f\partial_x g)\cr}$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 12 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 13 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 12 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 13
-->\Hnewline}
$$
\omega = h ( \eta , \varphi)
$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 13 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 14 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 13 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 14
-->\Hnewline}
$$
J = \psi[\eta(T),\varphi(T) ,h(T)] + \int_0 ^T
{l[\eta(\tau),\varphi(\tau),h(\tau)]}\, d\tau
$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 14 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 15 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 14 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 15
-->\Hnewline}
$$\eqalign{
\partial_t \eta (t) &= g(\eta(t),\varphi(t)) + W(t) \mu\cr
\varphi(t) &= f(\eta(t),\varphi(t))\cr
\omega(t) &= h ( \eta(t) , \varphi(t)) + \nu\cr
}$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 15 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 16 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 15 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 16
-->\Hnewline}
$$\left\{\eqalign{
\partial_t \eta_1 &= a_{11} \eta_1 + a_{12} \varphi_2 + a_{13} \varphi_3 +
W_{11} \mu_1 + W_{12} \mu_2\cr
\partial_t \eta_2 &= a_{21} \varphi_1 + a_{22} \eta_2 + a_{23} \varphi_3 +
W_{21} \mu_1 + W_{22} \mu_2\cr
@@ -91,11 +91,11 @@
\omega _2 &= \eta _2 + \nu_2 \cr
\omega _3 &= \eta _3 + \nu_3
}\right.$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 16 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 17 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 16 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 17
-->\Hnewline}
$$
U w V^\dagger
$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 17 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 17 -->\Hnewline
\Hnewline}
\bye
Index: test/many_input_files/tex_l2h_res/mini_ker_l2h.tex
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/many_input_files/tex_l2h_res/mini_ker_l2h.tex,v
retrieving revision 1.1
retrieving revision 1.2
diff -u -b -r1.1 -r1.2
--- test/many_input_files/tex_l2h_res/mini_ker_l2h.tex 1 Sep 2008 14:48:38
-0000 1.1
+++ test/many_input_files/tex_l2h_res/mini_ker_l2h.tex 22 Oct 2009 20:23:23
-0000 1.2
@@ -4,27 +4,34 @@
\usepackage{html}
\begin{document}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 1 -->
\end{rawhtml}
$$\partial_t \eta (t) = g(\eta(t),\varphi(t))$$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 1 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 2 -->
\end{rawhtml}
$\eta$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 2 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 3 -->
\end{rawhtml}
$\varphi$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 3 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 4 -->
\end{rawhtml}
$$
@@ -32,36 +39,46 @@
$$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 4 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 5 -->
\end{rawhtml}
$t$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 5 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 6 -->
\end{rawhtml}
$t + \delta t$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 6 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 7 -->
\end{rawhtml}
$\delta \eta$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 7 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 8 -->
\end{rawhtml}
$\delta \varphi$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 8 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 9 -->
\end{rawhtml}
$$\pmatrix{A & B\cr
@@ -70,29 +87,37 @@
\Omega\cr}$$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 9 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 10 -->
\end{rawhtml}
$f$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 10 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 11 -->
\end{rawhtml}
$g$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 11 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 12 -->
\end{rawhtml}
$\delta t$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 12 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 13 -->
\end{rawhtml}
$$\eqalign{\partial_t \eta (t) &= g(\eta(t),\varphi(t))\cr
@@ -100,139 +125,177 @@
}$$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 13 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 14 -->
\end{rawhtml}
$$\left\{\eqalign{\partial_t \eta _{prey} &= a \eta _{prey} - a \varphi
_{meet} \cr
\partial_t \eta _{pred} &= -c \eta _{pred} + c \varphi _{meet}\cr}\right.$$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 14 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 15 -->
\end{rawhtml}
$$\varphi _{meet} = \eta _{prey}\eta _{pred}$$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 15 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 16 -->
\end{rawhtml}
$a$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 16 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 17 -->
\end{rawhtml}
$c$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 17 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 18 -->
\end{rawhtml}
$\varphi_{meet}$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 18 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 19 -->
\end{rawhtml}
$\eta_{prey}$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 19 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 20 -->
\end{rawhtml}
$\eta_{pred}$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 20 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 21 -->
\end{rawhtml}
$\delta\eta$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 21 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 22 -->
\end{rawhtml}
$\varphi=f(\eta(t-dt)+d\varphi$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 22 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 23 -->
\end{rawhtml}
$d\varphi$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 23 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 24 -->
\end{rawhtml}
$\varphi=f(\eta),\varphi)$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 24 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 25 -->
\end{rawhtml}
$10^{-3}$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 25 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 26 -->
\end{rawhtml}
$$\partial_{\eta} g(\eta(t),\varphi(t));
$$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 26 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 27 -->
\end{rawhtml}
$$\partial_{\varphi} g(\eta(t),\varphi(t));
$$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 27 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 28 -->
\end{rawhtml}
$$\partial_{\eta} f(\eta(t),\varphi(t));
$$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 28 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 29 -->
\end{rawhtml}
$$\partial_{\varphi} f(\eta(t),\varphi(t));
$$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 29 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 30 -->
\end{rawhtml}
$(I-D)$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 30 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 31 -->
\end{rawhtml}
$k$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 31 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 32 -->
\end{rawhtml}
$$\left\{\eqalign{\partial_t \eta _{k} ^{pos} &= \eta _{k} ^{vel} \cr
@@ -247,72 +310,92 @@
\varphi ^{dmp}_{N+1} &= 0\cr}\right.$$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 32 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 33 -->
\end{rawhtml}
$m_k$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 33 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 34 -->
\end{rawhtml}
$r_k$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 34 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 35 -->
\end{rawhtml}
$d_k$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 35 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 36 -->
\end{rawhtml}
$N$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 36 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 37 -->
\end{rawhtml}
$N+1$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 37 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 38 -->
\end{rawhtml}
$$\eqalign{\partial_x f^g &= g f^{g-1}\partial_x f + f^g \log f\partial_x g\cr
&= f^{g-1}(g\partial_x f + f\partial_x g)\cr}$$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 38 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 39 -->
\end{rawhtml}
$x/\Delta$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 39 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 40 -->
\end{rawhtml}
$\omega$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 40 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 41 -->
\end{rawhtml}
$h$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 41 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 42 -->
\end{rawhtml}
$$
@@ -320,64 +403,82 @@
$$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 42 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 43 -->
\end{rawhtml}
$\eta_1(t)$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 43 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 44 -->
\end{rawhtml}
$\eta_1(t=0)$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 44 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 45 -->
\end{rawhtml}
$t=0$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 45 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 46 -->
\end{rawhtml}
$\phi_{j}(t)$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 46 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 47 -->
\end{rawhtml}
$\eta_i(t=0)$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 47 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 48 -->
\end{rawhtml}
$h(t)$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 48 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 49 -->
\end{rawhtml}
$J$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 49 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 50 -->
\end{rawhtml}
$T$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 50 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 51 -->
\end{rawhtml}
$$
@@ -385,22 +486,28 @@
$$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 51 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 52 -->
\end{rawhtml}
$\psi$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 52 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 53 -->
\end{rawhtml}
$l$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 53 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 54 -->
\end{rawhtml}
$$\eqalign{
@@ -410,50 +517,64 @@
}$$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 54 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 55 -->
\end{rawhtml}
$t=s_i$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 55 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 56 -->
\end{rawhtml}
$\mu$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 56 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 57 -->
\end{rawhtml}
$Q$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 57 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 58 -->
\end{rawhtml}
$\nu$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 58 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 59 -->
\end{rawhtml}
$R$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 59 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 60 -->
\end{rawhtml}
$W$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 60 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 61 -->
\end{rawhtml}
$$\left\{\eqalign{
@@ -473,78 +594,100 @@
}\right.$$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 61 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 62 -->
\end{rawhtml}
$g(\tau)$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 62 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 63 -->
\end{rawhtml}
$\tau$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 63 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 64 -->
\end{rawhtml}
$g(\tau;t)$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 64 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 65 -->
\end{rawhtml}
$2$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 65 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 66 -->
\end{rawhtml}
$tau$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 66 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 67 -->
\end{rawhtml}
$0.2$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 67 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 68 -->
\end{rawhtml}
$\sqrt{\sqrt{2}}$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 68 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 69 -->
\end{rawhtml}
$g(t,\tau)$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 69 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 70 -->
\end{rawhtml}
$A_{st}$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 70 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 71 -->
\end{rawhtml}
$A_{st} + A_{st}^\dagger$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 71 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 72 -->
\end{rawhtml}
$$
@@ -552,47 +695,60 @@
$$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 72 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 73 -->
\end{rawhtml}
$U$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 73 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 74 -->
\end{rawhtml}
$w$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 74 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 75 -->
\end{rawhtml}
$V$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 75 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 76 -->
\end{rawhtml}
$\Phi(t+\delta t,t)=\exp{A_{st} \delta t}$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 76 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 77 -->
\end{rawhtml}
$\Phi$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 77 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 78 -->
\end{rawhtml}
$\Phi(t,0)$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 78 -->
+
\end{rawhtml}
\end{document}
Index: test/many_input_files/tex_l2h_res/tex_l2h.tex
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/many_input_files/tex_l2h_res/tex_l2h.tex,v
retrieving revision 1.1
retrieving revision 1.2
diff -u -b -r1.1 -r1.2
--- test/many_input_files/tex_l2h_res/tex_l2h.tex 1 Sep 2008 14:48:40
-0000 1.1
+++ test/many_input_files/tex_l2h_res/tex_l2h.tex 22 Oct 2009 20:23:23
-0000 1.2
@@ -4,6 +4,7 @@
\usepackage{html}
\begin{document}
\begin{rawhtml}
+
<!-- l2h_begin tex_l2h 1 -->
\end{rawhtml}
some
@@ -13,8 +14,10 @@
\over \sigma_i\right)^2 $$
\begin{rawhtml}
<!-- l2h_end tex_l2h 1 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin tex_l2h 2 -->
\end{rawhtml}
some
@@ -22,33 +25,42 @@
tex \TeX
\begin{rawhtml}
<!-- l2h_end tex_l2h 2 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin tex_l2h 3 -->
\end{rawhtml}
${x^i}\over{\tan y}$
\begin{rawhtml}
<!-- l2h_end tex_l2h 3 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin tex_l2h 4 -->
\end{rawhtml}
$a @\ b$
\begin{rawhtml}
<!-- l2h_end tex_l2h 4 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin tex_l2h 5 -->
\end{rawhtml}
address@hidden code}$
\begin{rawhtml}
<!-- l2h_end tex_l2h 5 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin tex_l2h 6 -->
\end{rawhtml}
$ address@hidden \hbox{ code }}} \sum_{i}{\underline{f}}$
\begin{rawhtml}
<!-- l2h_end tex_l2h 6 -->
+
\end{rawhtml}
\end{document}
Index: test/many_input_files/tex_t4ht_res/mini_ker.html
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/many_input_files/tex_t4ht_res/mini_ker.html,v
retrieving revision 1.23
retrieving revision 1.24
diff -u -b -r1.23 -r1.24
--- test/many_input_files/tex_t4ht_res/mini_ker.html 6 Oct 2009 13:36:23
-0000 1.23
+++ test/many_input_files/tex_t4ht_res/mini_ker.html 22 Oct 2009 20:23:23
-0000 1.24
@@ -406,7 +406,6 @@
of f and g, and with δt. From this system the
elimination of δη leads to another formulation giving
the coupling between transfers, and allows for the δφ
-
computation. The δφ value is then substitued in
δη to complete the time-step solving process.
</p>
@@ -1314,8 +1313,7 @@
on a pseudo relative quadratic residual between
φ = f(η(t - dt) + dφ (<code> ffl</code>), where
dφ
is given by the system resolution in <code>ker</code>,and
- φ = f(η),φ)
-, Fortran variable (<code>ff</code>):
+ φ = f(η),φ), Fortran variable (<code>ff</code>):
</p>
<pre class="verbatim">!
========================================================
! test linearite ffl - ff
@@ -1752,8 +1750,7 @@
in the grid, from 1 to N, and two nodes outside of the grid,
a limiting node 0, and a limiting node N + 1. The limiting node
corresponding with node 0 is called the <em>down</em> node, while the limiting
-node corresponding with node N + 1
- is called the <em>up</em> node.
+node corresponding with node N + 1 is called the <em>up</em> node.
Other models not part of the 1D grid may be added if any.
</p>
<p>To enable 1D gridded models, one should set the select flag
‘<samp>grid1d</samp>’.
@@ -2930,8 +2927,7 @@
of the number of predators.
</p>
<p>In the same way, the <var>j+1</var>th column of
‘<tt>sigma.data</tt>’ will be the
-derivative of ϕj(t) with respect to ηi(t = 0)
-. Here:
+derivative of ϕj(t) with respect to ηi(t = 0). Here:
</p><table><tr><td> </td><td><pre class="example"># Sensy_to: eta_pray
eta_pred
# time \\ of: ff_interact ff_interact
0.00000E+00 1.60683E+00 8.47076E-01
@@ -3393,8 +3389,7 @@
<p>The observations ω are available at discrete time steps
t = si. The
stochastic perturbation on state, μ is characterized by a
-variance-covariance matrix Q
- and the noise on the observation,
+variance-covariance matrix Q and the noise on the observation,
ν has a variance-covariance matrix R. W relates states
with stochastic perturbations. At each time step the Kalman filter recomputes
an estimation of the state and the variance-covariance matrix of the state.
@@ -3849,8 +3844,7 @@
scheme for the time discretisation
symbolically gives the solution of the Borel transform of the system. One can
identify the <code>dt</code> variable with the Borel τ within a
-factor 2
-. Hence, to numerically study the τ dependency of
+factor 2. Hence, to numerically study the τ dependency of
the transform of various coefficients in the system coupling matrix at one
point in time, one can calculate the Borel transform of the TLS solutions
by making a time-step sweep.
Index: test/many_input_files/tex_t4ht_res/mini_ker_tex4ht_math.html
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/many_input_files/tex_t4ht_res/mini_ker_tex4ht_math.html,v
retrieving revision 1.1
retrieving revision 1.2
diff -u -b -r1.1 -r1.2
--- test/many_input_files/tex_t4ht_res/mini_ker_tex4ht_math.html 1 Sep
2008 14:48:41 -0000 1.1
+++ test/many_input_files/tex_t4ht_res/mini_ker_tex4ht_math.html 22 Oct
2009 20:23:23 -0000 1.2
@@ -22,6 +22,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 8 -->
φ
<!-- tex4ht_end mini_ker_tex4ht_math math 8 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 9 -->
f
<!-- tex4ht_end mini_ker_tex4ht_math math 9 -->
@@ -36,7 +37,6 @@
<!-- tex4ht_end mini_ker_tex4ht_math math 12 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 13 -->
δφ
-
<!-- tex4ht_end mini_ker_tex4ht_math math 13 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 14 -->
δφ
@@ -47,6 +47,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 16 -->
a
<!-- tex4ht_end mini_ker_tex4ht_math math 16 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 17 -->
c
<!-- tex4ht_end mini_ker_tex4ht_math math 17 -->
@@ -71,12 +72,12 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 24 -->
φ = f(η(t - dt) + dφ
<!-- tex4ht_end mini_ker_tex4ht_math math 24 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 25 -->
dφ
<!-- tex4ht_end mini_ker_tex4ht_math math 25 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 26 -->
φ = f(η),φ)
-
<!-- tex4ht_end mini_ker_tex4ht_math math 26 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 27 -->
10-3
@@ -96,6 +97,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 32 -->
mk
<!-- tex4ht_end mini_ker_tex4ht_math math 32 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 33 -->
k
<!-- tex4ht_end mini_ker_tex4ht_math math 33 -->
@@ -116,11 +118,11 @@
<!-- tex4ht_end mini_ker_tex4ht_math math 38 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 39 -->
N + 1
-
<!-- tex4ht_end mini_ker_tex4ht_math math 39 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 40 -->
k
<!-- tex4ht_end mini_ker_tex4ht_math math 40 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 41 -->
k
<!-- tex4ht_end mini_ker_tex4ht_math math 41 -->
@@ -145,6 +147,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 48 -->
η1(t)
<!-- tex4ht_end mini_ker_tex4ht_math math 48 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 49 -->
η1(t = 0)
<!-- tex4ht_end mini_ker_tex4ht_math math 49 -->
@@ -156,7 +159,6 @@
<!-- tex4ht_end mini_ker_tex4ht_math math 51 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 52 -->
ηi(t = 0)
-
<!-- tex4ht_end mini_ker_tex4ht_math math 52 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 53 -->
h(t)
@@ -170,6 +172,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 56 -->
J
<!-- tex4ht_end mini_ker_tex4ht_math math 56 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 57 -->
ψ
<!-- tex4ht_end mini_ker_tex4ht_math math 57 -->
@@ -194,9 +197,9 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 64 -->
μ
<!-- tex4ht_end mini_ker_tex4ht_math math 64 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 65 -->
Q
-
<!-- tex4ht_end mini_ker_tex4ht_math math 65 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 66 -->
ν
@@ -219,6 +222,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 72 -->
g(τ)
<!-- tex4ht_end mini_ker_tex4ht_math math 72 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 73 -->
τ
<!-- tex4ht_end mini_ker_tex4ht_math math 73 -->
@@ -236,7 +240,6 @@
<!-- tex4ht_end mini_ker_tex4ht_math math 77 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 78 -->
2
-
<!-- tex4ht_end mini_ker_tex4ht_math math 78 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 79 -->
τ
@@ -244,6 +247,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 80 -->
g(τ;t)
<!-- tex4ht_end mini_ker_tex4ht_math math 80 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 81 -->
τ
<!-- tex4ht_end mini_ker_tex4ht_math math 81 -->
@@ -270,13 +274,13 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 88 -->
τ
<!-- tex4ht_end mini_ker_tex4ht_math math 88 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 89 -->
τ
<!-- tex4ht_end mini_ker_tex4ht_math math 89 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 90 -->
τ
<!-- tex4ht_end mini_ker_tex4ht_math math 90 -->
-
<!-- tex4ht_begin mini_ker_tex4ht_math math 91 -->
g(τ)
<!-- tex4ht_end mini_ker_tex4ht_math math 91 -->
@@ -296,6 +300,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 96 -->
Ast
<!-- tex4ht_end mini_ker_tex4ht_math math 96 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 97 -->
U
<!-- tex4ht_end mini_ker_tex4ht_math math 97 -->
@@ -317,11 +322,11 @@
<!-- tex4ht_end mini_ker_tex4ht_math math 102 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 103 -->
w
-
<!-- tex4ht_end mini_ker_tex4ht_math math 103 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 104 -->
Φ
<!-- tex4ht_end mini_ker_tex4ht_math math 104 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 105 -->
t
<!-- tex4ht_end mini_ker_tex4ht_math math 105 -->
@@ -346,6 +351,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 112 -->
Φ
<!-- tex4ht_end mini_ker_tex4ht_math math 112 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 113 -->
Φ(t,0)
<!-- tex4ht_end mini_ker_tex4ht_math math 113 -->
Index: test/many_input_files/tex_t4ht_res/mini_ker_tex4ht_math.texi
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/many_input_files/tex_t4ht_res/mini_ker_tex4ht_math.texi,v
retrieving revision 1.1
retrieving revision 1.2
diff -u -b -r1.1 -r1.2
--- test/many_input_files/tex_t4ht_res/mini_ker_tex4ht_math.texi 1 Sep
2008 14:48:42 -0000 1.1
+++ test/many_input_files/tex_t4ht_res/mini_ker_tex4ht_math.texi 22 Oct
2009 20:23:23 -0000 1.2
@@ -2,802 +2,1030 @@
@setfilename mini_ker_tex4ht_math.info
@c Automatically generated
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 1 -->
@end verbatim
@math{\eta}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 1 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 2 -->
@end verbatim
@math{\varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 2 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 3 -->
@end verbatim
@math{t}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 3 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 4 -->
@end verbatim
@math{t + \delta t}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 4 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 5 -->
@end verbatim
@math{\delta \eta}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 5 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 6 -->
@end verbatim
@math{\eta}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 6 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 7 -->
@end verbatim
@math{\delta \varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 7 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 8 -->
@end verbatim
@math{\varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 8 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 9 -->
@end verbatim
@math{f}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 9 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 10 -->
@end verbatim
@math{g}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 10 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 11 -->
@end verbatim
@math{\delta t}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 11 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 12 -->
@end verbatim
@math{\delta \eta}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 12 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 13 -->
@end verbatim
@math{\delta \varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 13 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 14 -->
@end verbatim
@math{\delta \varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 14 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 15 -->
@end verbatim
@math{\delta \eta}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 15 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 16 -->
@end verbatim
@math{a}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 16 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 17 -->
@end verbatim
@math{c}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 17 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 18 -->
@end verbatim
@math{\varphi_{meet}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 18 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 19 -->
@end verbatim
@math{\eta_{prey}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 19 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 20 -->
@end verbatim
@math{\eta_{pred}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 20 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 21 -->
@end verbatim
@math{\varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 21 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 22 -->
@end verbatim
@math{\delta\eta}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 22 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 23 -->
@end verbatim
@math{\varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 23 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 24 -->
@end verbatim
@math{\varphi=f(\eta(t-dt)+d\varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 24 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 25 -->
@end verbatim
@math{d\varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 25 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 26 -->
@end verbatim
@math{\varphi=f(\eta),\varphi)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 26 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 27 -->
@end verbatim
@math{10^{-3}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 27 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 28 -->
@end verbatim
@math{(I-D)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 28 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 29 -->
@end verbatim
@math{(I-D)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 29 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 30 -->
@end verbatim
@math{(I-D)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 30 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 31 -->
@end verbatim
@math{k}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 31 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 32 -->
@end verbatim
@math{m_k}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 32 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 33 -->
@end verbatim
@math{k}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 33 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 34 -->
@end verbatim
@math{r_k}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 34 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 35 -->
@end verbatim
@math{d_k}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 35 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 36 -->
@end verbatim
@math{N}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 36 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 37 -->
@end verbatim
@math{N}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 37 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 38 -->
@end verbatim
@math{N+1}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 38 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 39 -->
@end verbatim
@math{N+1}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 39 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 40 -->
@end verbatim
@math{k}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 40 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 41 -->
@end verbatim
@math{k}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 41 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 42 -->
@end verbatim
@math{x/\Delta}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 42 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 43 -->
@end verbatim
@math{\omega}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 43 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 44 -->
@end verbatim
@math{h}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 44 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 45 -->
@end verbatim
@math{\varphi_{meet}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 45 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 46 -->
@end verbatim
@math{\eta_{prey}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 46 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 47 -->
@end verbatim
@math{\eta_{pred}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 47 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 48 -->
@end verbatim
@math{\eta_1(t)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 48 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 49 -->
@end verbatim
@math{\eta_1(t=0)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 49 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 50 -->
@end verbatim
@math{t=0}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 50 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 51 -->
@end verbatim
@math{\phi_{j}(t)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 51 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 52 -->
@end verbatim
@math{\eta_i(t=0)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 52 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 53 -->
@end verbatim
@math{h(t)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 53 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 54 -->
@end verbatim
@math{J}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 54 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 55 -->
@end verbatim
@math{T}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 55 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 56 -->
@end verbatim
@math{J}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 56 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 57 -->
@end verbatim
@math{\psi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 57 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 58 -->
@end verbatim
@math{l}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 58 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 59 -->
@end verbatim
@math{h}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 59 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 60 -->
@end verbatim
@math{J}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 60 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 61 -->
@end verbatim
@math{t=0}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 61 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 62 -->
@end verbatim
@math{\omega}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 62 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 63 -->
@end verbatim
@math{t=s_i}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 63 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 64 -->
@end verbatim
@math{\mu}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 64 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 65 -->
@end verbatim
@math{Q}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 65 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 66 -->
@end verbatim
@math{\nu}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 66 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 67 -->
@end verbatim
@math{R}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 67 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 68 -->
@end verbatim
@math{W}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 68 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 69 -->
@end verbatim
@math{W}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 69 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 70 -->
@end verbatim
@math{W}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 70 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 71 -->
@end verbatim
@math{g(\tau)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 71 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 72 -->
@end verbatim
@math{g(\tau)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 72 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 73 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 73 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 74 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 74 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 75 -->
@end verbatim
@math{g(\tau;t)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 75 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 76 -->
@end verbatim
@math{t}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 76 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 77 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 77 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 78 -->
@end verbatim
@math{2}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 78 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 79 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 79 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 80 -->
@end verbatim
@math{g(\tau;t)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 80 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 81 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 81 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 82 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 82 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 83 -->
@end verbatim
@math{tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 83 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 84 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 84 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 85 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 85 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 86 -->
@end verbatim
@math{0.2}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 86 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 87 -->
@end verbatim
@math{\sqrt{\sqrt{2}}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 87 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 88 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 88 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 89 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 89 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 90 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 90 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 91 -->
@end verbatim
@math{g(\tau)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 91 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 92 -->
@end verbatim
@math{g(t,\tau)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 92 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 93 -->
@end verbatim
@math{A_{st}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 93 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 94 -->
@end verbatim
@math{A_{st}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 94 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 95 -->
@end verbatim
@math{A_{st} + A_{st}^\dagger}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 95 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 96 -->
@end verbatim
@math{A_{st}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 96 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 97 -->
@end verbatim
@math{U}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 97 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 98 -->
@end verbatim
@math{w}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 98 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 99 -->
@end verbatim
@math{V}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 99 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 100 -->
@end verbatim
@math{A_{st} + A_{st}^\dagger}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 100 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 101 -->
@end verbatim
@math{A_{st}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 101 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 102 -->
@end verbatim
@math{\Phi(t+\delta t,t)=\exp{A_{st} \delta t}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 102 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 103 -->
@end verbatim
@math{w}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 103 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 104 -->
@end verbatim
@math{\Phi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 104 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 105 -->
@end verbatim
@math{t}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 105 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 106 -->
@end verbatim
@math{\Phi(t,0)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 106 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 107 -->
@end verbatim
@math{U}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 107 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 108 -->
@end verbatim
@math{\Phi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 108 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 109 -->
@end verbatim
@math{w}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 109 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 110 -->
@end verbatim
@math{\Phi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 110 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 111 -->
@end verbatim
@math{V}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 111 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 112 -->
@end verbatim
@math{\Phi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 112 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 113 -->
@end verbatim
@math{\Phi(t,0)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 113 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 114 -->
@end verbatim
@math{\Phi(t,0)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 114 -->
+
@end verbatim
@bye
Index: test/many_input_files/tex_t4ht_res/mini_ker_tex4ht_tex.tex
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/many_input_files/tex_t4ht_res/mini_ker_tex4ht_tex.tex,v
retrieving revision 1.1
retrieving revision 1.2
diff -u -b -r1.1 -r1.2
--- test/many_input_files/tex_t4ht_res/mini_ker_tex4ht_tex.tex 1 Sep 2008
14:48:43 -0000 1.1
+++ test/many_input_files/tex_t4ht_res/mini_ker_tex4ht_tex.tex 22 Oct 2009
20:23:23 -0000 1.2
@@ -1,48 +1,48 @@
% Automatically generated
\csname tex4ht\endcsname
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 1 -->\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 1
-->\Hnewline}
$$\partial_t \eta (t) = g(\eta(t),\varphi(t))$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 1 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 2 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 1 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 2
-->\Hnewline}
$$
\varphi(t) = f(\eta(t),\varphi(t))
$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 2 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 3 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 2 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 3
-->\Hnewline}
$$\pmatrix{A & B\cr
-C^+ & I-D\cr} \pmatrix{\delta \eta\cr
\delta \varphi\cr} = \pmatrix{\Gamma\cr
\Omega\cr}$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 3 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 4 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 3 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 4
-->\Hnewline}
$$\eqalign{\partial_t \eta (t) &= g(\eta(t),\varphi(t))\cr
\varphi(t) &= f(\eta(t),\varphi(t))\cr
}$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 4 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 5 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 4 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 5
-->\Hnewline}
$$\left\{\eqalign{\partial_t \eta _{prey} &= a \eta _{prey} - a \varphi
_{meet} \cr
\partial_t \eta _{pred} &= -c \eta _{pred} + c \varphi _{meet}\cr}\right.$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 5 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 6 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 5 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 6
-->\Hnewline}
$$\varphi _{meet} = \eta _{prey}\eta _{pred}$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 6 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 7 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 6 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 7
-->\Hnewline}
$$\partial_{\eta} g(\eta(t),\varphi(t));
$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 7 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 8 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 7 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 8
-->\Hnewline}
$$\partial_{\varphi} g(\eta(t),\varphi(t));
$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 8 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 9 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 8 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 9
-->\Hnewline}
$$\partial_{\eta} f(\eta(t),\varphi(t));
$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 9 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 10 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 9 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 10
-->\Hnewline}
$$\partial_{\varphi} f(\eta(t),\varphi(t));
$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 10 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 11 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 10 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 11
-->\Hnewline}
$$\left\{\eqalign{\partial_t \eta _{k} ^{pos} &= \eta _{k} ^{vel} \cr
\partial_t \eta _{k} ^{vel} &= ( \varphi_k ^{spr} -\varphi _{k+1} ^{spr} +
\varphi _{k} ^{dmp}-\varphi _{k+1} ^{dmp})\,/m_k \cr}\right.$$
$$\left\{\eqalign{
@@ -53,29 +53,29 @@
\eta ^{vel}_{0} &= 0\cr
\varphi ^{spr}_{N+1} &= 0\cr
\varphi ^{dmp}_{N+1} &= 0\cr}\right.$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 11 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 12 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 11 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 12
-->\Hnewline}
$$\eqalign{\partial_x f^g &= g f^{g-1}\partial_x f + f^g \log f\partial_x g\cr
&= f^{g-1}(g\partial_x f + f\partial_x g)\cr}$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 12 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 13 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 12 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 13
-->\Hnewline}
$$
\omega = h ( \eta , \varphi)
$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 13 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 14 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 13 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 14
-->\Hnewline}
$$
J = \psi[\eta(T),\varphi(T) ,h(T)] + \int_0 ^T
{l[\eta(\tau),\varphi(\tau),h(\tau)]}\, d\tau
$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 14 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 15 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 14 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 15
-->\Hnewline}
$$\eqalign{
\partial_t \eta (t) &= g(\eta(t),\varphi(t)) + W(t) \mu\cr
\varphi(t) &= f(\eta(t),\varphi(t))\cr
\omega(t) &= h ( \eta(t) , \varphi(t)) + \nu\cr
}$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 15 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 16 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 15 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 16
-->\Hnewline}
$$\left\{\eqalign{
\partial_t \eta_1 &= a_{11} \eta_1 + a_{12} \varphi_2 + a_{13} \varphi_3 +
W_{11} \mu_1 + W_{12} \mu_2\cr
\partial_t \eta_2 &= a_{21} \varphi_1 + a_{22} \eta_2 + a_{23} \varphi_3 +
W_{21} \mu_1 + W_{22} \mu_2\cr
@@ -91,11 +91,11 @@
\omega _2 &= \eta _2 + \nu_2 \cr
\omega _3 &= \eta _3 + \nu_3
}\right.$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 16 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 17 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 16 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 17
-->\Hnewline}
$$
U w V^\dagger
$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 17 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 17 -->\Hnewline
\Hnewline}
\bye
Index: test/many_input_files/tex_t4ht_res/tex_tex4ht_math.texi
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/many_input_files/tex_t4ht_res/tex_tex4ht_math.texi,v
retrieving revision 1.1
retrieving revision 1.2
diff -u -b -r1.1 -r1.2
--- test/many_input_files/tex_t4ht_res/tex_tex4ht_math.texi 1 Sep 2008
14:48:45 -0000 1.1
+++ test/many_input_files/tex_t4ht_res/tex_tex4ht_math.texi 22 Oct 2009
20:23:23 -0000 1.2
@@ -2,32 +2,40 @@
@setfilename tex_tex4ht_math.info
@c Automatically generated
@verbatim
+
<!-- tex4ht_begin tex_tex4ht_math math 1 -->
@end verbatim
@math{{x^i}\over{\tan y}}
@verbatim
<!-- tex4ht_end tex_tex4ht_math math 1 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin tex_tex4ht_math math 2 -->
@end verbatim
@math{a @\ b}
@verbatim
<!-- tex4ht_end tex_tex4ht_math math 2 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin tex_tex4ht_math math 3 -->
@end verbatim
@address@hidden code}}
@verbatim
<!-- tex4ht_end tex_tex4ht_math math 3 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin tex_tex4ht_math math 4 -->
@end verbatim
@math{ address@hidden \hbox{ code }}} \sum_{i}{\underline{f}}}
@verbatim
<!-- tex4ht_end tex_tex4ht_math math 4 -->
+
@end verbatim
@bye
Index: test/many_input_files/tex_t4ht_res/tex_tex4ht_tex.tex
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/many_input_files/tex_t4ht_res/tex_tex4ht_tex.tex,v
retrieving revision 1.1
retrieving revision 1.2
diff -u -b -r1.1 -r1.2
--- test/many_input_files/tex_t4ht_res/tex_tex4ht_tex.tex 1 Sep 2008
14:48:45 -0000 1.1
+++ test/many_input_files/tex_t4ht_res/tex_tex4ht_tex.tex 22 Oct 2009
20:23:23 -0000 1.2
@@ -1,6 +1,6 @@
% Automatically generated
\csname tex4ht\endcsname
-\HCode{\Hnewline <!-- tex4ht_begin tex_tex4ht_tex tex 1 -->\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin tex_tex4ht_tex tex 1 -->\Hnewline}
some
$$ \chi^2 = \sum_{i=1}^N
@@ -8,11 +8,11 @@
\over \sigma_i\right)^2 $$
-\HCode{\Hnewline <!-- tex4ht_end tex_tex4ht_tex tex 1 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin tex_tex4ht_tex tex 2 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end tex_tex4ht_tex tex 1 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin tex_tex4ht_tex tex 2 -->\Hnewline}
some
tex \TeX
-\HCode{\Hnewline <!-- tex4ht_end tex_tex4ht_tex tex 2 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end tex_tex4ht_tex tex 2 -->\Hnewline \Hnewline}
\bye
Index: test/misc/res/mini_ker_httex/mini_ker.html
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/misc/res/mini_ker_httex/mini_ker.html,v
retrieving revision 1.23
retrieving revision 1.24
diff -u -b -r1.23 -r1.24
--- test/misc/res/mini_ker_httex/mini_ker.html 6 Oct 2009 13:36:23 -0000
1.23
+++ test/misc/res/mini_ker_httex/mini_ker.html 22 Oct 2009 20:23:23 -0000
1.24
@@ -406,7 +406,6 @@
of f and g, and with δt. From this system the
elimination of δη leads to another formulation giving
the coupling between transfers, and allows for the δφ
-
computation. The δφ value is then substitued in
δη to complete the time-step solving process.
</p>
@@ -1314,8 +1313,7 @@
on a pseudo relative quadratic residual between
φ = f(η(t - dt) + dφ (<code> ffl</code>), where
dφ
is given by the system resolution in <code>ker</code>,and
- φ = f(η),φ)
-, Fortran variable (<code>ff</code>):
+ φ = f(η),φ), Fortran variable (<code>ff</code>):
</p>
<pre class="verbatim">!
========================================================
! test linearite ffl - ff
@@ -1752,8 +1750,7 @@
in the grid, from 1 to N, and two nodes outside of the grid,
a limiting node 0, and a limiting node N + 1. The limiting node
corresponding with node 0 is called the <em>down</em> node, while the limiting
-node corresponding with node N + 1
- is called the <em>up</em> node.
+node corresponding with node N + 1 is called the <em>up</em> node.
Other models not part of the 1D grid may be added if any.
</p>
<p>To enable 1D gridded models, one should set the select flag
‘<samp>grid1d</samp>’.
@@ -2930,8 +2927,7 @@
of the number of predators.
</p>
<p>In the same way, the <var>j+1</var>th column of
‘<tt>sigma.data</tt>’ will be the
-derivative of ϕj(t) with respect to ηi(t = 0)
-. Here:
+derivative of ϕj(t) with respect to ηi(t = 0). Here:
</p><table><tr><td> </td><td><pre class="example"># Sensy_to: eta_pray
eta_pred
# time \\ of: ff_interact ff_interact
0.00000E+00 1.60683E+00 8.47076E-01
@@ -3393,8 +3389,7 @@
<p>The observations ω are available at discrete time steps
t = si. The
stochastic perturbation on state, μ is characterized by a
-variance-covariance matrix Q
- and the noise on the observation,
+variance-covariance matrix Q and the noise on the observation,
ν has a variance-covariance matrix R. W relates states
with stochastic perturbations. At each time step the Kalman filter recomputes
an estimation of the state and the variance-covariance matrix of the state.
@@ -3849,8 +3844,7 @@
scheme for the time discretisation
symbolically gives the solution of the Borel transform of the system. One can
identify the <code>dt</code> variable with the Borel τ within a
-factor 2
-. Hence, to numerically study the τ dependency of
+factor 2. Hence, to numerically study the τ dependency of
the transform of various coefficients in the system coupling matrix at one
point in time, one can calculate the Borel transform of the TLS solutions
by making a time-step sweep.
Index: test/misc/res/mini_ker_httex/mini_ker_tex4ht_math.html
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/misc/res/mini_ker_httex/mini_ker_tex4ht_math.html,v
retrieving revision 1.1
retrieving revision 1.2
diff -u -b -r1.1 -r1.2
--- test/misc/res/mini_ker_httex/mini_ker_tex4ht_math.html 1 Sep 2008
14:48:47 -0000 1.1
+++ test/misc/res/mini_ker_httex/mini_ker_tex4ht_math.html 22 Oct 2009
20:23:23 -0000 1.2
@@ -22,6 +22,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 8 -->
φ
<!-- tex4ht_end mini_ker_tex4ht_math math 8 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 9 -->
f
<!-- tex4ht_end mini_ker_tex4ht_math math 9 -->
@@ -36,7 +37,6 @@
<!-- tex4ht_end mini_ker_tex4ht_math math 12 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 13 -->
δφ
-
<!-- tex4ht_end mini_ker_tex4ht_math math 13 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 14 -->
δφ
@@ -47,6 +47,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 16 -->
a
<!-- tex4ht_end mini_ker_tex4ht_math math 16 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 17 -->
c
<!-- tex4ht_end mini_ker_tex4ht_math math 17 -->
@@ -71,12 +72,12 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 24 -->
φ = f(η(t - dt) + dφ
<!-- tex4ht_end mini_ker_tex4ht_math math 24 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 25 -->
dφ
<!-- tex4ht_end mini_ker_tex4ht_math math 25 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 26 -->
φ = f(η),φ)
-
<!-- tex4ht_end mini_ker_tex4ht_math math 26 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 27 -->
10-3
@@ -96,6 +97,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 32 -->
mk
<!-- tex4ht_end mini_ker_tex4ht_math math 32 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 33 -->
k
<!-- tex4ht_end mini_ker_tex4ht_math math 33 -->
@@ -116,11 +118,11 @@
<!-- tex4ht_end mini_ker_tex4ht_math math 38 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 39 -->
N + 1
-
<!-- tex4ht_end mini_ker_tex4ht_math math 39 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 40 -->
k
<!-- tex4ht_end mini_ker_tex4ht_math math 40 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 41 -->
k
<!-- tex4ht_end mini_ker_tex4ht_math math 41 -->
@@ -145,6 +147,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 48 -->
η1(t)
<!-- tex4ht_end mini_ker_tex4ht_math math 48 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 49 -->
η1(t = 0)
<!-- tex4ht_end mini_ker_tex4ht_math math 49 -->
@@ -156,7 +159,6 @@
<!-- tex4ht_end mini_ker_tex4ht_math math 51 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 52 -->
ηi(t = 0)
-
<!-- tex4ht_end mini_ker_tex4ht_math math 52 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 53 -->
h(t)
@@ -170,6 +172,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 56 -->
J
<!-- tex4ht_end mini_ker_tex4ht_math math 56 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 57 -->
ψ
<!-- tex4ht_end mini_ker_tex4ht_math math 57 -->
@@ -194,9 +197,9 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 64 -->
μ
<!-- tex4ht_end mini_ker_tex4ht_math math 64 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 65 -->
Q
-
<!-- tex4ht_end mini_ker_tex4ht_math math 65 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 66 -->
ν
@@ -219,6 +222,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 72 -->
g(τ)
<!-- tex4ht_end mini_ker_tex4ht_math math 72 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 73 -->
τ
<!-- tex4ht_end mini_ker_tex4ht_math math 73 -->
@@ -236,7 +240,6 @@
<!-- tex4ht_end mini_ker_tex4ht_math math 77 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 78 -->
2
-
<!-- tex4ht_end mini_ker_tex4ht_math math 78 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 79 -->
τ
@@ -244,6 +247,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 80 -->
g(τ;t)
<!-- tex4ht_end mini_ker_tex4ht_math math 80 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 81 -->
τ
<!-- tex4ht_end mini_ker_tex4ht_math math 81 -->
@@ -270,13 +274,13 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 88 -->
τ
<!-- tex4ht_end mini_ker_tex4ht_math math 88 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 89 -->
τ
<!-- tex4ht_end mini_ker_tex4ht_math math 89 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 90 -->
τ
<!-- tex4ht_end mini_ker_tex4ht_math math 90 -->
-
<!-- tex4ht_begin mini_ker_tex4ht_math math 91 -->
g(τ)
<!-- tex4ht_end mini_ker_tex4ht_math math 91 -->
@@ -296,6 +300,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 96 -->
Ast
<!-- tex4ht_end mini_ker_tex4ht_math math 96 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 97 -->
U
<!-- tex4ht_end mini_ker_tex4ht_math math 97 -->
@@ -317,11 +322,11 @@
<!-- tex4ht_end mini_ker_tex4ht_math math 102 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 103 -->
w
-
<!-- tex4ht_end mini_ker_tex4ht_math math 103 -->
<!-- tex4ht_begin mini_ker_tex4ht_math math 104 -->
Φ
<!-- tex4ht_end mini_ker_tex4ht_math math 104 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 105 -->
t
<!-- tex4ht_end mini_ker_tex4ht_math math 105 -->
@@ -346,6 +351,7 @@
<!-- tex4ht_begin mini_ker_tex4ht_math math 112 -->
Φ
<!-- tex4ht_end mini_ker_tex4ht_math math 112 -->
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 113 -->
Φ(t,0)
<!-- tex4ht_end mini_ker_tex4ht_math math 113 -->
Index: test/misc/res/mini_ker_httex/mini_ker_tex4ht_math.texi
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/misc/res/mini_ker_httex/mini_ker_tex4ht_math.texi,v
retrieving revision 1.1
retrieving revision 1.2
diff -u -b -r1.1 -r1.2
--- test/misc/res/mini_ker_httex/mini_ker_tex4ht_math.texi 1 Sep 2008
14:48:48 -0000 1.1
+++ test/misc/res/mini_ker_httex/mini_ker_tex4ht_math.texi 22 Oct 2009
20:23:23 -0000 1.2
@@ -2,802 +2,1030 @@
@setfilename mini_ker_tex4ht_math.info
@c Automatically generated
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 1 -->
@end verbatim
@math{\eta}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 1 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 2 -->
@end verbatim
@math{\varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 2 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 3 -->
@end verbatim
@math{t}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 3 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 4 -->
@end verbatim
@math{t + \delta t}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 4 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 5 -->
@end verbatim
@math{\delta \eta}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 5 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 6 -->
@end verbatim
@math{\eta}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 6 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 7 -->
@end verbatim
@math{\delta \varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 7 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 8 -->
@end verbatim
@math{\varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 8 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 9 -->
@end verbatim
@math{f}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 9 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 10 -->
@end verbatim
@math{g}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 10 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 11 -->
@end verbatim
@math{\delta t}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 11 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 12 -->
@end verbatim
@math{\delta \eta}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 12 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 13 -->
@end verbatim
@math{\delta \varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 13 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 14 -->
@end verbatim
@math{\delta \varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 14 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 15 -->
@end verbatim
@math{\delta \eta}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 15 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 16 -->
@end verbatim
@math{a}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 16 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 17 -->
@end verbatim
@math{c}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 17 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 18 -->
@end verbatim
@math{\varphi_{meet}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 18 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 19 -->
@end verbatim
@math{\eta_{prey}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 19 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 20 -->
@end verbatim
@math{\eta_{pred}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 20 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 21 -->
@end verbatim
@math{\varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 21 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 22 -->
@end verbatim
@math{\delta\eta}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 22 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 23 -->
@end verbatim
@math{\varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 23 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 24 -->
@end verbatim
@math{\varphi=f(\eta(t-dt)+d\varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 24 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 25 -->
@end verbatim
@math{d\varphi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 25 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 26 -->
@end verbatim
@math{\varphi=f(\eta),\varphi)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 26 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 27 -->
@end verbatim
@math{10^{-3}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 27 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 28 -->
@end verbatim
@math{(I-D)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 28 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 29 -->
@end verbatim
@math{(I-D)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 29 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 30 -->
@end verbatim
@math{(I-D)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 30 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 31 -->
@end verbatim
@math{k}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 31 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 32 -->
@end verbatim
@math{m_k}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 32 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 33 -->
@end verbatim
@math{k}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 33 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 34 -->
@end verbatim
@math{r_k}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 34 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 35 -->
@end verbatim
@math{d_k}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 35 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 36 -->
@end verbatim
@math{N}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 36 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 37 -->
@end verbatim
@math{N}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 37 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 38 -->
@end verbatim
@math{N+1}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 38 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 39 -->
@end verbatim
@math{N+1}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 39 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 40 -->
@end verbatim
@math{k}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 40 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 41 -->
@end verbatim
@math{k}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 41 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 42 -->
@end verbatim
@math{x/\Delta}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 42 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 43 -->
@end verbatim
@math{\omega}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 43 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 44 -->
@end verbatim
@math{h}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 44 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 45 -->
@end verbatim
@math{\varphi_{meet}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 45 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 46 -->
@end verbatim
@math{\eta_{prey}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 46 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 47 -->
@end verbatim
@math{\eta_{pred}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 47 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 48 -->
@end verbatim
@math{\eta_1(t)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 48 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 49 -->
@end verbatim
@math{\eta_1(t=0)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 49 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 50 -->
@end verbatim
@math{t=0}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 50 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 51 -->
@end verbatim
@math{\phi_{j}(t)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 51 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 52 -->
@end verbatim
@math{\eta_i(t=0)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 52 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 53 -->
@end verbatim
@math{h(t)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 53 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 54 -->
@end verbatim
@math{J}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 54 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 55 -->
@end verbatim
@math{T}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 55 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 56 -->
@end verbatim
@math{J}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 56 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 57 -->
@end verbatim
@math{\psi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 57 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 58 -->
@end verbatim
@math{l}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 58 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 59 -->
@end verbatim
@math{h}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 59 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 60 -->
@end verbatim
@math{J}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 60 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 61 -->
@end verbatim
@math{t=0}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 61 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 62 -->
@end verbatim
@math{\omega}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 62 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 63 -->
@end verbatim
@math{t=s_i}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 63 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 64 -->
@end verbatim
@math{\mu}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 64 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 65 -->
@end verbatim
@math{Q}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 65 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 66 -->
@end verbatim
@math{\nu}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 66 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 67 -->
@end verbatim
@math{R}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 67 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 68 -->
@end verbatim
@math{W}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 68 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 69 -->
@end verbatim
@math{W}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 69 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 70 -->
@end verbatim
@math{W}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 70 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 71 -->
@end verbatim
@math{g(\tau)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 71 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 72 -->
@end verbatim
@math{g(\tau)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 72 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 73 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 73 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 74 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 74 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 75 -->
@end verbatim
@math{g(\tau;t)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 75 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 76 -->
@end verbatim
@math{t}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 76 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 77 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 77 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 78 -->
@end verbatim
@math{2}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 78 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 79 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 79 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 80 -->
@end verbatim
@math{g(\tau;t)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 80 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 81 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 81 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 82 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 82 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 83 -->
@end verbatim
@math{tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 83 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 84 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 84 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 85 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 85 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 86 -->
@end verbatim
@math{0.2}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 86 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 87 -->
@end verbatim
@math{\sqrt{\sqrt{2}}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 87 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 88 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 88 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 89 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 89 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 90 -->
@end verbatim
@math{\tau}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 90 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 91 -->
@end verbatim
@math{g(\tau)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 91 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 92 -->
@end verbatim
@math{g(t,\tau)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 92 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 93 -->
@end verbatim
@math{A_{st}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 93 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 94 -->
@end verbatim
@math{A_{st}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 94 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 95 -->
@end verbatim
@math{A_{st} + A_{st}^\dagger}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 95 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 96 -->
@end verbatim
@math{A_{st}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 96 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 97 -->
@end verbatim
@math{U}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 97 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 98 -->
@end verbatim
@math{w}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 98 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 99 -->
@end verbatim
@math{V}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 99 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 100 -->
@end verbatim
@math{A_{st} + A_{st}^\dagger}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 100 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 101 -->
@end verbatim
@math{A_{st}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 101 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 102 -->
@end verbatim
@math{\Phi(t+\delta t,t)=\exp{A_{st} \delta t}}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 102 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 103 -->
@end verbatim
@math{w}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 103 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 104 -->
@end verbatim
@math{\Phi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 104 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 105 -->
@end verbatim
@math{t}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 105 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 106 -->
@end verbatim
@math{\Phi(t,0)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 106 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 107 -->
@end verbatim
@math{U}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 107 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 108 -->
@end verbatim
@math{\Phi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 108 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 109 -->
@end verbatim
@math{w}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 109 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 110 -->
@end verbatim
@math{\Phi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 110 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 111 -->
@end verbatim
@math{V}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 111 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 112 -->
@end verbatim
@math{\Phi}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 112 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 113 -->
@end verbatim
@math{\Phi(t,0)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 113 -->
+
@end verbatim
@verbatim
+
<!-- tex4ht_begin mini_ker_tex4ht_math math 114 -->
@end verbatim
@math{\Phi(t,0)}
@verbatim
<!-- tex4ht_end mini_ker_tex4ht_math math 114 -->
+
@end verbatim
@bye
Index: test/misc/res/mini_ker_httex/mini_ker_tex4ht_tex.tex
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/misc/res/mini_ker_httex/mini_ker_tex4ht_tex.tex,v
retrieving revision 1.1
retrieving revision 1.2
diff -u -b -r1.1 -r1.2
--- test/misc/res/mini_ker_httex/mini_ker_tex4ht_tex.tex 1 Sep 2008
14:48:49 -0000 1.1
+++ test/misc/res/mini_ker_httex/mini_ker_tex4ht_tex.tex 22 Oct 2009
20:23:23 -0000 1.2
@@ -1,48 +1,48 @@
% Automatically generated
\csname tex4ht\endcsname
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 1 -->\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 1
-->\Hnewline}
$$\partial_t \eta (t) = g(\eta(t),\varphi(t))$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 1 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 2 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 1 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 2
-->\Hnewline}
$$
\varphi(t) = f(\eta(t),\varphi(t))
$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 2 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 3 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 2 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 3
-->\Hnewline}
$$\pmatrix{A & B\cr
-C^+ & I-D\cr} \pmatrix{\delta \eta\cr
\delta \varphi\cr} = \pmatrix{\Gamma\cr
\Omega\cr}$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 3 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 4 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 3 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 4
-->\Hnewline}
$$\eqalign{\partial_t \eta (t) &= g(\eta(t),\varphi(t))\cr
\varphi(t) &= f(\eta(t),\varphi(t))\cr
}$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 4 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 5 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 4 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 5
-->\Hnewline}
$$\left\{\eqalign{\partial_t \eta _{prey} &= a \eta _{prey} - a \varphi
_{meet} \cr
\partial_t \eta _{pred} &= -c \eta _{pred} + c \varphi _{meet}\cr}\right.$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 5 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 6 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 5 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 6
-->\Hnewline}
$$\varphi _{meet} = \eta _{prey}\eta _{pred}$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 6 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 7 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 6 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 7
-->\Hnewline}
$$\partial_{\eta} g(\eta(t),\varphi(t));
$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 7 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 8 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 7 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 8
-->\Hnewline}
$$\partial_{\varphi} g(\eta(t),\varphi(t));
$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 8 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 9 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 8 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 9
-->\Hnewline}
$$\partial_{\eta} f(\eta(t),\varphi(t));
$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 9 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 10 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 9 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 10
-->\Hnewline}
$$\partial_{\varphi} f(\eta(t),\varphi(t));
$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 10 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 11 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 10 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 11
-->\Hnewline}
$$\left\{\eqalign{\partial_t \eta _{k} ^{pos} &= \eta _{k} ^{vel} \cr
\partial_t \eta _{k} ^{vel} &= ( \varphi_k ^{spr} -\varphi _{k+1} ^{spr} +
\varphi _{k} ^{dmp}-\varphi _{k+1} ^{dmp})\,/m_k \cr}\right.$$
$$\left\{\eqalign{
@@ -53,29 +53,29 @@
\eta ^{vel}_{0} &= 0\cr
\varphi ^{spr}_{N+1} &= 0\cr
\varphi ^{dmp}_{N+1} &= 0\cr}\right.$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 11 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 12 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 11 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 12
-->\Hnewline}
$$\eqalign{\partial_x f^g &= g f^{g-1}\partial_x f + f^g \log f\partial_x g\cr
&= f^{g-1}(g\partial_x f + f\partial_x g)\cr}$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 12 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 13 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 12 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 13
-->\Hnewline}
$$
\omega = h ( \eta , \varphi)
$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 13 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 14 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 13 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 14
-->\Hnewline}
$$
J = \psi[\eta(T),\varphi(T) ,h(T)] + \int_0 ^T
{l[\eta(\tau),\varphi(\tau),h(\tau)]}\, d\tau
$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 14 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 15 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 14 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 15
-->\Hnewline}
$$\eqalign{
\partial_t \eta (t) &= g(\eta(t),\varphi(t)) + W(t) \mu\cr
\varphi(t) &= f(\eta(t),\varphi(t))\cr
\omega(t) &= h ( \eta(t) , \varphi(t)) + \nu\cr
}$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 15 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 16 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 15 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 16
-->\Hnewline}
$$\left\{\eqalign{
\partial_t \eta_1 &= a_{11} \eta_1 + a_{12} \varphi_2 + a_{13} \varphi_3 +
W_{11} \mu_1 + W_{12} \mu_2\cr
\partial_t \eta_2 &= a_{21} \varphi_1 + a_{22} \eta_2 + a_{23} \varphi_3 +
W_{21} \mu_1 + W_{22} \mu_2\cr
@@ -91,11 +91,11 @@
\omega _2 &= \eta _2 + \nu_2 \cr
\omega _3 &= \eta _3 + \nu_3
}\right.$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 16 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 17 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 16 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin mini_ker_tex4ht_tex tex 17
-->\Hnewline}
$$
U w V^\dagger
$$
-\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 17 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end mini_ker_tex4ht_tex tex 17 -->\Hnewline
\Hnewline}
\bye
Index: test/misc/res/mini_ker_l2h/mini_ker_l2h.tex
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/misc/res/mini_ker_l2h/mini_ker_l2h.tex,v
retrieving revision 1.1
retrieving revision 1.2
diff -u -b -r1.1 -r1.2
--- test/misc/res/mini_ker_l2h/mini_ker_l2h.tex 1 Sep 2008 14:48:50 -0000
1.1
+++ test/misc/res/mini_ker_l2h/mini_ker_l2h.tex 22 Oct 2009 20:23:23 -0000
1.2
@@ -4,27 +4,34 @@
\usepackage{html}
\begin{document}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 1 -->
\end{rawhtml}
$$\partial_t \eta (t) = g(\eta(t),\varphi(t))$$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 1 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 2 -->
\end{rawhtml}
$\eta$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 2 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 3 -->
\end{rawhtml}
$\varphi$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 3 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 4 -->
\end{rawhtml}
$$
@@ -32,36 +39,46 @@
$$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 4 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 5 -->
\end{rawhtml}
$t$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 5 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 6 -->
\end{rawhtml}
$t + \delta t$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 6 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 7 -->
\end{rawhtml}
$\delta \eta$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 7 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 8 -->
\end{rawhtml}
$\delta \varphi$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 8 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 9 -->
\end{rawhtml}
$$\pmatrix{A & B\cr
@@ -70,29 +87,37 @@
\Omega\cr}$$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 9 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 10 -->
\end{rawhtml}
$f$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 10 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 11 -->
\end{rawhtml}
$g$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 11 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 12 -->
\end{rawhtml}
$\delta t$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 12 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 13 -->
\end{rawhtml}
$$\eqalign{\partial_t \eta (t) &= g(\eta(t),\varphi(t))\cr
@@ -100,139 +125,177 @@
}$$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 13 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 14 -->
\end{rawhtml}
$$\left\{\eqalign{\partial_t \eta _{prey} &= a \eta _{prey} - a \varphi
_{meet} \cr
\partial_t \eta _{pred} &= -c \eta _{pred} + c \varphi _{meet}\cr}\right.$$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 14 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 15 -->
\end{rawhtml}
$$\varphi _{meet} = \eta _{prey}\eta _{pred}$$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 15 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 16 -->
\end{rawhtml}
$a$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 16 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 17 -->
\end{rawhtml}
$c$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 17 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 18 -->
\end{rawhtml}
$\varphi_{meet}$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 18 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 19 -->
\end{rawhtml}
$\eta_{prey}$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 19 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 20 -->
\end{rawhtml}
$\eta_{pred}$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 20 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 21 -->
\end{rawhtml}
$\delta\eta$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 21 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 22 -->
\end{rawhtml}
$\varphi=f(\eta(t-dt)+d\varphi$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 22 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 23 -->
\end{rawhtml}
$d\varphi$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 23 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 24 -->
\end{rawhtml}
$\varphi=f(\eta),\varphi)$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 24 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 25 -->
\end{rawhtml}
$10^{-3}$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 25 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 26 -->
\end{rawhtml}
$$\partial_{\eta} g(\eta(t),\varphi(t));
$$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 26 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 27 -->
\end{rawhtml}
$$\partial_{\varphi} g(\eta(t),\varphi(t));
$$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 27 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 28 -->
\end{rawhtml}
$$\partial_{\eta} f(\eta(t),\varphi(t));
$$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 28 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 29 -->
\end{rawhtml}
$$\partial_{\varphi} f(\eta(t),\varphi(t));
$$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 29 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 30 -->
\end{rawhtml}
$(I-D)$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 30 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 31 -->
\end{rawhtml}
$k$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 31 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 32 -->
\end{rawhtml}
$$\left\{\eqalign{\partial_t \eta _{k} ^{pos} &= \eta _{k} ^{vel} \cr
@@ -247,72 +310,92 @@
\varphi ^{dmp}_{N+1} &= 0\cr}\right.$$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 32 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 33 -->
\end{rawhtml}
$m_k$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 33 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 34 -->
\end{rawhtml}
$r_k$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 34 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 35 -->
\end{rawhtml}
$d_k$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 35 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 36 -->
\end{rawhtml}
$N$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 36 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 37 -->
\end{rawhtml}
$N+1$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 37 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 38 -->
\end{rawhtml}
$$\eqalign{\partial_x f^g &= g f^{g-1}\partial_x f + f^g \log f\partial_x g\cr
&= f^{g-1}(g\partial_x f + f\partial_x g)\cr}$$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 38 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 39 -->
\end{rawhtml}
$x/\Delta$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 39 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 40 -->
\end{rawhtml}
$\omega$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 40 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 41 -->
\end{rawhtml}
$h$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 41 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 42 -->
\end{rawhtml}
$$
@@ -320,64 +403,82 @@
$$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 42 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 43 -->
\end{rawhtml}
$\eta_1(t)$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 43 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 44 -->
\end{rawhtml}
$\eta_1(t=0)$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 44 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 45 -->
\end{rawhtml}
$t=0$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 45 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 46 -->
\end{rawhtml}
$\phi_{j}(t)$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 46 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 47 -->
\end{rawhtml}
$\eta_i(t=0)$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 47 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 48 -->
\end{rawhtml}
$h(t)$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 48 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 49 -->
\end{rawhtml}
$J$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 49 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 50 -->
\end{rawhtml}
$T$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 50 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 51 -->
\end{rawhtml}
$$
@@ -385,22 +486,28 @@
$$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 51 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 52 -->
\end{rawhtml}
$\psi$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 52 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 53 -->
\end{rawhtml}
$l$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 53 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 54 -->
\end{rawhtml}
$$\eqalign{
@@ -410,50 +517,64 @@
}$$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 54 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 55 -->
\end{rawhtml}
$t=s_i$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 55 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 56 -->
\end{rawhtml}
$\mu$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 56 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 57 -->
\end{rawhtml}
$Q$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 57 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 58 -->
\end{rawhtml}
$\nu$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 58 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 59 -->
\end{rawhtml}
$R$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 59 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 60 -->
\end{rawhtml}
$W$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 60 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 61 -->
\end{rawhtml}
$$\left\{\eqalign{
@@ -473,78 +594,100 @@
}\right.$$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 61 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 62 -->
\end{rawhtml}
$g(\tau)$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 62 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 63 -->
\end{rawhtml}
$\tau$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 63 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 64 -->
\end{rawhtml}
$g(\tau;t)$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 64 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 65 -->
\end{rawhtml}
$2$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 65 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 66 -->
\end{rawhtml}
$tau$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 66 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 67 -->
\end{rawhtml}
$0.2$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 67 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 68 -->
\end{rawhtml}
$\sqrt{\sqrt{2}}$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 68 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 69 -->
\end{rawhtml}
$g(t,\tau)$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 69 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 70 -->
\end{rawhtml}
$A_{st}$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 70 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 71 -->
\end{rawhtml}
$A_{st} + A_{st}^\dagger$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 71 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 72 -->
\end{rawhtml}
$$
@@ -552,47 +695,60 @@
$$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 72 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 73 -->
\end{rawhtml}
$U$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 73 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 74 -->
\end{rawhtml}
$w$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 74 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 75 -->
\end{rawhtml}
$V$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 75 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 76 -->
\end{rawhtml}
$\Phi(t+\delta t,t)=\exp{A_{st} \delta t}$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 76 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 77 -->
\end{rawhtml}
$\Phi$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 77 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin mini_ker_l2h 78 -->
\end{rawhtml}
$\Phi(t,0)$
\begin{rawhtml}
<!-- l2h_end mini_ker_l2h 78 -->
+
\end{rawhtml}
\end{document}
Index: test/singular_manual/res/singular/sing_l2h.tex
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/singular_manual/res/singular/sing_l2h.tex,v
retrieving revision 1.1
retrieving revision 1.2
diff -u -b -r1.1 -r1.2
--- test/singular_manual/res/singular/sing_l2h.tex 18 Aug 2008 18:08:01
-0000 1.1
+++ test/singular_manual/res/singular/sing_l2h.tex 22 Oct 2009 20:23:23
-0000 1.2
@@ -4,510 +4,655 @@
\usepackage{html}
\begin{document}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 1 -->
\end{rawhtml}
H.\ Sch\"onemann; Humboldt-Universit\"at
\begin{rawhtml}
<!-- l2h_end sing_l2h 1 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 2 -->
\end{rawhtml}
$3 \times 3$
\begin{rawhtml}
<!-- l2h_end sing_l2h 2 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 3 -->
\end{rawhtml}
$0$
\begin{rawhtml}
<!-- l2h_end sing_l2h 3 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 4 -->
\end{rawhtml}
$Q$
\begin{rawhtml}
<!-- l2h_end sing_l2h 4 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 5 -->
\end{rawhtml}
$a$
\begin{rawhtml}
<!-- l2h_end sing_l2h 5 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 6 -->
\end{rawhtml}
$Z/32003[x,y,z]$
\begin{rawhtml}
<!-- l2h_end sing_l2h 6 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 7 -->
\end{rawhtml}
$x^3$
\begin{rawhtml}
<!-- l2h_end sing_l2h 7 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 8 -->
\end{rawhtml}
$K[x,y,z]/\hbox{\rm jacob}(f)$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 8 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 9 -->
\end{rawhtml}
$12-4=8$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 9 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 10 -->
\end{rawhtml}
$1 \times 1$-minors
\begin{rawhtml}
<!-- l2h_end sing_l2h 10 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 11 -->
\end{rawhtml}
$1 \times 1$-minors,
\begin{rawhtml}
<!-- l2h_end sing_l2h 11 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 12 -->
\end{rawhtml}
$MD$
\begin{rawhtml}
<!-- l2h_end sing_l2h 12 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 13 -->
\end{rawhtml}
$r^3/MD$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 13 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 14 -->
\end{rawhtml}
$M = r^3/U$,
\begin{rawhtml}
<!-- l2h_end sing_l2h 14 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 15 -->
\end{rawhtml}
$M$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 15 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 16 -->
\end{rawhtml}
$\hbox{ann}(M) = \{a \mid aM = 0 \}$
\begin{rawhtml}
<!-- l2h_end sing_l2h 16 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 17 -->
\end{rawhtml}
$\{ a \mid ar^3 \in U \}$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 17 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 18 -->
\end{rawhtml}
$U \colon r^3 $.
\begin{rawhtml}
<!-- l2h_end sing_l2h 18 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 19 -->
\end{rawhtml}
$n$
\begin{rawhtml}
<!-- l2h_end sing_l2h 19 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 20 -->
\end{rawhtml}
$n=0$
\begin{rawhtml}
<!-- l2h_end sing_l2h 20 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 21 -->
\end{rawhtml}
$R^5$
\begin{rawhtml}
<!-- l2h_end sing_l2h 21 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 22 -->
\end{rawhtml}
$(z^3,0,-y+4z,x+2z,0)$ and $(-xyz-y^2z-4xz^2+16z^3,-y^2,48z,48z,x+y-z)$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 22 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 23 -->
\end{rawhtml}
finite fields $Z/p$, $p$ a prime $\le 2147483629$,
\begin{rawhtml}
<!-- l2h_end sing_l2h 23 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 24 -->
\end{rawhtml}
finite fields $\hbox{GF}(p^n)$ with $p^n$ elements, $p$ a prime, $p^n \le
2^{15}$,
\begin{rawhtml}
<!-- l2h_end sing_l2h 24 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 25 -->
\end{rawhtml}
$Z/p$
\begin{rawhtml}
<!-- l2h_end sing_l2h 25 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 26 -->
\end{rawhtml}
$Q[a,b,c,d]$
\begin{rawhtml}
<!-- l2h_end sing_l2h 26 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 27 -->
\end{rawhtml}
$Z/7[x,y,z]$
\begin{rawhtml}
<!-- l2h_end sing_l2h 27 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 28 -->
\end{rawhtml}
$Z/7[x_1,\ldots,x_6]$
\begin{rawhtml}
<!-- l2h_end sing_l2h 28 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 29 -->
\end{rawhtml}
$x_1,x_2,x_3$
\begin{rawhtml}
<!-- l2h_end sing_l2h 29 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 30 -->
\end{rawhtml}
$x_4,x_5,x_6$:
\begin{rawhtml}
<!-- l2h_end sing_l2h 30 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 31 -->
\end{rawhtml}
$(Q[a,b,c])[x,y,z]$
\begin{rawhtml}
<!-- l2h_end sing_l2h 31 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 32 -->
\end{rawhtml}
$(x,y,z)$
\begin{rawhtml}
<!-- l2h_end sing_l2h 32 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 33 -->
\end{rawhtml}
$Q[x,y,z]$
\begin{rawhtml}
<!-- l2h_end sing_l2h 33 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 34 -->
\end{rawhtml}
$x$
\begin{rawhtml}
<!-- l2h_end sing_l2h 34 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 35 -->
\end{rawhtml}
$y$
\begin{rawhtml}
<!-- l2h_end sing_l2h 35 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 36 -->
\end{rawhtml}
$z$
\begin{rawhtml}
<!-- l2h_end sing_l2h 36 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 37 -->
\end{rawhtml}
$K[x,y,z]$
\begin{rawhtml}
<!-- l2h_end sing_l2h 37 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 38 -->
\end{rawhtml}
$K=Z/7(a,b,c)$
\begin{rawhtml}
<!-- l2h_end sing_l2h 38 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 39 -->
\end{rawhtml}
$Z/7$
\begin{rawhtml}
<!-- l2h_end sing_l2h 39 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 40 -->
\end{rawhtml}
$b$
\begin{rawhtml}
<!-- l2h_end sing_l2h 40 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 41 -->
\end{rawhtml}
$c$
\begin{rawhtml}
<!-- l2h_end sing_l2h 41 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 42 -->
\end{rawhtml}
$K=Z/7[a]$
\begin{rawhtml}
<!-- l2h_end sing_l2h 42 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 43 -->
\end{rawhtml}
$a.$
\begin{rawhtml}
<!-- l2h_end sing_l2h 43 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 44 -->
\end{rawhtml}
$K$
\begin{rawhtml}
<!-- l2h_end sing_l2h 44 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 45 -->
\end{rawhtml}
$\mu_a=a^2+a+3$,
\begin{rawhtml}
<!-- l2h_end sing_l2h 45 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 46 -->
\end{rawhtml}
$R[x,y,z]$
\begin{rawhtml}
<!-- l2h_end sing_l2h 46 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 47 -->
\end{rawhtml}
$R$
\begin{rawhtml}
<!-- l2h_end sing_l2h 47 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 48 -->
\end{rawhtml}
$R(j)[x,y,z]$
\begin{rawhtml}
<!-- l2h_end sing_l2h 48 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 49 -->
\end{rawhtml}
$j$
\begin{rawhtml}
<!-- l2h_end sing_l2h 49 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 50 -->
\end{rawhtml}
$R(i)[x,y,z]$
\begin{rawhtml}
<!-- l2h_end sing_l2h 50 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 51 -->
\end{rawhtml}
$i$
\begin{rawhtml}
<!-- l2h_end sing_l2h 51 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 52 -->
\end{rawhtml}
$\hbox{GF}(p^n)$ with $p^n$ elements, where $p^n$ has to be smaller or equal
$2^{15}$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 52 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 53 -->
\end{rawhtml}
$\hbox{GF}(p^n)$
\begin{rawhtml}
<!-- l2h_end sing_l2h 53 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 54 -->
\end{rawhtml}
$K[x_1,\ldots,x_n]$,
\begin{rawhtml}
<!-- l2h_end sing_l2h 54 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 55 -->
\end{rawhtml}
$\hbox{Loc}_{(x)}K[x_1,\ldots,x_n])$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 55 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 56 -->
\end{rawhtml}
$1 < x$
\begin{rawhtml}
<!-- l2h_end sing_l2h 56 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 57 -->
\end{rawhtml}
$ m \times n $
\begin{rawhtml}
<!-- l2h_end sing_l2h 57 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 58 -->
\end{rawhtml}
\quad
\begin{rawhtml}
<!-- l2h_end sing_l2h 58 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 59 -->
\end{rawhtml}
$\alpha$
\begin{rawhtml}
<!-- l2h_end sing_l2h 59 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 60 -->
\end{rawhtml}
$ i_{1,1} $
\begin{rawhtml}
<!-- l2h_end sing_l2h 60 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 61 -->
\end{rawhtml}
$i+i+i$
\begin{rawhtml}
<!-- l2h_end sing_l2h 61 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 62 -->
\end{rawhtml}
$\alpha, \beta$
\begin{rawhtml}
<!-- l2h_end sing_l2h 62 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 63 -->
\end{rawhtml}
$i_1$
\begin{rawhtml}
<!-- l2h_end sing_l2h 63 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 64 -->
\end{rawhtml}
$i_{1,1}$
\begin{rawhtml}
<!-- l2h_end sing_l2h 64 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 65 -->
\end{rawhtml}
$(h1+h2)/h1 \cong h2/(h1 \cap h2)$
\begin{rawhtml}
<!-- l2h_end sing_l2h 65 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 66 -->
\end{rawhtml}
$Q \rightarrow Q(a, \ldots)$
\begin{rawhtml}
<!-- l2h_end sing_l2h 66 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 67 -->
\end{rawhtml}
$Q \rightarrow R$
\begin{rawhtml}
<!-- l2h_end sing_l2h 67 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 68 -->
\end{rawhtml}
$Q \rightarrow C$
\begin{rawhtml}
<!-- l2h_end sing_l2h 68 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 69 -->
\end{rawhtml}
$Z/p \rightarrow (Z/p)(a, \ldots)$
\begin{rawhtml}
<!-- l2h_end sing_l2h 69 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 70 -->
\end{rawhtml}
$Z/p \rightarrow GF(p^n)$
\begin{rawhtml}
<!-- l2h_end sing_l2h 70 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 71 -->
\end{rawhtml}
$Z/p \rightarrow R$
\begin{rawhtml}
<!-- l2h_end sing_l2h 71 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 72 -->
\end{rawhtml}
$R \rightarrow C$
\begin{rawhtml}
<!-- l2h_end sing_l2h 72 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 73 -->
\end{rawhtml}
% This is quite a hack, but for now it works.
@@ -517,8 +662,10 @@
\subseteq Z$
\begin{rawhtml}
<!-- l2h_end sing_l2h 73 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 74 -->
\end{rawhtml}
$Z/p \rightarrow Z/p^\prime,
@@ -527,127 +674,163 @@
i \mapsto [i]_{p^\prime} \in Z/p^\prime$
\begin{rawhtml}
<!-- l2h_end sing_l2h 74 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 75 -->
\end{rawhtml}
$C \rightarrow R, \quad$ the real part
\begin{rawhtml}
<!-- l2h_end sing_l2h 75 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 76 -->
\end{rawhtml}
$Q \rightarrow Z/p$
\begin{rawhtml}
<!-- l2h_end sing_l2h 76 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 77 -->
\end{rawhtml}
$Q \rightarrow (Z/p)(a, \ldots)$
\begin{rawhtml}
<!-- l2h_end sing_l2h 77 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 78 -->
\end{rawhtml}
$M$
\begin{rawhtml}
<!-- l2h_end sing_l2h 78 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 79 -->
\end{rawhtml}
$R^n$,
\begin{rawhtml}
<!-- l2h_end sing_l2h 79 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 80 -->
\end{rawhtml}
$v_1, \ldots, v_k$, then $v_1, \ldots, v_k$
\begin{rawhtml}
<!-- l2h_end sing_l2h 80 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 81 -->
\end{rawhtml}
$R^n/M$
\begin{rawhtml}
<!-- l2h_end sing_l2h 81 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 82 -->
\end{rawhtml}
n$\times$k
\begin{rawhtml}
<!-- l2h_end sing_l2h 82 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 83 -->
\end{rawhtml}
R$^n$/M,
\begin{rawhtml}
<!-- l2h_end sing_l2h 83 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 84 -->
\end{rawhtml}
$v_1, \ldots, v_k$
\begin{rawhtml}
<!-- l2h_end sing_l2h 84 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 85 -->
\end{rawhtml}
$(h1+h2)/h1=h2/(h1 \cap h2)$
\begin{rawhtml}
<!-- l2h_end sing_l2h 85 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 86 -->
\end{rawhtml}
$k[X,Y]$
\begin{rawhtml}
<!-- l2h_end sing_l2h 86 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 87 -->
\end{rawhtml}
$k_1[X]$
\begin{rawhtml}
<!-- l2h_end sing_l2h 87 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 88 -->
\end{rawhtml}
$k_2[Y]$
\begin{rawhtml}
<!-- l2h_end sing_l2h 88 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 89 -->
\end{rawhtml}
$k_1$
\begin{rawhtml}
<!-- l2h_end sing_l2h 89 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 90 -->
\end{rawhtml}
$k_2$
\begin{rawhtml}
<!-- l2h_end sing_l2h 90 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 91 -->
\end{rawhtml}
$C$
\begin{rawhtml}
<!-- l2h_end sing_l2h 91 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 92 -->
\end{rawhtml}
$R^n/M$, if $R$ denotes the basering and
@@ -656,8 +839,10 @@
$R^n/M$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 92 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 93 -->
\end{rawhtml}
The entry d of the intmat at place (i,j) is the minimal number of
@@ -666,8 +851,10 @@
$R^n$ (resp.\ $M$)).
\begin{rawhtml}
<!-- l2h_end sing_l2h 93 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 94 -->
\end{rawhtml}
$$
@@ -679,23 +866,29 @@
$$
\begin{rawhtml}
<!-- l2h_end sing_l2h 94 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 95 -->
\end{rawhtml}
The third argument is used to return the matrix T of coefficients
such that {\tt matrix}(J) = T*M.
\begin{rawhtml}
<!-- l2h_end sing_l2h 95 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 96 -->
\end{rawhtml}
$M=(m_{ij})$
\begin{rawhtml}
<!-- l2h_end sing_l2h 96 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 97 -->
\end{rawhtml}
$$J_j = z^0 \cdot m_{1j} + z^1 \cdot m_{2j} + ... + z^{d-1} \cdot m_{dj},$$
@@ -703,45 +896,57 @@
equal to the entry [i,j] of {\tt matrix}(J), and we get
\begin{rawhtml}
<!-- l2h_end sing_l2h 97 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 98 -->
\end{rawhtml}
$$ J_{i,j} = z^0 \cdot m_{(i-1)d+1,j} + z^1 \cdot m_{(i-1)d+2,j} + ... +
z^{d-1} \cdot m_{id,j}.$$
\begin{rawhtml}
<!-- l2h_end sing_l2h 98 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 99 -->
\end{rawhtml}
$${\rm contract}(x^A , x^B) := \cases{ x^{(B-A)}, &if $B\ge A$
componentwise\cr 0,&otherwise.\cr}$$
\begin{rawhtml}
<!-- l2h_end sing_l2h 99 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 100 -->
\end{rawhtml}
$x$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 100 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 101 -->
\end{rawhtml}
$x_i$
\begin{rawhtml}
<!-- l2h_end sing_l2h 101 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 102 -->
\end{rawhtml}
$x_i>1$ then $x_i$
\begin{rawhtml}
<!-- l2h_end sing_l2h 102 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 103 -->
\end{rawhtml}
$f_1,\dots,f_k$ of I, let $f'_i$ be obtained from
@@ -749,8 +954,10 @@
Then $f'_1,\dots,f'_k$ generate I.
\begin{rawhtml}
<!-- l2h_end sing_l2h 103 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 104 -->
\end{rawhtml}
$$...\longrightarrow F_2 \buildrel{A_2}\over{\longrightarrow} F_1
@@ -758,151 +965,193 @@
\longrightarrow 0.$$
\begin{rawhtml}
<!-- l2h_end sing_l2h 104 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 105 -->
\end{rawhtml}
$M_i={\tt module} (A_i)$, i=1..k.
\begin{rawhtml}
<!-- l2h_end sing_l2h 105 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 106 -->
\end{rawhtml}
${\tt L[i]}=M_i$
\begin{rawhtml}
<!-- l2h_end sing_l2h 106 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 107 -->
\end{rawhtml}
$I \cap K[U]=(0)$,
\begin{rawhtml}
<!-- l2h_end sing_l2h 107 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 108 -->
\end{rawhtml}
input: $f_1,\dots,f_n$
\begin{rawhtml}
<!-- l2h_end sing_l2h 108 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 109 -->
\end{rawhtml}
output: $g_1,\dots,g_s$ with $s \leq n$ and the properties
\begin{rawhtml}
<!-- l2h_end sing_l2h 109 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 110 -->
\end{rawhtml}
$(f_1,\dots,f_n) = (g_1,\dots,g_s)$
\begin{rawhtml}
<!-- l2h_end sing_l2h 110 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 111 -->
\end{rawhtml}
$L(g_i)\neq L(g_j)$ for all $i\neq j$
\begin{rawhtml}
<!-- l2h_end sing_l2h 111 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 112 -->
\end{rawhtml}
$L(g_i)$
\begin{rawhtml}
<!-- l2h_end sing_l2h 112 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 113 -->
\end{rawhtml}
$\{g_1,\dots,g_{i-1},g_{i+1},\dots,g_s\}$
\begin{rawhtml}
<!-- l2h_end sing_l2h 113 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 114 -->
\end{rawhtml}
$L(g_i) | L(g_j)$ for any $i \neq j$,
\begin{rawhtml}
<!-- l2h_end sing_l2h 114 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 115 -->
\end{rawhtml}
$ecart(g_i) > ecart(g_j)$
\begin{rawhtml}
<!-- l2h_end sing_l2h 115 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 116 -->
\end{rawhtml}
Here, $L(g)$ denotes the leading term of $g$ and
$ecart(g):=deg(g)-deg(L(g))$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 116 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 117 -->
\end{rawhtml}
$M_i={\tt module}(A_i)$, i=1..k.
\begin{rawhtml}
<!-- l2h_end sing_l2h 117 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 118 -->
\end{rawhtml}
represents $h_1/(h_1 \cap h_2) \cong (h_1+h_2)/h_2$
\begin{rawhtml}
<!-- l2h_end sing_l2h 118 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 119 -->
\end{rawhtml}
$h_1$ and $h_2$
\begin{rawhtml}
<!-- l2h_end sing_l2h 119 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 120 -->
\end{rawhtml}
$R^l$
\begin{rawhtml}
<!-- l2h_end sing_l2h 120 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 121 -->
\end{rawhtml}
$H_1$, resp.\ $H_2$,
\begin{rawhtml}
<!-- l2h_end sing_l2h 121 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 122 -->
\end{rawhtml}
be the matrices of size $l \times k$, resp.\ $l \times m$, having the
generators of $h_1$, resp.\ $h_2$,
\begin{rawhtml}
<!-- l2h_end sing_l2h 122 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 123 -->
\end{rawhtml}
$h_1/(h_1 \cap h_2) \cong R^k / ker(\overline{H_1})$
\begin{rawhtml}
<!-- l2h_end sing_l2h 123 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 124 -->
\end{rawhtml}
$\overline{H_1}: R^k \rightarrow R^l/Im(H_2)=R^l/h_2$
is the induced map.
\begin{rawhtml}
<!-- l2h_end sing_l2h 124 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 125 -->
\end{rawhtml}
$coker(A)=F_0/M$
@@ -911,93 +1160,119 @@
\longrightarrow 0,$$
\begin{rawhtml}
<!-- l2h_end sing_l2h 125 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 126 -->
\end{rawhtml}
$A_1$
\begin{rawhtml}
<!-- l2h_end sing_l2h 126 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 127 -->
\end{rawhtml}
$M_i={\tt module}(A_i)$, i=1...k.
\begin{rawhtml}
<!-- l2h_end sing_l2h 127 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 128 -->
\end{rawhtml}
${\tt L[i]}\neq 0$ for $i \le p$,
\begin{rawhtml}
<!-- l2h_end sing_l2h 128 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 129 -->
\end{rawhtml}
$A_1$=matrix(M),
\begin{rawhtml}
<!-- l2h_end sing_l2h 129 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 130 -->
\end{rawhtml}
$coker(A_1)=F_0/M$
$$...\longrightarrow F_2 \buildrel{A_2}\over{\longrightarrow} F_1
\buildrel{A_1}\over{\longrightarrow} F_0\longrightarrow F_0/M\longrightarrow
0,$$
\begin{rawhtml}
<!-- l2h_end sing_l2h 130 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 131 -->
\end{rawhtml}
(${\tt L[i]}=M_i$
\begin{rawhtml}
<!-- l2h_end sing_l2h 131 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 132 -->
\end{rawhtml}
$d$ in row $i$ and column $j$
\begin{rawhtml}
<!-- l2h_end sing_l2h 132 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 133 -->
\end{rawhtml}
$i+j$ of the $j$-th
\begin{rawhtml}
<!-- l2h_end sing_l2h 133 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 134 -->
\end{rawhtml}
$R^n/M$ (the 0th and 1st syzygy module of $R^n/M$ is $R^n$ and $M$, resp.).
\begin{rawhtml}
<!-- l2h_end sing_l2h 134 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 135 -->
\end{rawhtml}
${\tt R}^n$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 135 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 136 -->
\end{rawhtml}
$\{a \in R \mid aJ \subset I\}$,
\begin{rawhtml}
<!-- l2h_end sing_l2h 136 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 137 -->
\end{rawhtml}
$\{b \in R^n \mid bJ \subset M\}$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 137 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 138 -->
\end{rawhtml}
\noindent
@@ -1009,8 +1284,10 @@
\leq s+i$ for all $i$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 138 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 139 -->
\end{rawhtml}
computes the permutation {\tt v}
@@ -1019,23 +1296,29 @@
{\tt i}.
\begin{rawhtml}
<!-- l2h_end sing_l2h 139 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 140 -->
\end{rawhtml}
$A_1={\tt matrix}(M)$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 140 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 141 -->
\end{rawhtml}
$coker(A_1)=F_0/M$
$$...\longrightarrow F_2 \buildrel{A_2}\over{\longrightarrow} F_1
\buildrel{A_1}\over{\longrightarrow} F_0\longrightarrow F_0/M\longrightarrow
0.$$
\begin{rawhtml}
<!-- l2h_end sing_l2h 141 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 142 -->
\end{rawhtml}
{\tt vandermonde(p,v,d)} computes the (unique) polynomial of degree
@@ -1053,8 +1336,10 @@
{\tt v}[k], \quad k=1,\dots,{\tt N}.$$
\begin{rawhtml}
<!-- l2h_end sing_l2h 142 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 143 -->
\end{rawhtml}
the ground field has to be the field of rational
@@ -1064,15 +1349,19 @@
to be numbers.
\begin{rawhtml}
<!-- l2h_end sing_l2h 143 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 144 -->
\end{rawhtml}
$K[[x_1,\ldots,x_n]]$
\begin{rawhtml}
<!-- l2h_end sing_l2h 144 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 145 -->
\end{rawhtml}
$$
@@ -1085,92 +1374,118 @@
where
\begin{rawhtml}
<!-- l2h_end sing_l2h 145 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 146 -->
\end{rawhtml}
$\hbox{Loc}_{(x)}K[x_1,\ldots,x_n]$,
\begin{rawhtml}
<!-- l2h_end sing_l2h 146 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 147 -->
\end{rawhtml}
$K[x_1,\ldots,x_n]$
\begin{rawhtml}
<!-- l2h_end sing_l2h 147 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 148 -->
\end{rawhtml}
$(x_1,\ldots,x_n)$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 148 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 149 -->
\end{rawhtml}
$\hbox{Loc}_{(x)}K[x_1,\ldots,x_n])$
\begin{rawhtml}
<!-- l2h_end sing_l2h 149 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 150 -->
\end{rawhtml}
$\hbox{dim}_K(\hbox{Loc}_{(x,y,z)}K[x,y,z]/\hbox{jacob}(f))$
\begin{rawhtml}
<!-- l2h_end sing_l2h 150 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 151 -->
\end{rawhtml}
$\hbox{dim}_K(K[x,y,z]/\hbox{jacob}(f))$
\begin{rawhtml}
<!-- l2h_end sing_l2h 151 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 152 -->
\end{rawhtml}
$\hbox{dim}_K(\hbox{Loc}_{(x,y,z)}K[x,y,z]/(\hbox{jacob}(f)+(f)))$
\begin{rawhtml}
<!-- l2h_end sing_l2h 152 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 153 -->
\end{rawhtml}
$\hbox{dim}_K(K[x,y,z]/(\hbox{jacob}(f)+(f)))$,
\begin{rawhtml}
<!-- l2h_end sing_l2h 153 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 154 -->
\end{rawhtml}
$j+(f)$
\begin{rawhtml}
<!-- l2h_end sing_l2h 154 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 155 -->
\end{rawhtml}
$f=0$
\begin{rawhtml}
<!-- l2h_end sing_l2h 155 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 156 -->
\end{rawhtml}
$m$
\begin{rawhtml}
<!-- l2h_end sing_l2h 156 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 157 -->
\end{rawhtml}
$i, j$
\begin{rawhtml}
<!-- l2h_end sing_l2h 157 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 158 -->
\end{rawhtml}
$$
@@ -1179,64 +1494,82 @@
= \bigcup_{n=1}^\infty i:j^n$$
\begin{rawhtml}
<!-- l2h_end sing_l2h 158 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 159 -->
\end{rawhtml}
$sat(j+(f),m)$
\begin{rawhtml}
<!-- l2h_end sing_l2h 159 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 160 -->
\end{rawhtml}
$dim_{Q(t)}Q(t)[x,y]/j$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 160 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 161 -->
\end{rawhtml}
$a \in Q$
\begin{rawhtml}
<!-- l2h_end sing_l2h 161 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 162 -->
\end{rawhtml}
$dim_Q Q[x,y]/j_0$,
\begin{rawhtml}
<!-- l2h_end sing_l2h 162 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 163 -->
\end{rawhtml}
$j_0=j|_{t=a}$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 163 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 164 -->
\end{rawhtml}
$T^1$
\begin{rawhtml}
<!-- l2h_end sing_l2h 164 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 165 -->
\end{rawhtml}
$T^2$
\begin{rawhtml}
<!-- l2h_end sing_l2h 165 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 166 -->
\end{rawhtml}
$h_1,\ldots,h_r$
\begin{rawhtml}
<!-- l2h_end sing_l2h 166 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 167 -->
\end{rawhtml}
$I \subset R$ is the ideal generated by $f_1,...,f_s$, then any infinitesimal
@@ -1245,29 +1578,37 @@
where $f=(f_1,...,f_s)$, $g$ a $K$-linear combination of the $h_i$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 167 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 168 -->
\end{rawhtml}
$d$
\begin{rawhtml}
<!-- l2h_end sing_l2h 168 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 169 -->
\end{rawhtml}
$p^k$
\begin{rawhtml}
<!-- l2h_end sing_l2h 169 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 170 -->
\end{rawhtml}
$f=(f_1,\ldots,f_n):k^r\rightarrow k^n$
\begin{rawhtml}
<!-- l2h_end sing_l2h 170 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 171 -->
\end{rawhtml}
$$
@@ -1279,296 +1620,380 @@
$$
\begin{rawhtml}
<!-- l2h_end sing_l2h 171 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 172 -->
\end{rawhtml}
$t_1,\ldots,t_r$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 172 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 173 -->
\end{rawhtml}
$f:(k^r,0)\rightarrow(k^n,0)$,
\begin{rawhtml}
<!-- l2h_end sing_l2h 173 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 174 -->
\end{rawhtml}
$k^r\times(k^n,0)$,
\begin{rawhtml}
<!-- l2h_end sing_l2h 174 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 175 -->
\end{rawhtml}
$$\hbox{pr}:k^r\times(k^n,0)\rightarrow(k^n,0)$$
can be computed.
\begin{rawhtml}
<!-- l2h_end sing_l2h 175 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 176 -->
\end{rawhtml}
$\hbox{T}[7]^\prime$
\begin{rawhtml}
<!-- l2h_end sing_l2h 176 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 177 -->
\end{rawhtml}
$P^4$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 177 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 178 -->
\end{rawhtml}
$K^3$
\begin{rawhtml}
<!-- l2h_end sing_l2h 178 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 179 -->
\end{rawhtml}
$K^3$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 179 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 180 -->
\end{rawhtml}
$P^4$
\begin{rawhtml}
<!-- l2h_end sing_l2h 180 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 181 -->
\end{rawhtml}
$\hbox{\rm ker} / \hbox{\rm Im}$
\begin{rawhtml}
<!-- l2h_end sing_l2h 181 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 182 -->
\end{rawhtml}
$(n-1)$
\begin{rawhtml}
<!-- l2h_end sing_l2h 182 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 183 -->
\end{rawhtml}
$A/(A \cap B)$
\begin{rawhtml}
<!-- l2h_end sing_l2h 183 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 184 -->
\end{rawhtml}
$\hbox{Ext}^1(M,M)$, resp.\ $\hbox{Ext}^2(M,M)$,
\begin{rawhtml}
<!-- l2h_end sing_l2h 184 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 185 -->
\end{rawhtml}
$\hbox{Ext}^1$
\begin{rawhtml}
<!-- l2h_end sing_l2h 185 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 186 -->
\end{rawhtml}
$\hbox{Ext}^1$, $\hbox{Ext}^2$
\begin{rawhtml}
<!-- l2h_end sing_l2h 186 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 187 -->
\end{rawhtml}
$\hbox{Ext}^k(R/J,R)$
\begin{rawhtml}
<!-- l2h_end sing_l2h 187 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 188 -->
\end{rawhtml}
$J$
\begin{rawhtml}
<!-- l2h_end sing_l2h 188 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 189 -->
\end{rawhtml}
($=\hbox{Ext}^1(K,K)$)
\begin{rawhtml}
<!-- l2h_end sing_l2h 189 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 190 -->
\end{rawhtml}
($=\hbox{Ext}^2(K,K)$)
\begin{rawhtml}
<!-- l2h_end sing_l2h 190 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 191 -->
\end{rawhtml}
$K=R/m$
\begin{rawhtml}
<!-- l2h_end sing_l2h 191 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 192 -->
\end{rawhtml}
$R=Loc_m K[x,y]/(x^2-y^3)$, $m=(x,y)$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 192 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 193 -->
\end{rawhtml}
$\hbox{Ext}^1(m,m)$
\begin{rawhtml}
<!-- l2h_end sing_l2h 193 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 194 -->
\end{rawhtml}
$\hbox{Ext}^2(K,K)$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 194 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 195 -->
\end{rawhtml}
$\hbox{Ext}^k(R/i,R)$
\begin{rawhtml}
<!-- l2h_end sing_l2h 195 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 196 -->
\end{rawhtml}
$f\in k[x_1,\ldots,x_n,t]$
\begin{rawhtml}
<!-- l2h_end sing_l2h 196 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 197 -->
\end{rawhtml}
$t$
\begin{rawhtml}
<!-- l2h_end sing_l2h 197 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 198 -->
\end{rawhtml}
$V(\partial f/\partial x_1,\ldots,\partial f/\partial x_n) \setminus V(f)$
\begin{rawhtml}
<!-- l2h_end sing_l2h 198 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 199 -->
\end{rawhtml}
$V(\partial f/\partial x_1,\ldots,\partial f/\partial x_n)$
\begin{rawhtml}
<!-- l2h_end sing_l2h 199 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 200 -->
\end{rawhtml}
(in $P^n$),
\begin{rawhtml}
<!-- l2h_end sing_l2h 200 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 201 -->
\end{rawhtml}
(in $k^n$)
\begin{rawhtml}
<!-- l2h_end sing_l2h 201 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 202 -->
\end{rawhtml}
(in $(k^n,0)$),
\begin{rawhtml}
<!-- l2h_end sing_l2h 202 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 203 -->
\end{rawhtml}
D$_k$(R)
\begin{rawhtml}
<!-- l2h_end sing_l2h 203 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 204 -->
\end{rawhtml}
$(m+1)$
\begin{rawhtml}
<!-- l2h_end sing_l2h 204 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 205 -->
\end{rawhtml}
$(n \times n)$-matrix.
\begin{rawhtml}
<!-- l2h_end sing_l2h 205 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 206 -->
\end{rawhtml}
$\hbox{depth}(\hbox{D}_k(R))\geq m(m+1)/2 + m-1$
\begin{rawhtml}
<!-- l2h_end sing_l2h 206 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 207 -->
\end{rawhtml}
$\sum x_i \partial /\partial x_{i+1}$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 207 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 208 -->
\end{rawhtml}
$f$
\begin{rawhtml}
<!-- l2h_end sing_l2h 208 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 209 -->
\end{rawhtml}
$R/I$
\begin{rawhtml}
<!-- l2h_end sing_l2h 209 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 210 -->
\end{rawhtml}
$A$
\begin{rawhtml}
<!-- l2h_end sing_l2h 210 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 211 -->
\end{rawhtml}
$B$
\begin{rawhtml}
<!-- l2h_end sing_l2h 211 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 212 -->
\end{rawhtml}
$m\times r$ and $m\times s$
\begin{rawhtml}
<!-- l2h_end sing_l2h 212 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 213 -->
\end{rawhtml}
$$
@@ -1577,8 +2002,10 @@
$$
\begin{rawhtml}
<!-- l2h_end sing_l2h 213 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 214 -->
\end{rawhtml}
$R^r \buildrel{A}\over{\longrightarrow}
@@ -1586,8 +2013,10 @@
R^m/\hbox{Im}(B) \;.$
\begin{rawhtml}
<!-- l2h_end sing_l2h 214 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 215 -->
\end{rawhtml}
$$
@@ -1596,289 +2025,371 @@
$$
\begin{rawhtml}
<!-- l2h_end sing_l2h 215 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 216 -->
\end{rawhtml}
$g$, $f_1$, \dots, $f_r\in K[x_1,\ldots,x_n]$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 216 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 217 -->
\end{rawhtml}
$f_1$, \dots, $f_r$
\begin{rawhtml}
<!-- l2h_end sing_l2h 217 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 218 -->
\end{rawhtml}
$I=\langle Y_1-f_1,\ldots,Y_r-f_r \rangle \subseteq
K[x_1,\ldots,x_n,Y_1,\ldots,Y_r]$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 218 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 219 -->
\end{rawhtml}
$I \cap K[Y_1,\ldots,Y_r]$
\begin{rawhtml}
<!-- l2h_end sing_l2h 219 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 220 -->
\end{rawhtml}
$f_1$, \dots, $f_r$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 220 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 221 -->
\end{rawhtml}
$g \in K [f_1,\ldots,f_r]$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 221 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 222 -->
\end{rawhtml}
$g \in K[f_1,\ldots,f_r]$
\begin{rawhtml}
<!-- l2h_end sing_l2h 222 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 223 -->
\end{rawhtml}
$g$
\begin{rawhtml}
<!-- l2h_end sing_l2h 223 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 224 -->
\end{rawhtml}
$I$
\begin{rawhtml}
<!-- l2h_end sing_l2h 224 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 225 -->
\end{rawhtml}
$X=(x_1,\ldots,x_n)$ and $Y=(Y_1,\ldots,Y_r)$ with $X>Y$
\begin{rawhtml}
<!-- l2h_end sing_l2h 225 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 226 -->
\end{rawhtml}
$K[Y]$
\begin{rawhtml}
<!-- l2h_end sing_l2h 226 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 227 -->
\end{rawhtml}
$[f_1,...,f_n]$ or $f_1*gen(1)+...+f_n*gen(n)$, where $gen(i)$
\begin{rawhtml}
<!-- l2h_end sing_l2h 227 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 228 -->
\end{rawhtml}
$gen(i)$
\begin{rawhtml}
<!-- l2h_end sing_l2h 228 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 229 -->
\end{rawhtml}
$[f_1,...,f_n]$
\begin{rawhtml}
<!-- l2h_end sing_l2h 229 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 230 -->
\end{rawhtml}
$v=[f_1,...,f_n]$
\begin{rawhtml}
<!-- l2h_end sing_l2h 230 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 231 -->
\end{rawhtml}
nrows($v$)
\begin{rawhtml}
<!-- l2h_end sing_l2h 231 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 232 -->
\end{rawhtml}
$r$
\begin{rawhtml}
<!-- l2h_end sing_l2h 232 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 233 -->
\end{rawhtml}
$f_r \not= 0$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 233 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 234 -->
\end{rawhtml}
$v$
\begin{rawhtml}
<!-- l2h_end sing_l2h 234 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 235 -->
\end{rawhtml}
$f_i*gen(i)$
\begin{rawhtml}
<!-- l2h_end sing_l2h 235 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 236 -->
\end{rawhtml}
$f_i=0$
\begin{rawhtml}
<!-- l2h_end sing_l2h 236 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 237 -->
\end{rawhtml}
$v_1,...,v_k$
\begin{rawhtml}
<!-- l2h_end sing_l2h 237 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 238 -->
\end{rawhtml}
nrows($M$)
\begin{rawhtml}
<!-- l2h_end sing_l2h 238 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 239 -->
\end{rawhtml}
nrows($v_i$).
\begin{rawhtml}
<!-- l2h_end sing_l2h 239 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 240 -->
\end{rawhtml}
$R$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 240 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 241 -->
\end{rawhtml}
$N$,
\begin{rawhtml}
<!-- l2h_end sing_l2h 241 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 242 -->
\end{rawhtml}
$N = R^n/M$ where $n$
\begin{rawhtml}
<!-- l2h_end sing_l2h 242 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 243 -->
\end{rawhtml}
$N$ and $M \subseteq R^n$
\begin{rawhtml}
<!-- l2h_end sing_l2h 243 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 244 -->
\end{rawhtml}
$R^n$
\begin{rawhtml}
<!-- l2h_end sing_l2h 244 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 245 -->
\end{rawhtml}
$N = R^n/M$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 245 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 246 -->
\end{rawhtml}
$M$,
\begin{rawhtml}
<!-- l2h_end sing_l2h 246 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 247 -->
\end{rawhtml}
$N = R^n/M$ instead of $M$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 247 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 248 -->
\end{rawhtml}
$N$ as $N = R^n/$std($M$)).
\begin{rawhtml}
<!-- l2h_end sing_l2h 248 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 249 -->
\end{rawhtml}
dim$(R^n/M)$, resp.@: dim$_k(R^n/M)$
\begin{rawhtml}
<!-- l2h_end sing_l2h 249 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 250 -->
\end{rawhtml}
$N$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 250 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 251 -->
\end{rawhtml}
$N = R^n/M$
\begin{rawhtml}
<!-- l2h_end sing_l2h 251 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 252 -->
\end{rawhtml}
$\hbox{Loc}_{(x)}K[x_1,\ldots,x_n]$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 252 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 253 -->
\end{rawhtml}
$\hbox{Wp}(w_1, \ldots, w_n)$
\begin{rawhtml}
<!-- l2h_end sing_l2h 253 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 254 -->
\end{rawhtml}
$\hbox{Ws}(w_1, \ldots, w_n)$)
\begin{rawhtml}
<!-- l2h_end sing_l2h 254 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 255 -->
\end{rawhtml}
$w_1$, $\ldots$, $w_n$ of $x_1$, $\ldots$, $x_n$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 255 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 256 -->
\end{rawhtml}
A monomial ordering (term ordering) on $K[x_1, \ldots, x_n]$ is
@@ -1891,15 +2402,19 @@
$<$ to be a well ordering.
\begin{rawhtml}
<!-- l2h_end sing_l2h 256 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 257 -->
\end{rawhtml}
$M$ in $GL(n,R)$,
\begin{rawhtml}
<!-- l2h_end sing_l2h 257 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 258 -->
\end{rawhtml}
Global orderings are well orderings (i.e., \hbox{$1 < x_i$} for each variable
@@ -1916,15 +2431,19 @@
computations has to be interpreted in Loc $K[x]$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 258 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 259 -->
\end{rawhtml}
For all these orderings: Loc $K[x]$ = $K[x]$
\begin{rawhtml}
<!-- l2h_end sing_l2h 259 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 260 -->
\end{rawhtml}
$x^\alpha < x^\beta \Leftrightarrow \exists\; 1 \le i \le n :
@@ -1932,8 +2451,10 @@
\beta_i$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 260 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 261 -->
\end{rawhtml}
$x^\alpha < x^\beta \Leftrightarrow \exists\; 1 \le i \le n :
@@ -1941,22 +2462,28 @@
\ldots, \alpha_{i+1} = \beta_{i+1}, \alpha_i > \beta_i.$
\begin{rawhtml}
<!-- l2h_end sing_l2h 261 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 262 -->
\end{rawhtml}
let $\deg(x^\alpha) = \alpha_1 + \cdots + \alpha_n,$ then
\begin{rawhtml}
<!-- l2h_end sing_l2h 262 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 263 -->
\end{rawhtml}
$x^\alpha < x^\beta \Leftrightarrow \deg(x^\alpha) < \deg(x^\beta)$ or
\begin{rawhtml}
<!-- l2h_end sing_l2h 263 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 264 -->
\end{rawhtml}
\phantom{$x^\alpha < x^\beta \Leftrightarrow $}$ \deg(x^\alpha) =
@@ -1964,8 +2491,10 @@
\ldots, \alpha_{i+1} = \beta_{i+1}, \alpha_i > \beta_i.$
\begin{rawhtml}
<!-- l2h_end sing_l2h 264 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 265 -->
\end{rawhtml}
\phantom{ $x^\alpha < x^\beta \Leftrightarrow $} $\deg(x^\alpha) =
@@ -1973,52 +2502,66 @@
\ldots, \alpha_{i-1} = \beta_{i-1}, \alpha_i < \beta_i.$
\begin{rawhtml}
<!-- l2h_end sing_l2h 265 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 266 -->
\end{rawhtml}
let $w_1, \ldots, w_n$ be positive integers. Then ${\tt wp}(w_1, \ldots,
w_n)$
\begin{rawhtml}
<!-- l2h_end sing_l2h 266 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 267 -->
\end{rawhtml}
$\deg(x^\alpha) = w_1 \alpha_1 + \cdots + w_n\alpha_n.$
\begin{rawhtml}
<!-- l2h_end sing_l2h 267 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 268 -->
\end{rawhtml}
let $w_1, \ldots, w_n$ be positive integers. Then ${\tt Wp}(w_1, \ldots,
w_n)$
\begin{rawhtml}
<!-- l2h_end sing_l2h 268 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 269 -->
\end{rawhtml}
Loc $K[x]$ = $K[x]_{(x)}$,
\begin{rawhtml}
<!-- l2h_end sing_l2h 269 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 270 -->
\end{rawhtml}
$K[x]$
\begin{rawhtml}
<!-- l2h_end sing_l2h 270 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 271 -->
\end{rawhtml}
\ $(x_1, ..., x_n)$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 271 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 272 -->
\end{rawhtml}
$x^\alpha < x^\beta \Leftrightarrow \exists\; 1 \le i \le n :
@@ -2026,15 +2569,19 @@
\beta_i$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 272 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 273 -->
\end{rawhtml}
$x^\alpha < x^\beta \Leftrightarrow \deg(x^\alpha) > \deg(x^\beta)$ or
\begin{rawhtml}
<!-- l2h_end sing_l2h 273 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 274 -->
\end{rawhtml}
\phantom{ $x^\alpha < x^\beta \Leftrightarrow$}$ \deg(x^\alpha) =
@@ -2042,8 +2589,10 @@
\ldots, \alpha_{i+1} = \beta_{i+1}, \alpha_i > \beta_i.$
\begin{rawhtml}
<!-- l2h_end sing_l2h 274 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 275 -->
\end{rawhtml}
\phantom{ $ x^\alpha < x^\beta \Leftrightarrow$}$ \deg(x^\alpha) =
@@ -2051,29 +2600,37 @@
\ldots, \alpha_{i-1} = \beta_{i-1}, \alpha_i < \beta_i.$
\begin{rawhtml}
<!-- l2h_end sing_l2h 275 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 276 -->
\end{rawhtml}
${\tt ws}(w_1, \ldots, w_n),\; w_1$
\begin{rawhtml}
<!-- l2h_end sing_l2h 276 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 277 -->
\end{rawhtml}
$w_2,\ldots,w_n$
\begin{rawhtml}
<!-- l2h_end sing_l2h 277 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 278 -->
\end{rawhtml}
${\tt Ws}(w_1, \ldots, w_n),\; w_1$
\begin{rawhtml}
<!-- l2h_end sing_l2h 278 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 279 -->
\end{rawhtml}
$\{ x^a e_i \mid a \in N^n, 1 \leq i \leq r \}$ in Loc $K[x]^r$ = Loc
@@ -2083,127 +2640,161 @@
(The function {\tt gen(i)} yields $e_i$).
\begin{rawhtml}
<!-- l2h_end sing_l2h 279 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 280 -->
\end{rawhtml}
Loc $K[x]^r$
\begin{rawhtml}
<!-- l2h_end sing_l2h 280 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 281 -->
\end{rawhtml}
Loc $K[x]$
\begin{rawhtml}
<!-- l2h_end sing_l2h 281 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 282 -->
\end{rawhtml}
$<_m = (<,C)$ denotes the module ordering (giving priority to the
coefficients):
\begin{rawhtml}
<!-- l2h_end sing_l2h 282 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 283 -->
\end{rawhtml}
\quad \quad $x^\alpha e_i <_m x^\beta e_j \Leftrightarrow x^\alpha <
x^\beta$ or ($x^\alpha = x^\beta $ and $ i < j$).
\begin{rawhtml}
<!-- l2h_end sing_l2h 283 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 284 -->
\end{rawhtml}
$<_m = (C, <)$ denotes the module ordering (giving priority to the component):
\begin{rawhtml}
<!-- l2h_end sing_l2h 284 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 285 -->
\end{rawhtml}
\quad \quad $x^\alpha e_i <_m x^\beta e_j \Leftrightarrow i < j$ or ($
i = j $ and $ x^\alpha < x^\beta $).
\begin{rawhtml}
<!-- l2h_end sing_l2h 285 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 286 -->
\end{rawhtml}
$<_m = (<,c)$ denotes the module ordering (giving priority to the
coefficients):
\begin{rawhtml}
<!-- l2h_end sing_l2h 286 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 287 -->
\end{rawhtml}
\quad \quad $x^\alpha e_i <_m x^\beta e_j \Leftrightarrow x^\alpha <
x^\beta$ or ($x^\alpha = x^\beta $ and $ i > j$).
\begin{rawhtml}
<!-- l2h_end sing_l2h 287 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 288 -->
\end{rawhtml}
$<_m = (c, <)$ denotes the module ordering (giving priority to the component):
\begin{rawhtml}
<!-- l2h_end sing_l2h 288 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 289 -->
\end{rawhtml}
\quad \quad $x^\alpha e_i <_m x^\beta e_j \Leftrightarrow i > j$ or ($
i = j $ and $ x^\alpha < x^\beta $).
\begin{rawhtml}
<!-- l2h_end sing_l2h 289 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 290 -->
\end{rawhtml}
The output of a vector $v$ in $K[x]^r$ with components $v_1,
\ldots, v_r$ has the format $v_1 * gen(1) + \ldots + v_r * gen(r)$
\begin{rawhtml}
<!-- l2h_end sing_l2h 290 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 291 -->
\end{rawhtml}
In this case a vector is written as $[v_1, \ldots, v_r]$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 291 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 292 -->
\end{rawhtml}
$(n \times n)$-matrix
\begin{rawhtml}
<!-- l2h_end sing_l2h 292 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 293 -->
\end{rawhtml}
$M_1, \ldots, M_n$ the rows of $M$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 293 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 294 -->
\end{rawhtml}
\quad \quad $x^a < x^b \Leftrightarrow \exists\ 1 \leq i \leq n :
M_1 a = \; M_1 b, \ldots, M_{i-1} a = \; M_{i-1} b$ and $M_i a < \; M_i b$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 294 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 295 -->
\end{rawhtml}
$x^a < x^b$
if and only if $M a$ is smaller than $M b$
\begin{rawhtml}
<!-- l2h_end sing_l2h 295 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 296 -->
\end{rawhtml}
@@ -2272,8 +2863,10 @@
}\right)$
\begin{rawhtml}
<!-- l2h_end sing_l2h 296 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 297 -->
\end{rawhtml}
$\quad$ (dp(3), wp(1,2,3)):
@@ -2297,8 +2890,10 @@
}\right)$
\begin{rawhtml}
<!-- l2h_end sing_l2h 297 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 298 -->
\end{rawhtml}
$\quad$ (dp(3), a(1,2,3),dp(3)):
@@ -2324,22 +2919,28 @@
}\right)$
\begin{rawhtml}
<!-- l2h_end sing_l2h 298 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 299 -->
\end{rawhtml}
$n \times n$
\begin{rawhtml}
<!-- l2h_end sing_l2h 299 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 300 -->
\end{rawhtml}
$x = (x_1, \ldots, x_n)$ and $y = (y_1, \ldots, y_m)$
\begin{rawhtml}
<!-- l2h_end sing_l2h 300 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 301 -->
\end{rawhtml}
$<_1$ a monomial
@@ -2347,51 +2948,65 @@
ordering (or block ordering) $<\ := (<_1,<_2)$ on $K[x,y]$ is the following:
\begin{rawhtml}
<!-- l2h_end sing_l2h 301 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 302 -->
\end{rawhtml}
\quad \quad $x^a y^b < x^A y^B \Leftrightarrow x^a <_1 x^A $ or ($x^a =
x^A$ and $y^b <_2 y^B$).
\begin{rawhtml}
<!-- l2h_end sing_l2h 302 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 303 -->
\end{rawhtml}
${\tt a}(w_1, \ldots, w_n),\; $
\begin{rawhtml}
<!-- l2h_end sing_l2h 303 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 304 -->
\end{rawhtml}
$w_1,\ldots,w_n$
\begin{rawhtml}
<!-- l2h_end sing_l2h 304 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 305 -->
\end{rawhtml}
$\deg(x^\alpha) = w_1 \alpha_1 + \cdots + w_n\alpha_n$
\begin{rawhtml}
<!-- l2h_end sing_l2h 305 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 306 -->
\end{rawhtml}
$$\deg(x^\alpha) < \deg(x^\beta) \Rightarrow x^\alpha < x^\beta,$$
\begin{rawhtml}
<!-- l2h_end sing_l2h 306 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 307 -->
\end{rawhtml}
$$\deg(x^\alpha) > \deg(x^\beta) \Rightarrow x^\alpha > x^\beta. $$
\begin{rawhtml}
<!-- l2h_end sing_l2h 307 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 308 -->
\end{rawhtml}
Let $R = \hbox{Loc}_< K[\underline{x}]$ and let $I$ be a submodule of $R^r$.
@@ -2402,8 +3017,10 @@
if $L(f_1), \ldots, L(f_s)$ generate $L(I)$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 308 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 309 -->
\end{rawhtml}
A function $\hbox{NF} : R^r \times \{G \mid G\ \hbox{ a standard
@@ -2417,16 +3034,20 @@
respect to} $G$ (note that such a function is not unique).
\begin{rawhtml}
<!-- l2h_end sing_l2h 309 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 310 -->
\end{rawhtml}
For a standard basis $G$ of $I$ the following holds:
$f \in I$ if and only if $\hbox{NF}(f,G) = 0$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 310 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 311 -->
\end{rawhtml}
Let \hbox{$I \subseteq K[\underline{x}]^r$} be a homogeneous module, then the
Hilbert function
@@ -2436,8 +3057,10 @@
$H_I=H_{L(I)}$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 311 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 312 -->
\end{rawhtml}
Let M $=\bigoplus_i M_i$ be a graded module over $K[x_1,..,x_n]$ with
@@ -2458,8 +3081,10 @@
(the {\bf Hilbert polynomial}) for $s \ge N$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 312 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 313 -->
\end{rawhtml}
Generalizing these to quasihomogeneous modules we get
@@ -2468,31 +3093,39 @@
$Q(t)$ is called the {\bf first (weighted) Hilbert series} of M.
\begin{rawhtml}
<!-- l2h_end sing_l2h 313 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 314 -->
\end{rawhtml}
Let $R$ be a quotient of $\hbox{Loc}_< K[\underline{x}]$ and let
\hbox{$I=(g_1, ..., g_s)$} be a submodule of $R^r$.
Then the {\bf module of syzygies} (or {\bf 1st syzygy module}, {\bf module of
relations}) of $I$, syz($I$), is defined to be the kernel of the map \hbox{$R^s
\rightarrow R^r,\; \sum_{i=1}^s w_ie_i \mapsto \sum_{i=1}^s w_ig_i$.}
\begin{rawhtml}
<!-- l2h_end sing_l2h 314 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 315 -->
\end{rawhtml}
$(k-1)$-st
\begin{rawhtml}
<!-- l2h_end sing_l2h 315 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 316 -->
\end{rawhtml}
Note, that the syzygy modules of $I$ depend on a choice of generators $g_1,
..., g_s$.
But one can show that they depend on $I$ uniquely up to direct summands.
\begin{rawhtml}
<!-- l2h_end sing_l2h 316 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 317 -->
\end{rawhtml}
Let $I=(g_1,...,g_s)\subseteq R^r$ and $M= R^r/I$.
@@ -2502,15 +3135,19 @@
0,$$
\begin{rawhtml}
<!-- l2h_end sing_l2h 317 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 318 -->
\end{rawhtml}
$R=\hbox{Loc}_< K[\underline{x}]$
\begin{rawhtml}
<!-- l2h_end sing_l2h 318 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 319 -->
\end{rawhtml}
Let $R$ be a graded ring (e.g., $R = \hbox{Loc}_< K[\underline{x}]$) and
@@ -2528,15 +3165,19 @@
and the 1st syzygy module of $R^r/I$ is $I$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 319 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 320 -->
\end{rawhtml}
$s$
\begin{rawhtml}
<!-- l2h_end sing_l2h 320 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 321 -->
\end{rawhtml}
$$
@@ -2544,8 +3185,10 @@
$$
\begin{rawhtml}
<!-- l2h_end sing_l2h 321 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 322 -->
\end{rawhtml}
Let $<$ be the lexicographical ordering on $R=K[x_1,...,x_n]$ with $x_1
@@ -2585,8 +3228,10 @@
the ideal $(G)$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 322 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 323 -->
\end{rawhtml}
Let $f\colon(C^{n+1},0)\rightarrow(C,0)$ be a complex isolated hypersurface
singularity given by a polynomial with algebraic coefficients which we also
denote by $f$.
@@ -2621,65 +3266,83 @@
Using the library {\tt gaussman.lib} one can compute the {\bf monodromy}, the
V-filtration on $H''/H'$, and the spectrum.
\begin{rawhtml}
<!-- l2h_end sing_l2h 323 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 324 -->
\end{rawhtml}
$f=x^5+x^2y^2+y^5$
\begin{rawhtml}
<!-- l2h_end sing_l2h 324 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 325 -->
\end{rawhtml}
$\exp(2\pi iM)$
\begin{rawhtml}
<!-- l2h_end sing_l2h 325 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 326 -->
\end{rawhtml}
$H''/H'$
\begin{rawhtml}
<!-- l2h_end sing_l2h 326 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 327 -->
\end{rawhtml}
$O/J_f\cong H''/H'$
\begin{rawhtml}
<!-- l2h_end sing_l2h 327 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 328 -->
\end{rawhtml}
If the principal part of $f$ is $C$-nondegenerate, one can compute the
spectrum using the library {\tt spectrum.lib}.
In this case, the V-filtration on $H''$ coincides with the Newton-filtration
on $H''$ which allows to compute the spectrum more efficiently.
\begin{rawhtml}
<!-- l2h_end sing_l2h 328 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 329 -->
\end{rawhtml}
$\tilde{E}_6$ on a surface $X\subset{P}^3$
\begin{rawhtml}
<!-- l2h_end sing_l2h 329 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 330 -->
\end{rawhtml}
$\mu(f)$, the geometric genus $p_g(f)$
\begin{rawhtml}
<!-- l2h_end sing_l2h 330 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 331 -->
\end{rawhtml}
$x^7+y^7+z^7=0$
\begin{rawhtml}
<!-- l2h_end sing_l2h 331 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 332 -->
\end{rawhtml}
${3 \over 7}, {4 \over 7}, {5 \over 7}, {6 \over 7}, {1 \over 1},
@@ -2688,8 +3351,10 @@
{18 \over 7}$
\begin{rawhtml}
<!-- l2h_end sing_l2h 332 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 333 -->
\end{rawhtml}
The singularities of type $\tilde{E}_6$ form a
@@ -2697,29 +3362,37 @@
$x^3+y^3+z^3+\lambda xyz=0,\quad \lambda^3\neq-27$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 333 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 334 -->
\end{rawhtml}
$x^3+y^3+z^3$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 334 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 335 -->
\end{rawhtml}
$\tilde{E}_6$ on a septic in $P^3$. But $x^7+y^7+z^7$
\begin{rawhtml}
<!-- l2h_end sing_l2h 335 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 336 -->
\end{rawhtml}
$\tilde{E}_6$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 336 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 337 -->
\end{rawhtml}
Let $A$ denote an $m\times n$ matrix with integral coefficients. For $u
@@ -2742,15 +3415,19 @@
$$ I=<x^{v_i^+}-x^{v_i^-}|i=1,\ldots,r> $$
\begin{rawhtml}
<!-- l2h_end sing_l2h 337 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 338 -->
\end{rawhtml}
section Algorithms.
\begin{rawhtml}
<!-- l2h_end sing_l2h 338 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 339 -->
\end{rawhtml}
computes $I_A$ via the
@@ -2770,8 +3447,10 @@
$t,y_1,\ldots,y_m$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 339 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 340 -->
\end{rawhtml}
basis $v_1,\ldots,v_r$ for the integer kernel of $A$ using the
@@ -2784,8 +3463,10 @@
$t$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 340 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 341 -->
\end{rawhtml}
compute $I_A$ without any auxiliary variables, provided that $A$ contains a
vector $w$
@@ -2815,8 +3496,10 @@
number can be reduced to at most $n/2$
\begin{rawhtml}
<!-- l2h_end sing_l2h 341 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 342 -->
\end{rawhtml}
to $n/2$ Groebner basis
@@ -2851,8 +3534,10 @@
is a generating set for $I_A$.
\begin{rawhtml}
<!-- l2h_end sing_l2h 342 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 343 -->
\end{rawhtml}
variable $u$ and one supplementary generator $x_1\cdot\ldots\cdot x_n -
@@ -2861,8 +3546,10 @@
get rid of the variable $u$ again.
\begin{rawhtml}
<!-- l2h_end sing_l2h 343 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 344 -->
\end{rawhtml}
Let $A$ be an $m\times n$ matrix with integral coefficients, $b\in
@@ -2884,82 +3571,105 @@
$v_0$ (i.e., with $c^T v_0$ minimal) by the following procedure:
\begin{rawhtml}
<!-- l2h_end sing_l2h 344 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 345 -->
\end{rawhtml}
$>_c$
\begin{rawhtml}
<!-- l2h_end sing_l2h 345 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 346 -->
\end{rawhtml}
$x^v$
\begin{rawhtml}
<!-- l2h_end sing_l2h 346 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 347 -->
\end{rawhtml}
$x^(v_0)$
\begin{rawhtml}
<!-- l2h_end sing_l2h 347 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 348 -->
\end{rawhtml}
$v_0$
\begin{rawhtml}
<!-- l2h_end sing_l2h 348 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 349 -->
\end{rawhtml}
Faug\`ere,
\begin{rawhtml}
<!-- l2h_end sing_l2h 349 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 350 -->
\end{rawhtml}
$ 2*genus-2 < deg(G) < size(D) $
\begin{rawhtml}
<!-- l2h_end sing_l2h 350 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 351 -->
\end{rawhtml}
$\Omega(G-D)$
\begin{rawhtml}
<!-- l2h_end sing_l2h 351 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 352 -->
\end{rawhtml}
$epsilon$
\begin{rawhtml}
<!-- l2h_end sing_l2h 352 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 353 -->
\end{rawhtml}
$delta$
\begin{rawhtml}
<!-- l2h_end sing_l2h 353 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 354 -->
\end{rawhtml}
$epsilon + genus$
\begin{rawhtml}
<!-- l2h_end sing_l2h 354 -->
+
\end{rawhtml}
\begin{rawhtml}
+
<!-- l2h_begin sing_l2h 355 -->
\end{rawhtml}
$epsilon:=[(deg(G)-3*genus+1)/2]$
\begin{rawhtml}
<!-- l2h_end sing_l2h 355 -->
+
\end{rawhtml}
\end{document}
Index: test/singular_manual/res/singular_httex/sing_tex4ht_tex.tex
===================================================================
RCS file:
/cvsroot/texi2html/texi2html/test/singular_manual/res/singular_httex/sing_tex4ht_tex.tex,v
retrieving revision 1.1
retrieving revision 1.2
diff -u -b -r1.1 -r1.2
--- test/singular_manual/res/singular_httex/sing_tex4ht_tex.tex 18 Aug 2008
18:09:29 -0000 1.1
+++ test/singular_manual/res/singular_httex/sing_tex4ht_tex.tex 22 Oct 2009
20:23:23 -0000 1.2
@@ -1,412 +1,412 @@
% Automatically generated
\csname tex4ht\endcsname
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 1 -->\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 1
-->\Hnewline}
H.\ Sch\"onemann; Humboldt-Universit\"at
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 1 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 2 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 1 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 2
-->\Hnewline}
$3 \times 3$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 2 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 3 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 2 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 3
-->\Hnewline}
$0$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 3 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 4 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 3 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 4
-->\Hnewline}
$Q$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 4 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 5 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 4 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 5
-->\Hnewline}
$a$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 5 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 6 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 5 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 6
-->\Hnewline}
$Z/32003[x,y,z]$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 6 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 7 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 6 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 7
-->\Hnewline}
$x^3$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 7 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 8 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 7 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 8
-->\Hnewline}
$K[x,y,z]/\hbox{\rm jacob}(f)$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 8 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 9 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 8 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 9
-->\Hnewline}
$12-4=8$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 9 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 10 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 9 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 10
-->\Hnewline}
$1 \times 1$-minors
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 10 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 11 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 10 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 11
-->\Hnewline}
$1 \times 1$-minors,
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 11 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 12 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 11 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 12
-->\Hnewline}
$MD$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 12 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 13 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 12 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 13
-->\Hnewline}
$r^3/MD$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 13 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 14 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 13 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 14
-->\Hnewline}
$MD$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 14 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 15 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 14 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 15
-->\Hnewline}
$M = r^3/U$,
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 15 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 16 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 15 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 16
-->\Hnewline}
$M$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 16 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 17 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 16 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 17
-->\Hnewline}
$\hbox{ann}(M) = \{a \mid aM = 0 \}$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 17 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 18 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 17 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 18
-->\Hnewline}
$\{ a \mid ar^3 \in U \}$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 18 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 19 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 18 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 19
-->\Hnewline}
$U \colon r^3 $.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 19 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 20 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 19 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 20
-->\Hnewline}
$n$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 20 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 21 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 20 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 21
-->\Hnewline}
$n=0$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 21 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 22 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 21 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 22
-->\Hnewline}
$R^5$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 22 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 23 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 22 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 23
-->\Hnewline}
$(z^3,0,-y+4z,x+2z,0)$ and $(-xyz-y^2z-4xz^2+16z^3,-y^2,48z,48z,x+y-z)$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 23 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 24 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 23 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 24
-->\Hnewline}
$Q$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 24 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 25 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 24 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 25
-->\Hnewline}
finite fields $Z/p$, $p$ a prime $\le 2147483629$,
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 25 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 26 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 25 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 26
-->\Hnewline}
finite fields $\hbox{GF}(p^n)$ with $p^n$ elements, $p$ a prime, $p^n \le
2^{15}$,
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 26 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 27 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 26 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 27
-->\Hnewline}
$Q$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 27 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 28 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 27 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 28
-->\Hnewline}
$Z/p$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 28 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 29 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 28 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 29
-->\Hnewline}
$Q$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 29 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 30 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 29 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 30
-->\Hnewline}
$Z/p$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 30 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 31 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 30 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 31
-->\Hnewline}
$Z/32003[x,y,z]$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 31 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 32 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 31 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 32
-->\Hnewline}
$Q[a,b,c,d]$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 32 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 33 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 32 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 33
-->\Hnewline}
$Z/7[x,y,z]$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 33 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 34 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 33 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 34
-->\Hnewline}
$Z/7[x_1,\ldots,x_6]$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 34 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 35 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 34 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 35
-->\Hnewline}
$x_1,x_2,x_3$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 35 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 36 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 35 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 36
-->\Hnewline}
$x_4,x_5,x_6$:
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 36 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 37 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 36 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 37
-->\Hnewline}
$(Q[a,b,c])[x,y,z]$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 37 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 38 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 37 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 38
-->\Hnewline}
$(x,y,z)$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 38 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 39 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 38 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 39
-->\Hnewline}
$Q[x,y,z]$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 39 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 40 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 39 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 40
-->\Hnewline}
$x$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 40 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 41 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 40 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 41
-->\Hnewline}
$y$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 41 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 42 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 41 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 42
-->\Hnewline}
$z$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 42 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 43 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 42 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 43
-->\Hnewline}
$K[x,y,z]$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 43 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 44 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 43 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 44
-->\Hnewline}
$K=Z/7(a,b,c)$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 44 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 45 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 44 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 45
-->\Hnewline}
$Z/7$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 45 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 46 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 45 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 46
-->\Hnewline}
$a$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 46 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 47 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 46 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 47
-->\Hnewline}
$b$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 47 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 48 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 47 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 48
-->\Hnewline}
$c$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 48 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 49 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 48 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 49
-->\Hnewline}
$K[x,y,z]$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 49 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 50 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 49 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 50
-->\Hnewline}
$K=Z/7[a]$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 50 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 51 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 50 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 51
-->\Hnewline}
$Z/7$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 51 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 52 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 51 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 52
-->\Hnewline}
$a.$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 52 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 53 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 52 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 53
-->\Hnewline}
$K$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 53 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 54 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 53 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 54
-->\Hnewline}
$a$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 54 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 55 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 54 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 55
-->\Hnewline}
$Z/7$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 55 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 56 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 55 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 56
-->\Hnewline}
$\mu_a=a^2+a+3$,
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 56 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 57 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 56 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 57
-->\Hnewline}
$a$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 57 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 58 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 57 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 58
-->\Hnewline}
$K$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 58 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 59 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 58 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 59
-->\Hnewline}
$R[x,y,z]$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 59 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 60 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 59 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 60
-->\Hnewline}
$R$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 60 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 61 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 60 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 61
-->\Hnewline}
$R[x,y,z]$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 61 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 62 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 61 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 62
-->\Hnewline}
$R$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 62 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 63 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 62 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 63
-->\Hnewline}
$R[x,y,z]$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 63 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 64 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 63 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 64
-->\Hnewline}
$R$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 64 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 65 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 64 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 65
-->\Hnewline}
$R(j)[x,y,z]$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 65 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 66 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 65 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 66
-->\Hnewline}
$R$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 66 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 67 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 66 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 67
-->\Hnewline}
$j$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 67 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 68 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 67 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 68
-->\Hnewline}
$R(i)[x,y,z]$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 68 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 69 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 68 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 69
-->\Hnewline}
$R$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 69 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 70 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 69 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 70
-->\Hnewline}
$i$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 70 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 71 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 70 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 71
-->\Hnewline}
$Z/7[x,y,z]$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 71 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 72 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 71 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 72
-->\Hnewline}
$(x,y,z)$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 72 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 73 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 72 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 73
-->\Hnewline}
$\hbox{GF}(p^n)$ with $p^n$ elements, where $p^n$ has to be smaller or equal
$2^{15}$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 73 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 74 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 73 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 74
-->\Hnewline}
$\hbox{GF}(p^n)$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 74 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 75 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 74 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 75
-->\Hnewline}
$K[x_1,\ldots,x_n]$,
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 75 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 76 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 75 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 76
-->\Hnewline}
$\hbox{Loc}_{(x)}K[x_1,\ldots,x_n])$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 76 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 77 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 76 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 77
-->\Hnewline}
$1 < x$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 77 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 78 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 77 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 78
-->\Hnewline}
$x$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 78 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 79 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 78 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 79
-->\Hnewline}
$ m \times n $
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 79 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 80 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 79 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 80
-->\Hnewline}
\quad
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 80 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 81 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 80 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 81
-->\Hnewline}
\quad
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 81 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 82 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 81 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 82
-->\Hnewline}
$\alpha$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 82 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 83 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 82 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 83
-->\Hnewline}
$ i_{1,1} $
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 83 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 84 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 83 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 84
-->\Hnewline}
$i+i+i$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 84 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 85 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 84 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 85
-->\Hnewline}
$\alpha, \beta$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 85 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 86 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 85 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 86
-->\Hnewline}
$i_1$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 86 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 87 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 86 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 87
-->\Hnewline}
$i_{1,1}$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 87 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 88 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 87 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 88
-->\Hnewline}
$(h1+h2)/h1 \cong h2/(h1 \cap h2)$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 88 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 89 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 88 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 89
-->\Hnewline}
$Q \rightarrow Q(a, \ldots)$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 89 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 90 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 89 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 90
-->\Hnewline}
$Q \rightarrow R$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 90 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 91 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 90 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 91
-->\Hnewline}
$Q \rightarrow C$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 91 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 92 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 91 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 92
-->\Hnewline}
$Z/p \rightarrow (Z/p)(a, \ldots)$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 92 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 93 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 92 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 93
-->\Hnewline}
$Z/p \rightarrow GF(p^n)$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 93 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 94 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 93 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 94
-->\Hnewline}
$Z/p \rightarrow R$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 94 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 95 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 94 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 95
-->\Hnewline}
$R \rightarrow C$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 95 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 96 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 95 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 96
-->\Hnewline}
% This is quite a hack, but for now it works.
$Z/p \rightarrow Q,
\quad
[i]_p \mapsto i \in [-p/2, \, p/2]
\subseteq Z$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 96 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 97 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 96 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 97
-->\Hnewline}
$Z/p \rightarrow Z/p^\prime,
\quad
[i]_p \mapsto i \in [-p/2, \, p/2] \subseteq Z, \;
i \mapsto [i]_{p^\prime} \in Z/p^\prime$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 97 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 98 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 97 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 98
-->\Hnewline}
$C \rightarrow R, \quad$ the real part
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 98 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 99 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 98 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 99
-->\Hnewline}
$Q \rightarrow Z/p$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 99 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 100 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 99 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 100
-->\Hnewline}
$Q \rightarrow (Z/p)(a, \ldots)$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 100 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 101 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 100 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 101
-->\Hnewline}
$M$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 101 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 102 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 101 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 102
-->\Hnewline}
$R^n$,
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 102 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 103 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 102 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 103
-->\Hnewline}
$R$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 103 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 104 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 103 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 104
-->\Hnewline}
$v_1, \ldots, v_k$, then $v_1, \ldots, v_k$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 104 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 105 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 104 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 105
-->\Hnewline}
$R^n/M$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 105 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 106 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 105 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 106
-->\Hnewline}
$R$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 106 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 107 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 106 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 107
-->\Hnewline}
n$\times$k
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 107 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 108 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 107 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 108
-->\Hnewline}
R$^n$/M,
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 108 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 109 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 108 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 109
-->\Hnewline}
$v_1, \ldots, v_k$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 109 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 110 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 109 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 110
-->\Hnewline}
$(h1+h2)/h1=h2/(h1 \cap h2)$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 110 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 111 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 110 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 111
-->\Hnewline}
\quad
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 111 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 112 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 111 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 112
-->\Hnewline}
\quad
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 112 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 113 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 112 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 113
-->\Hnewline}
$k[X,Y]$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 113 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 114 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 113 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 114
-->\Hnewline}
$k_1[X]$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 114 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 115 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 114 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 115
-->\Hnewline}
$k_2[Y]$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 115 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 116 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 115 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 116
-->\Hnewline}
$k_1$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 116 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 117 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 116 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 117
-->\Hnewline}
$k_2$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 117 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 118 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 117 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 118
-->\Hnewline}
$k_1$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 118 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 119 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 118 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 119
-->\Hnewline}
$k_2$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 119 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 120 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 119 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 120
-->\Hnewline}
$R$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 120 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 121 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 120 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 121
-->\Hnewline}
$C$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 121 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 122 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 121 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 122
-->\Hnewline}
$k_1$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 122 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 123 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 122 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 123
-->\Hnewline}
$k_2$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 123 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 124 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 123 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 124
-->\Hnewline}
$Q$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 124 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 125 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 124 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 125
-->\Hnewline}
$k_1$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 125 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 126 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 125 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 126
-->\Hnewline}
$k_2$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 126 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 127 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 126 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 127
-->\Hnewline}
$k_1$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 127 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 128 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 127 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 128
-->\Hnewline}
$k_2$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 128 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 129 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 128 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 129
-->\Hnewline}
$Z/p$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 129 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 130 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 129 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 130
-->\Hnewline}
$R^n/M$, if $R$ denotes the basering and
$M$ a homogeneous submodule of $R^n$ and the argument represents a
resolution of
$R^n/M$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 130 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 131 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 130 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 131
-->\Hnewline}
The entry d of the intmat at place (i,j) is the minimal number of
generators in degree i+j of the j-th syzygy module (= module of
relations) of $R^n/M$ (the 0th (resp.\ 1st) syzygy module of $R^n/M$ is
$R^n$ (resp.\ $M$)).
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 131 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 132 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 131 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 132
-->\Hnewline}
$$
0 \longleftarrow r/j \longleftarrow r(1)
\buildrel{T[1]}\over{\longleftarrow} r(2) \oplus r^3(3)
@@ -414,167 +414,167 @@
\buildrel{T[3]}\over{\longleftarrow} r(5)
\longleftarrow 0 \quad .
$$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 132 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 133 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 132 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 133
-->\Hnewline}
The third argument is used to return the matrix T of coefficients
such that {\tt matrix}(J) = T*M.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 133 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 134 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 133 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 134
-->\Hnewline}
$M=(m_{ij})$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 134 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 135 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 134 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 135
-->\Hnewline}
$$J_j = z^0 \cdot m_{1j} + z^1 \cdot m_{2j} + ... + z^{d-1} \cdot m_{dj},$$
while for a module J the i-th component of the j-th generator is
equal to the entry [i,j] of {\tt matrix}(J), and we get
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 135 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 136 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 135 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 136
-->\Hnewline}
$$ J_{i,j} = z^0 \cdot m_{(i-1)d+1,j} + z^1 \cdot m_{(i-1)d+2,j} + ... +
z^{d-1} \cdot m_{id,j}.$$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 136 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 137 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 136 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 137
-->\Hnewline}
$${\rm contract}(x^A , x^B) := \cases{ x^{(B-A)}, &if $B\ge A$
componentwise\cr 0,&otherwise.\cr}$$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 137 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 138 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 137 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 138
-->\Hnewline}
$x$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 138 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 139 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 138 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 139
-->\Hnewline}
$x_i$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 139 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 140 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 139 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 140
-->\Hnewline}
$x_i>1$ then $x_i$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 140 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 141 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 140 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 141
-->\Hnewline}
$f_1,\dots,f_k$ of I, let $f'_i$ be obtained from
$f_i$ by deleting the terms divisible by $x_i\cdot m$ for all i with $x_i<1$.
Then $f'_1,\dots,f'_k$ generate I.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 141 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 142 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 141 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 142
-->\Hnewline}
$$...\longrightarrow F_2 \buildrel{A_2}\over{\longrightarrow} F_1
\buildrel{A_1}\over{\longrightarrow} R\longrightarrow R/I
\longrightarrow 0.$$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 142 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 143 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 142 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 143
-->\Hnewline}
$M_i={\tt module} (A_i)$, i=1..k.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 143 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 144 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 143 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 144
-->\Hnewline}
${\tt L[i]}=M_i$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 144 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 145 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 144 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 145
-->\Hnewline}
$I \cap K[U]=(0)$,
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 145 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 146 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 145 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 146
-->\Hnewline}
input: $f_1,\dots,f_n$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 146 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 147 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 146 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 147
-->\Hnewline}
output: $g_1,\dots,g_s$ with $s \leq n$ and the properties
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 147 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 148 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 147 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 148
-->\Hnewline}
$(f_1,\dots,f_n) = (g_1,\dots,g_s)$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 148 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 149 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 148 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 149
-->\Hnewline}
$L(g_i)\neq L(g_j)$ for all $i\neq j$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 149 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 150 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 149 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 150
-->\Hnewline}
$L(g_i)$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 150 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 151 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 150 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 151
-->\Hnewline}
$\{g_1,\dots,g_{i-1},g_{i+1},\dots,g_s\}$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 151 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 152 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 151 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 152
-->\Hnewline}
$L(g_i) | L(g_j)$ for any $i \neq j$,
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 152 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 153 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 152 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 153
-->\Hnewline}
$ecart(g_i) > ecart(g_j)$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 153 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 154 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 153 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 154
-->\Hnewline}
Here, $L(g)$ denotes the leading term of $g$ and
$ecart(g):=deg(g)-deg(L(g))$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 154 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 155 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 154 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 155
-->\Hnewline}
$$...\longrightarrow F_2 \buildrel{A_2}\over{\longrightarrow} F_1
\buildrel{A_1}\over{\longrightarrow} R\longrightarrow R/I
\longrightarrow 0.$$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 155 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 156 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 155 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 156
-->\Hnewline}
$M_i={\tt module}(A_i)$, i=1..k.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 156 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 157 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 156 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 157
-->\Hnewline}
${\tt L[i]}=M_i$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 157 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 158 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 157 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 158
-->\Hnewline}
represents $h_1/(h_1 \cap h_2) \cong (h_1+h_2)/h_2$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 158 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 159 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 158 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 159
-->\Hnewline}
$h_1$ and $h_2$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 159 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 160 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 159 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 160
-->\Hnewline}
$R^l$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 160 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 161 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 160 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 161
-->\Hnewline}
$H_1$, resp.\ $H_2$,
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 161 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 162 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 161 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 162
-->\Hnewline}
be the matrices of size $l \times k$, resp.\ $l \times m$, having the
generators of $h_1$, resp.\ $h_2$,
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 162 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 163 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 162 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 163
-->\Hnewline}
$h_1/(h_1 \cap h_2) \cong R^k / ker(\overline{H_1})$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 163 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 164 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 163 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 164
-->\Hnewline}
$\overline{H_1}: R^k \rightarrow R^l/Im(H_2)=R^l/h_2$
is the induced map.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 164 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 165 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 164 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 165
-->\Hnewline}
$coker(A)=F_0/M$
$$...\longrightarrow F_2 \buildrel{A_2}\over{\longrightarrow} F_1
\buildrel{A_1}\over{\longrightarrow} F_0\longrightarrow F_0/M
\longrightarrow 0,$$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 165 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 166 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 165 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 166
-->\Hnewline}
$A_1$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 166 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 167 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 166 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 167
-->\Hnewline}
$M_i={\tt module}(A_i)$, i=1...k.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 167 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 168 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 167 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 168
-->\Hnewline}
${\tt L[i]}\neq 0$ for $i \le p$,
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 168 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 169 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 168 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 169
-->\Hnewline}
$A_1$=matrix(M),
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 169 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 170 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 169 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 170
-->\Hnewline}
$coker(A_1)=F_0/M$
$$...\longrightarrow F_2 \buildrel{A_2}\over{\longrightarrow} F_1
\buildrel{A_1}\over{\longrightarrow} F_0\longrightarrow F_0/M\longrightarrow
0,$$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 170 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 171 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 170 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 171
-->\Hnewline}
$A_1$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 171 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 172 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 171 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 172
-->\Hnewline}
$M_i={\tt module}(A_i)$, i=1..k.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 172 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 173 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 172 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 173
-->\Hnewline}
(${\tt L[i]}=M_i$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 173 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 174 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 173 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 174
-->\Hnewline}
$d$ in row $i$ and column $j$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 174 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 175 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 174 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 175
-->\Hnewline}
$i+j$ of the $j$-th
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 175 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 176 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 175 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 176
-->\Hnewline}
$R^n/M$ (the 0th and 1st syzygy module of $R^n/M$ is $R^n$ and $M$, resp.).
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 176 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 177 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 176 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 177
-->\Hnewline}
${\tt R}^n$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 177 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 178 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 177 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 178
-->\Hnewline}
$\{a \in R \mid aJ \subset I\}$,
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 178 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 179 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 178 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 179
-->\Hnewline}
$\{b \in R^n \mid bJ \subset M\}$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 179 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 180 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 179 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 180
-->\Hnewline}
\noindent
Let $0 \rightarrow\ \bigoplus_a K[x]e_{a,n}\ \rightarrow\ \dots
\rightarrow\ \bigoplus_a K[x]e_{a,0}\ \rightarrow\
@@ -582,27 +582,27 @@
be a minimal resolution of I considered with homogeneous maps of degree 0.
The regularity is the smallest number $s$ with the property deg($e_{a,i})
\leq s+i$ for all $i$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 180 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 181 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 180 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 181
-->\Hnewline}
computes the permutation {\tt v}
which orders the ideal, resp.\ module, {\tt I} by its initial terms,
starting with the smallest, that is, {\tt I(v[i]) < I(v[i+1])} for all
{\tt i}.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 181 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 182 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 181 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 182
-->\Hnewline}
$A_1={\tt matrix}(M)$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 182 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 183 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 182 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 183
-->\Hnewline}
$coker(A_1)=F_0/M$
$$...\longrightarrow F_2 \buildrel{A_2}\over{\longrightarrow} F_1
\buildrel{A_1}\over{\longrightarrow} F_0\longrightarrow F_0/M\longrightarrow
0.$$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 183 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 184 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 183 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 184
-->\Hnewline}
$M_i={\tt module}(A_i)$, i=1..k.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 184 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 185 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 184 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 185
-->\Hnewline}
(${\tt L[i]}=M_i$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 185 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 186 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 185 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 186
-->\Hnewline}
{\tt vandermonde(p,v,d)} computes the (unique) polynomial of degree
@code{d} with prescribed values {\tt v[1],...,v[N]} at the points
{\tt p}$^0,\dots,$ {\tt p}$^{N-1}$, {\tt N=(d+1)}$^n$, $n$ the
@@ -616,18 +616,18 @@
$$ \sum_{\alpha_1+\ldots+\alpha_n\leq d} c_{\alpha_1\ldots\alpha_n} \cdot
{\tt p}_1^{(k-1)\alpha_1}\cdot\dots\cdot {\tt p}_n^{(k-1)\alpha_n} =
{\tt v}[k], \quad k=1,\dots,{\tt N}.$$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 186 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 187 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 186 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 187
-->\Hnewline}
the ground field has to be the field of rational
numbers. Moreover, {\tt ncols(p)==}$n$, the number of variables in the
basering, and all the given generators have to be numbers different from
0,1 or -1. Finally, {\tt ncols(v)==(d+1)$^n$}, and all given generators have
to be numbers.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 187 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 188 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 187 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 188
-->\Hnewline}
$K[[x_1,\ldots,x_n]]$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 188 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 189 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 188 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 189
-->\Hnewline}
$$
\hbox{milnor}(f) = \hbox{dim}_K(K[[x_1,\ldots,x_n]]/\hbox{jacob}(f)),
$$
@@ -636,125 +636,125 @@
\hbox{tjurina}(f) = \hbox{dim}_K(K[[x_1,\ldots,x_n]]/((f)+\hbox{jacob}(f)))
$$
where
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 189 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 190 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 189 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 190
-->\Hnewline}
$\hbox{Loc}_{(x)}K[x_1,\ldots,x_n]$,
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 190 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 191 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 190 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 191
-->\Hnewline}
$K[x_1,\ldots,x_n]$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 191 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 192 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 191 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 192
-->\Hnewline}
$(x_1,\ldots,x_n)$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 192 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 193 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 192 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 193
-->\Hnewline}
$K[x_1,\ldots,x_n]$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 193 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 194 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 193 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 194
-->\Hnewline}
$\hbox{Loc}_{(x)}K[x_1,\ldots,x_n])$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 194 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 195 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 194 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 195
-->\Hnewline}
$\hbox{dim}_K(\hbox{Loc}_{(x,y,z)}K[x,y,z]/\hbox{jacob}(f))$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 195 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 196 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 195 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 196
-->\Hnewline}
$\hbox{dim}_K(K[x,y,z]/\hbox{jacob}(f))$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 196 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 197 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 196 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 197
-->\Hnewline}
$\hbox{dim}_K(\hbox{Loc}_{(x,y,z)}K[x,y,z]/(\hbox{jacob}(f)+(f)))$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 197 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 198 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 197 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 198
-->\Hnewline}
$\hbox{dim}_K(K[x,y,z]/(\hbox{jacob}(f)+(f)))$,
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 198 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 199 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 198 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 199
-->\Hnewline}
$j+(f)$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 199 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 200 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 199 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 200
-->\Hnewline}
$f=0$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 200 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 201 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 200 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 201
-->\Hnewline}
$j+(f)$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 201 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 202 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 201 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 202
-->\Hnewline}
$m$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 202 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 203 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 202 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 203
-->\Hnewline}
$i, j$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 203 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 204 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 203 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 204
-->\Hnewline}
$R$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 204 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 205 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 204 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 205
-->\Hnewline}
$$
\hbox{sat}(i,j)=\{x\in R\;|\; \exists\;n\hbox{ s.t. }
x\cdot(j^n)\subseteq i\}
= \bigcup_{n=1}^\infty i:j^n$$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 205 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 206 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 205 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 206
-->\Hnewline}
$i$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 206 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 207 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 206 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 207
-->\Hnewline}
$j$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 207 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 208 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 207 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 208
-->\Hnewline}
$j$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 208 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 209 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 208 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 209
-->\Hnewline}
$i$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 209 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 210 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 209 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 210
-->\Hnewline}
$i$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 210 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 211 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 210 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 211
-->\Hnewline}
$i$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 211 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 212 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 211 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 212
-->\Hnewline}
$sat(j+(f),m)$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 212 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 213 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 212 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 213
-->\Hnewline}
$dim_{Q(t)}Q(t)[x,y]/j$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 213 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 214 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 213 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 214
-->\Hnewline}
$a \in Q$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 214 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 215 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 214 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 215
-->\Hnewline}
$dim_Q Q[x,y]/j_0$,
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 215 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 216 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 215 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 216
-->\Hnewline}
$j_0=j|_{t=a}$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 216 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 217 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 216 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 217
-->\Hnewline}
$T^1$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 217 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 218 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 217 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 218
-->\Hnewline}
$T^2$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 218 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 219 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 218 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 219
-->\Hnewline}
$j$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 219 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 220 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 219 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 220
-->\Hnewline}
$h_1,\ldots,h_r$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 220 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 221 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 220 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 221
-->\Hnewline}
$I \subset R$ is the ideal generated by $f_1,...,f_s$, then any infinitesimal
deformation of $R/I$ over $K[\varepsilon]/(\varepsilon^2)$ is given
by $f+\varepsilon g$,
where $f=(f_1,...,f_s)$, $g$ a $K$-linear combination of the $h_i$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 221 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 222 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 221 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 222
-->\Hnewline}
$n$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 222 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 223 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 222 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 223
-->\Hnewline}
$d$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 223 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 224 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 223 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 224
-->\Hnewline}
$Z/p$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 224 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 225 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 224 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 225
-->\Hnewline}
$p^k$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 225 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 226 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 225 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 226
-->\Hnewline}
$f=(f_1,\ldots,f_n):k^r\rightarrow k^n$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 226 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 227 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 226 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 227
-->\Hnewline}
$$
\displaylines{
j=J \cap k[x_1,\ldots,x_n], \;\quad\hbox{\rm where}\cr
@@ -762,345 +762,345 @@
k[t_1,\ldots,t_r,x_1,\ldots,x_n]
}
$$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 227 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 228 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 227 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 228
-->\Hnewline}
$t_1,\ldots,t_r$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 228 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 229 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 228 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 229
-->\Hnewline}
$f:(k^r,0)\rightarrow(k^n,0)$,
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 229 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 230 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 229 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 230
-->\Hnewline}
$k^r\times(k^n,0)$,
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 230 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 231 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 230 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 231
-->\Hnewline}
$$\hbox{pr}:k^r\times(k^n,0)\rightarrow(k^n,0)$$
can be computed.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 231 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 232 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 231 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 232
-->\Hnewline}
$\hbox{T}[7]^\prime$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 232 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 233 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 232 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 233
-->\Hnewline}
$P^4$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 233 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 234 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 233 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 234
-->\Hnewline}
$K^3$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 234 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 235 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 234 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 235
-->\Hnewline}
$K^3$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 235 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 236 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 235 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 236
-->\Hnewline}
$P^4$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 236 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 237 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 236 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 237
-->\Hnewline}
$n$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 237 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 238 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 237 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 238
-->\Hnewline}
$n$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 238 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 239 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 238 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 239
-->\Hnewline}
$n$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 239 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 240 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 239 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 240
-->\Hnewline}
$\hbox{\rm ker} / \hbox{\rm Im}$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 240 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 241 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 240 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 241
-->\Hnewline}
$(n-1)$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 241 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 242 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 241 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 242
-->\Hnewline}
$(n-1)$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 242 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 243 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 242 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 243
-->\Hnewline}
$A/(A \cap B)$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 243 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 244 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 243 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 244
-->\Hnewline}
$M$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 244 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 245 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 244 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 245
-->\Hnewline}
$\hbox{Ext}^1(M,M)$, resp.\ $\hbox{Ext}^2(M,M)$,
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 245 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 246 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 245 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 246
-->\Hnewline}
$M$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 246 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 247 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 246 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 247
-->\Hnewline}
$M$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 247 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 248 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 247 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 248
-->\Hnewline}
$\hbox{Ext}^1$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 248 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 249 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 248 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 249
-->\Hnewline}
$\hbox{Ext}^1$, $\hbox{Ext}^2$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 249 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 250 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 249 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 250
-->\Hnewline}
$\hbox{Ext}^k(R/J,R)$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 250 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 251 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 250 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 251
-->\Hnewline}
$J$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 251 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 252 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 251 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 252
-->\Hnewline}
$R$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 252 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 253 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 252 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 253
-->\Hnewline}
($=\hbox{Ext}^1(K,K)$)
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 253 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 254 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 253 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 254
-->\Hnewline}
($=\hbox{Ext}^2(K,K)$)
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 254 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 255 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 254 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 255
-->\Hnewline}
$K=R/m$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 255 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 256 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 255 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 256
-->\Hnewline}
$R=Loc_m K[x,y]/(x^2-y^3)$, $m=(x,y)$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 256 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 257 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 256 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 257
-->\Hnewline}
$\hbox{Ext}^1(m,m)$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 257 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 258 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 257 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 258
-->\Hnewline}
$m$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 258 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 259 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 258 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 259
-->\Hnewline}
$\hbox{Ext}^2(K,K)$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 259 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 260 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 259 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 260
-->\Hnewline}
$\hbox{Ext}^k(R/i,R)$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 260 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 261 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 260 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 261
-->\Hnewline}
$i$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 261 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 262 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 261 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 262
-->\Hnewline}
$f\in k[x_1,\ldots,x_n,t]$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 262 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 263 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 262 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 263
-->\Hnewline}
$t$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 263 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 264 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 263 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 264
-->\Hnewline}
$f=0$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 264 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 265 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 264 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 265
-->\Hnewline}
$t$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 265 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 266 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 265 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 266
-->\Hnewline}
$V(\partial f/\partial x_1,\ldots,\partial f/\partial x_n) \setminus V(f)$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 266 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 267 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 266 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 267
-->\Hnewline}
$V(\partial f/\partial x_1,\ldots,\partial f/\partial x_n)$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 267 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 268 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 267 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 268
-->\Hnewline}
(in $P^n$),
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 268 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 269 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 268 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 269
-->\Hnewline}
(in $k^n$)
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 269 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 270 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 269 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 270
-->\Hnewline}
(in $(k^n,0)$),
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 270 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 271 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 270 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 271
-->\Hnewline}
D$_k$(R)
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 271 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 272 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 271 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 272
-->\Hnewline}
$(m+1)$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 272 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 273 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 272 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 273
-->\Hnewline}
$(n \times n)$-matrix.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 273 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 274 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 273 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 274
-->\Hnewline}
$\hbox{depth}(\hbox{D}_k(R))\geq m(m+1)/2 + m-1$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 274 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 275 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 274 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 275
-->\Hnewline}
$\sum x_i \partial /\partial x_{i+1}$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 275 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 276 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 275 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 276
-->\Hnewline}
$f$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 276 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 277 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 276 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 277
-->\Hnewline}
$f$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 277 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 278 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 277 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 278
-->\Hnewline}
$f$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 278 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 279 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 278 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 279
-->\Hnewline}
$R/I$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 279 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 280 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 279 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 280
-->\Hnewline}
$R/I$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 280 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 281 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 280 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 281
-->\Hnewline}
$A$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 281 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 282 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 281 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 282
-->\Hnewline}
$B$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 282 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 283 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 282 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 283
-->\Hnewline}
$m\times r$ and $m\times s$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 283 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 284 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 283 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 284
-->\Hnewline}
$R$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 284 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 285 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 284 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 285
-->\Hnewline}
$$
R^r \buildrel{A}\over{\longrightarrow}
R^m \buildrel{B}\over{\longleftarrow} R^s\;.
$$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 285 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 286 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 285 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 286
-->\Hnewline}
$R^r \buildrel{A}\over{\longrightarrow}
R^m\longrightarrow
R^m/\hbox{Im}(B) \;.$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 286 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 287 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 286 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 287
-->\Hnewline}
$$
\hbox{\tt modulo}(A,B)=\hbox{ker}(R^r
\buildrel{A}\over{\longrightarrow}R^m/\hbox{Im}(B)) \; .
$$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 287 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 288 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 287 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 288
-->\Hnewline}
$g$, $f_1$, \dots, $f_r\in K[x_1,\ldots,x_n]$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 288 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 289 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 288 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 289
-->\Hnewline}
$f_1$, \dots, $f_r$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 289 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 290 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 289 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 290
-->\Hnewline}
$I=\langle Y_1-f_1,\ldots,Y_r-f_r \rangle \subseteq
K[x_1,\ldots,x_n,Y_1,\ldots,Y_r]$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 290 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 291 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 290 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 291
-->\Hnewline}
$I \cap K[Y_1,\ldots,Y_r]$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 291 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 292 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 291 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 292
-->\Hnewline}
$f_1$, \dots, $f_r$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 292 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 293 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 292 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 293
-->\Hnewline}
$g \in K [f_1,\ldots,f_r]$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 293 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 294 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 293 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 294
-->\Hnewline}
$g \in K[f_1,\ldots,f_r]$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 294 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 295 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 294 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 295
-->\Hnewline}
$g$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 295 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 296 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 295 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 296
-->\Hnewline}
$I$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 296 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 297 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 296 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 297
-->\Hnewline}
$X=(x_1,\ldots,x_n)$ and $Y=(Y_1,\ldots,Y_r)$ with $X>Y$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 297 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 298 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 297 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 298
-->\Hnewline}
$K[Y]$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 298 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 299 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 298 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 299
-->\Hnewline}
$[f_1,...,f_n]$ or $f_1*gen(1)+...+f_n*gen(n)$, where $gen(i)$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 299 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 300 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 299 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 300
-->\Hnewline}
$gen(i)$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 300 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 301 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 300 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 301
-->\Hnewline}
$[f_1,...,f_n]$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 301 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 302 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 301 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 302
-->\Hnewline}
$v=[f_1,...,f_n]$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 302 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 303 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 302 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 303
-->\Hnewline}
nrows($v$)
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 303 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 304 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 303 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 304
-->\Hnewline}
nrows($v$)
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 304 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 305 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 304 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 305
-->\Hnewline}
$r$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 305 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 306 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 305 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 306
-->\Hnewline}
$f_r \not= 0$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 306 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 307 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 306 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 307
-->\Hnewline}
$v$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 307 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 308 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 307 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 308
-->\Hnewline}
$f_i*gen(i)$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 308 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 309 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 308 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 309
-->\Hnewline}
$f_i=0$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 309 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 310 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 309 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 310
-->\Hnewline}
$v$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 310 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 311 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 310 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 311
-->\Hnewline}
$M$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 311 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 312 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 311 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 312
-->\Hnewline}
$v_1,...,v_k$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 312 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 313 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 312 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 313
-->\Hnewline}
nrows($M$)
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 313 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 314 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 313 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 314
-->\Hnewline}
nrows($v_i$).
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 314 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 315 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 314 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 315
-->\Hnewline}
$R$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 315 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 316 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 315 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 316
-->\Hnewline}
$N$,
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 316 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 317 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 316 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 317
-->\Hnewline}
$N = R^n/M$ where $n$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 317 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 318 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 317 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 318
-->\Hnewline}
$N$ and $M \subseteq R^n$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 318 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 319 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 318 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 319
-->\Hnewline}
$M$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 319 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 320 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 319 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 320
-->\Hnewline}
$R^n$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 320 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 321 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 320 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 321
-->\Hnewline}
$N = R^n/M$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 321 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 322 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 321 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 322
-->\Hnewline}
$M$,
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 322 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 323 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 322 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 323
-->\Hnewline}
$M$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 323 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 324 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 323 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 324
-->\Hnewline}
$N = R^n/M$ instead of $M$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 324 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 325 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 324 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 325
-->\Hnewline}
$M$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 325 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 326 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 325 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 326
-->\Hnewline}
$N$ as $N = R^n/$std($M$)).
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 326 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 327 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 326 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 327
-->\Hnewline}
dim$(R^n/M)$, resp.@: dim$_k(R^n/M)$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 327 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 328 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 327 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 328
-->\Hnewline}
$M$,
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 328 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 329 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 328 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 329
-->\Hnewline}
$M$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 329 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 330 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 329 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 330
-->\Hnewline}
$N$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 330 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 331 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 330 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 331
-->\Hnewline}
$N = R^n/M$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 331 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 332 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 331 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 332
-->\Hnewline}
$K[x_1,\ldots,x_n]$,
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 332 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 333 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 332 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 333
-->\Hnewline}
$\hbox{Loc}_{(x)}K[x_1,\ldots,x_n]$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 333 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 334 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 333 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 334
-->\Hnewline}
$\hbox{Wp}(w_1, \ldots, w_n)$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 334 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 335 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 334 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 335
-->\Hnewline}
$\hbox{Ws}(w_1, \ldots, w_n)$)
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 335 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 336 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 335 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 336
-->\Hnewline}
$w_1$, $\ldots$, $w_n$ of $x_1$, $\ldots$, $x_n$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 336 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 337 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 336 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 337
-->\Hnewline}
A monomial ordering (term ordering) on $K[x_1, \ldots, x_n]$ is
a total ordering $<$ on the
set of monomials (power products) $\{x^\alpha \mid \alpha \in \bf{N}^n\}$
@@ -1109,11 +1109,11 @@
x^\alpha < x^\gamma x^\beta$ for any $\gamma \in \bf{N}^n$.
We do not require
$<$ to be a well ordering.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 337 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 338 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 337 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 338
-->\Hnewline}
$M$ in $GL(n,R)$,
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 338 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 339 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 338 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 339
-->\Hnewline}
Global orderings are well orderings (i.e., \hbox{$1 < x_i$} for each variable
$x_i$), local orderings satisfy $1 > x_i$ for each variable. If some
variables are ordered globally and others locally we
call it a mixed ordering. Local or mixed orderings are not well orderings.
@@ -1126,176 +1126,176 @@
denotes the leading monomial of $g$, i.e., the biggest monomial of $g$ with
respect to $<$. The result of any computation which uses standard basis
computations has to be interpreted in Loc $K[x]$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 339 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 340 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 339 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 340
-->\Hnewline}
For all these orderings: Loc $K[x]$ = $K[x]$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 340 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 341 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 340 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 341
-->\Hnewline}
$x^\alpha < x^\beta \Leftrightarrow \exists\; 1 \le i \le n :
\alpha_1 = \beta_1, \ldots, \alpha_{i-1} = \beta_{i-1}, \alpha_i <
\beta_i$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 341 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 342 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 341 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 342
-->\Hnewline}
$x^\alpha < x^\beta \Leftrightarrow \exists\; 1 \le i \le n :
\alpha_n = \beta_n,
\ldots, \alpha_{i+1} = \beta_{i+1}, \alpha_i > \beta_i.$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 342 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 343 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 342 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 343
-->\Hnewline}
let $\deg(x^\alpha) = \alpha_1 + \cdots + \alpha_n,$ then
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 343 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 344 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 343 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 344
-->\Hnewline}
$x^\alpha < x^\beta \Leftrightarrow \deg(x^\alpha) < \deg(x^\beta)$ or
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 344 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 345 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 344 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 345
-->\Hnewline}
\phantom{$x^\alpha < x^\beta \Leftrightarrow $}$ \deg(x^\alpha) =
\deg(x^\beta)$ and $\exists\ 1 \le i \le n: \alpha_n = \beta_n,
\ldots, \alpha_{i+1} = \beta_{i+1}, \alpha_i > \beta_i.$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 345 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 346 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 345 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 346
-->\Hnewline}
let $\deg(x^\alpha) = \alpha_1 + \cdots + \alpha_n,$ then
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 346 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 347 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 346 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 347
-->\Hnewline}
$x^\alpha < x^\beta \Leftrightarrow \deg(x^\alpha) < \deg(x^\beta)$ or
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 347 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 348 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 347 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 348
-->\Hnewline}
\phantom{ $x^\alpha < x^\beta \Leftrightarrow $} $\deg(x^\alpha) =
\deg(x^\beta)$ and $\exists\ 1 \le i \le n:\alpha_1 = \beta_1,
\ldots, \alpha_{i-1} = \beta_{i-1}, \alpha_i < \beta_i.$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 348 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 349 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 348 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 349
-->\Hnewline}
let $w_1, \ldots, w_n$ be positive integers. Then ${\tt wp}(w_1, \ldots,
w_n)$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 349 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 350 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 349 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 350
-->\Hnewline}
$\deg(x^\alpha) = w_1 \alpha_1 + \cdots + w_n\alpha_n.$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 350 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 351 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 350 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 351
-->\Hnewline}
let $w_1, \ldots, w_n$ be positive integers. Then ${\tt Wp}(w_1, \ldots,
w_n)$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 351 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 352 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 351 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 352
-->\Hnewline}
$\deg(x^\alpha) = w_1 \alpha_1 + \cdots + w_n\alpha_n.$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 352 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 353 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 352 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 353
-->\Hnewline}
Loc $K[x]$ = $K[x]_{(x)}$,
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 353 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 354 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 353 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 354
-->\Hnewline}
$K[x]$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 354 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 355 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 354 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 355
-->\Hnewline}
\ $(x_1, ..., x_n)$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 355 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 356 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 355 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 356
-->\Hnewline}
$x^\alpha < x^\beta \Leftrightarrow \exists\; 1 \le i \le n :
\alpha_1 = \beta_1, \ldots, \alpha_{i-1} = \beta_{i-1}, \alpha_i >
\beta_i$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 356 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 357 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 356 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 357
-->\Hnewline}
let $\deg(x^\alpha) = \alpha_1 + \cdots + \alpha_n,$ then
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 357 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 358 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 357 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 358
-->\Hnewline}
$x^\alpha < x^\beta \Leftrightarrow \deg(x^\alpha) > \deg(x^\beta)$ or
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 358 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 359 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 358 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 359
-->\Hnewline}
\phantom{ $x^\alpha < x^\beta \Leftrightarrow$}$ \deg(x^\alpha) =
\deg(x^\beta)$ and $\exists\ 1 \le i \le n: \alpha_n = \beta_n,
\ldots, \alpha_{i+1} = \beta_{i+1}, \alpha_i > \beta_i.$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 359 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 360 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 359 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 360
-->\Hnewline}
let $\deg(x^\alpha) = \alpha_1 + \cdots + \alpha_n,$ then
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 360 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 361 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 360 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 361
-->\Hnewline}
$x^\alpha < x^\beta \Leftrightarrow \deg(x^\alpha) > \deg(x^\beta)$ or
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 361 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 362 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 361 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 362
-->\Hnewline}
\phantom{ $ x^\alpha < x^\beta \Leftrightarrow$}$ \deg(x^\alpha) =
\deg(x^\beta)$ and $\exists\ 1 \le i \le n:\alpha_1 = \beta_1,
\ldots, \alpha_{i-1} = \beta_{i-1}, \alpha_i < \beta_i.$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 362 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 363 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 362 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 363
-->\Hnewline}
${\tt ws}(w_1, \ldots, w_n),\; w_1$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 363 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 364 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 363 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 364
-->\Hnewline}
$w_2,\ldots,w_n$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 364 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 365 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 364 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 365
-->\Hnewline}
$\deg(x^\alpha) = w_1 \alpha_1 + \cdots + w_n\alpha_n.$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 365 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 366 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 365 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 366
-->\Hnewline}
${\tt Ws}(w_1, \ldots, w_n),\; w_1$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 366 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 367 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 366 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 367
-->\Hnewline}
$w_2,\ldots,w_n$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 367 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 368 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 367 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 368
-->\Hnewline}
$\deg(x^\alpha) = w_1 \alpha_1 + \cdots + w_n\alpha_n.$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 368 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 369 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 368 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 369
-->\Hnewline}
$\{ x^a e_i \mid a \in N^n, 1 \leq i \leq r \}$ in Loc $K[x]^r$ = Loc
$K[x]e_1
+ \ldots +$Loc $K[x]e_r$, where $e_1, \ldots, e_r$ denote the canonical
generators of Loc $K[x]^r$, the r-fold direct sum of Loc $K[x]$.
(The function {\tt gen(i)} yields $e_i$).
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 369 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 370 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 369 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 370
-->\Hnewline}
Loc $K[x]^r$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 370 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 371 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 370 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 371
-->\Hnewline}
Loc $K[x]$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 371 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 372 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 371 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 372
-->\Hnewline}
$<_m = (<,C)$ denotes the module ordering (giving priority to the
coefficients):
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 372 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 373 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 372 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 373
-->\Hnewline}
\quad \quad $x^\alpha e_i <_m x^\beta e_j \Leftrightarrow x^\alpha <
x^\beta$ or ($x^\alpha = x^\beta $ and $ i < j$).
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 373 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 374 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 373 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 374
-->\Hnewline}
$<_m = (C, <)$ denotes the module ordering (giving priority to the component):
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 374 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 375 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 374 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 375
-->\Hnewline}
\quad \quad $x^\alpha e_i <_m x^\beta e_j \Leftrightarrow i < j$ or ($
i = j $ and $ x^\alpha < x^\beta $).
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 375 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 376 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 375 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 376
-->\Hnewline}
$<_m = (<,c)$ denotes the module ordering (giving priority to the
coefficients):
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 376 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 377 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 376 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 377
-->\Hnewline}
\quad \quad $x^\alpha e_i <_m x^\beta e_j \Leftrightarrow x^\alpha <
x^\beta$ or ($x^\alpha = x^\beta $ and $ i > j$).
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 377 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 378 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 377 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 378
-->\Hnewline}
$<_m = (c, <)$ denotes the module ordering (giving priority to the component):
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 378 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 379 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 378 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 379
-->\Hnewline}
\quad \quad $x^\alpha e_i <_m x^\beta e_j \Leftrightarrow i > j$ or ($
i = j $ and $ x^\alpha < x^\beta $).
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 379 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 380 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 379 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 380
-->\Hnewline}
The output of a vector $v$ in $K[x]^r$ with components $v_1,
\ldots, v_r$ has the format $v_1 * gen(1) + \ldots + v_r * gen(r)$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 380 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 381 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 380 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 381
-->\Hnewline}
In this case a vector is written as $[v_1, \ldots, v_r]$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 381 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 382 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 381 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 382
-->\Hnewline}
$M$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 382 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 383 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 382 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 383
-->\Hnewline}
$(n \times n)$-matrix
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 383 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 384 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 383 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 384
-->\Hnewline}
$M_1, \ldots, M_n$ the rows of $M$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 384 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 385 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 384 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 385
-->\Hnewline}
\quad \quad $x^a < x^b \Leftrightarrow \exists\ 1 \leq i \leq n :
M_1 a = \; M_1 b, \ldots, M_{i-1} a = \; M_{i-1} b$ and $M_i a < \; M_i b$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 385 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 386 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 385 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 386
-->\Hnewline}
$x^a < x^b$
if and only if $M a$ is smaller than $M b$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 386 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 387 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 386 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 387
-->\Hnewline}
$\quad$ lp:
$\left(\matrix{
@@ -1360,8 +1360,8 @@
1 & 0 & 0 \cr
0 & 1 & 0 \cr
}\right)$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 387 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 388 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 387 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 388
-->\Hnewline}
$\quad$ (dp(3), wp(1,2,3)):
$\left(\matrix{
1& 1& 1& 0& 0& 0 \cr
@@ -1381,8 +1381,8 @@
0& 0& 0& 0& 0& -1 \cr
0& 0& 0& 0& -1& 0 \cr
}\right)$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 388 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 389 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 388 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 389
-->\Hnewline}
$\quad$ (dp(3), a(1,2,3),dp(3)):
$\left(\matrix{
1& 1& 1& 0& 0& 0 \cr
@@ -1404,49 +1404,49 @@
0& 0& 0& 0& 0 & -1 \cr
0& 0& 0& 0& -1& 0 \cr
}\right)$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 389 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 390 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 389 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 390
-->\Hnewline}
$n$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 390 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 391 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 390 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 391
-->\Hnewline}
$n \times n$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 391 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 392 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 391 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 392
-->\Hnewline}
$x = (x_1, \ldots, x_n)$ and $y = (y_1, \ldots, y_m)$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 392 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 393 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 392 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 393
-->\Hnewline}
$<_1$ a monomial
ordering on $K[x]$ and $<_2$ a monomial ordering on $K[y]$. The product
ordering (or block ordering) $<\ := (<_1,<_2)$ on $K[x,y]$ is the following:
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 393 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 394 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 393 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 394
-->\Hnewline}
\quad \quad $x^a y^b < x^A y^B \Leftrightarrow x^a <_1 x^A $ or ($x^a =
x^A$ and $y^b <_2 y^B$).
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 394 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 395 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 394 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 395
-->\Hnewline}
${\tt a}(w_1, \ldots, w_n),\; $
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 395 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 396 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 395 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 396
-->\Hnewline}
$w_1,\ldots,w_n$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 396 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 397 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 396 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 397
-->\Hnewline}
$\deg(x^\alpha) = w_1 \alpha_1 + \cdots + w_n\alpha_n$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 397 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 398 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 397 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 398
-->\Hnewline}
$$\deg(x^\alpha) < \deg(x^\beta) \Rightarrow x^\alpha < x^\beta,$$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 398 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 399 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 398 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 399
-->\Hnewline}
$$\deg(x^\alpha) > \deg(x^\beta) \Rightarrow x^\alpha > x^\beta. $$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 399 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 400 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 399 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 400
-->\Hnewline}
Let $R = \hbox{Loc}_< K[\underline{x}]$ and let $I$ be a submodule of $R^r$.
Note that for r=1 this means that $I$ is an ideal in $R$.
Denote by $L(I)$ the submodule of $R^r$ generated by the leading terms
of elements of $I$, i.e. by $\left\{L(f) \mid f \in I\right\}$.
Then $f_1, \ldots, f_s \in I$ is called a {\bf standard basis} of $I$
if $L(f_1), \ldots, L(f_s)$ generate $L(I)$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 400 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 401 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 400 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 401
-->\Hnewline}
A function $\hbox{NF} : R^r \times \{G \mid G\ \hbox{ a standard
basis}\} \to R^r, (p,G) \mapsto \hbox{NF}(p|G)$, is called a {\bf normal
form} if for any $p \in R^r$ and any standard basis $G$ the following
@@ -1456,19 +1456,19 @@
\noindent
$\hbox{NF}(p|G)$ is called a {\bf normal form of} $p$ {\bf with
respect to} $G$ (note that such a function is not unique).
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 401 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 402 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 401 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 402
-->\Hnewline}
For a standard basis $G$ of $I$ the following holds:
$f \in I$ if and only if $\hbox{NF}(f,G) = 0$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 402 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 403 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 402 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 403
-->\Hnewline}
Let \hbox{$I \subseteq K[\underline{x}]^r$} be a homogeneous module, then the
Hilbert function
$H_I$ of $I$ (see below)
and the Hilbert function $H_{L(I)}$ of the leading module $L(I)$
coincide, i.e.,
$H_I=H_{L(I)}$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 403 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 404 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 403 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 404
-->\Hnewline}
Let M $=\bigoplus_i M_i$ be a graded module over $K[x_1,..,x_n]$ with
respect to weights $(w_1,..w_n)$.
The {\bf Hilbert function} of $M$, $H_M$, is defined (on the integers) by
@@ -1485,41 +1485,41 @@
If \hbox{$P(t)=\sum_{k=0}^N a_k t^k$}, and \hbox{$d = dim(M)$},
then \hbox{$H_M(s)=\sum_{k=0}^N a_k$ ${d+s-k-1}\choose{d-1}$}
(the {\bf Hilbert polynomial}) for $s \ge N$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 404 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 405 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 404 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 405
-->\Hnewline}
Generalizing these to quasihomogeneous modules we get
$$\hbox{HP}_M(t)={Q(t)\over {\Pi_{i=1}^n(1-t^{w_i})}}$$
where $Q(t)$ is a polynomial in ${\bf Z}[t]$.
$Q(t)$ is called the {\bf first (weighted) Hilbert series} of M.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 405 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 406 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 405 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 406
-->\Hnewline}
Let $R$ be a quotient of $\hbox{Loc}_< K[\underline{x}]$ and let
\hbox{$I=(g_1, ..., g_s)$} be a submodule of $R^r$.
Then the {\bf module of syzygies} (or {\bf 1st syzygy module}, {\bf module of
relations}) of $I$, syz($I$), is defined to be the kernel of the map \hbox{$R^s
\rightarrow R^r,\; \sum_{i=1}^s w_ie_i \mapsto \sum_{i=1}^s w_ig_i$.}
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 406 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 407 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 406 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 407
-->\Hnewline}
$(k-1)$-st
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 407 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 408 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 407 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 408
-->\Hnewline}
Note, that the syzygy modules of $I$ depend on a choice of generators $g_1,
..., g_s$.
But one can show that they depend on $I$ uniquely up to direct summands.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 408 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 409 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 408 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 409
-->\Hnewline}
Let $I=(g_1,...,g_s)\subseteq R^r$ and $M= R^r/I$.
A {\bf free resolution of $M$} is a long exact sequence
$$...\longrightarrow F_2 \buildrel{A_2}\over{\longrightarrow} F_1
\buildrel{A_1}\over{\longrightarrow} F_0\longrightarrow M\longrightarrow
0,$$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 409 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 410 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 409 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 410
-->\Hnewline}
$A_1$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 410 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 411 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 410 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 411
-->\Hnewline}
$I$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 411 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 412 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 411 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 412
-->\Hnewline}
$R=\hbox{Loc}_< K[\underline{x}]$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 412 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 413 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 412 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 413
-->\Hnewline}
Let $R$ be a graded ring (e.g., $R = \hbox{Loc}_< K[\underline{x}]$) and
let $I \subset R^r$ be a graded submodule. Let
$$
@@ -1533,19 +1533,19 @@
syzygy module of $R^r/I$ (i.e., the $(j-1)$-st syzygy module of
$I$). Note, that by definition the $0$-th syzygy module of $R^r/I$ is $R^r$
and the 1st syzygy module of $R^r/I$ is $I$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 413 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 414 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 413 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 414
-->\Hnewline}
$I$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 414 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 415 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 414 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 415
-->\Hnewline}
$s$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 415 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 416 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 415 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 416
-->\Hnewline}
$$
\hbox{deg}(e_{a,j}) \le s+j-1 \quad \hbox{for all $j$.}
$$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 416 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 417 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 416 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 417
-->\Hnewline}
Let $<$ be the lexicographical ordering on $R=K[x_1,...,x_n]$ with $x_1
< ... < x_n$.
For $f \in R$ let lvar($f$) (the leading variable of $f$) be the largest
@@ -1581,8 +1581,8 @@
where $I_i=\{\hbox{ini}(f) \mid f \in T_i \}$. Such a set
$\{T_1,...,T_l\}$ is called an {\bf irreducible characteristic series} of
the ideal $(G)$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 417 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 418 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 417 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 418
-->\Hnewline}
Let $f\colon(C^{n+1},0)\rightarrow(C,0)$ be a complex isolated hypersurface
singularity given by a polynomial with algebraic coefficients which we also
denote by $f$.
Let $O=C[x_0,\ldots,x_n]_{(x_0,\ldots,x_n)}$ be the local ring at the origin
and $J_f$ the Jacobian ideal of $f$.
@@ -1613,80 +1613,80 @@
The cone itself being a $\mu$-constant deformation of $x_0^d+\dots+x_n^d=0$,
the singularities are bounded by the spectrum of $x_0^d+\dots+x_n^d$.
Using the library {\tt gaussman.lib} one can compute the {\bf monodromy}, the
V-filtration on $H''/H'$, and the spectrum.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 418 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 419 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 418 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 419
-->\Hnewline}
$f=x^5+x^2y^2+y^5$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 419 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 420 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 419 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 420
-->\Hnewline}
$M$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 420 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 421 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 420 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 421
-->\Hnewline}
$\exp(2\pi iM)$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 421 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 422 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 421 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 422
-->\Hnewline}
$f$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 422 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 423 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 422 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 423
-->\Hnewline}
$M$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 423 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 424 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 423 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 424
-->\Hnewline}
$H''/H'$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 424 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 425 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 424 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 425
-->\Hnewline}
$C$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 425 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 426 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 425 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 426
-->\Hnewline}
$H''/H'$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 426 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 427 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 426 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 427
-->\Hnewline}
$O/J_f\cong H''/H'$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 427 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 428 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 427 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 428
-->\Hnewline}
If the principal part of $f$ is $C$-nondegenerate, one can compute the
spectrum using the library {\tt spectrum.lib}.
In this case, the V-filtration on $H''$ coincides with the Newton-filtration
on $H''$ which allows to compute the spectrum more efficiently.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 428 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 429 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 428 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 429
-->\Hnewline}
$\tilde{E}_6$ on a surface $X\subset{P}^3$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 429 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 430 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 429 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 430
-->\Hnewline}
$Q[x,y,z]$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 430 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 431 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 430 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 431
-->\Hnewline}
$f$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 431 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 432 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 431 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 432
-->\Hnewline}
$\mu(f)$, the geometric genus $p_g(f)$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 432 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 433 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 432 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 433
-->\Hnewline}
$x^7+y^7+z^7=0$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 433 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 434 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 433 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 434
-->\Hnewline}
${3 \over 7}, {4 \over 7}, {5 \over 7}, {6 \over 7}, {1 \over 1},
{8 \over 7}, {9 \over 7}, {10 \over 7}, {11 \over 7}, {12 \over 7},
{13 \over 7}, {2 \over 1}, {15 \over 7}, {16 \over 7}, {17 \over 7},
{18 \over 7}$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 434 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 435 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 434 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 435
-->\Hnewline}
The singularities of type $\tilde{E}_6$ form a
$\mu$-constant one parameter family given by
$x^3+y^3+z^3+\lambda xyz=0,\quad \lambda^3\neq-27$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 435 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 436 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 435 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 436
-->\Hnewline}
$x^3+y^3+z^3$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 436 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 437 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 436 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 437
-->\Hnewline}
$\tilde{E}_6$ on a septic in $P^3$. But $x^7+y^7+z^7$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 437 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 438 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 437 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 438
-->\Hnewline}
$\tilde{E}_6$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 438 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 439 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 438 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 439
-->\Hnewline}
$f$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 439 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 440 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 439 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 440
-->\Hnewline}
$f$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 440 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 441 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 440 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 441
-->\Hnewline}
Let $A$ denote an $m\times n$ matrix with integral coefficients. For $u
\in Z\!\!\! Z^n$, we define $u^+,u^-$ to be the uniquely determined
vectors with nonnegative coefficients and disjoint support (i.e.,
@@ -1705,11 +1705,11 @@
$$ I_A:=I:(x_1\cdot\ldots\cdot x_n)^\infty $$
where
$$ I=<x^{v_i^+}-x^{v_i^-}|i=1,\ldots,r> $$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 441 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 442 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 441 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 442
-->\Hnewline}
section Algorithms.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 442 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 443 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 442 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 443
-->\Hnewline}
computes $I_A$ via the
extended matrix $B=(I_m|A)$,
where $I_m$ is the $m\times m$ unity matrix. A lattice basis of $B$ is
@@ -1725,8 +1725,8 @@
variables because all variables are invertible modulo $I_2$. Now $I_A$
can be computed from $I_2$ by eliminating the variables
$t,y_1,\ldots,y_m$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 443 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 444 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 443 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 444
-->\Hnewline}
basis $v_1,\ldots,v_r$ for the integer kernel of $A$ using the
LLL-algorithm. The ideal corresponding to the lattice basis vectors
$$ I_1=<x^{v_i^+}-x^{v_i^-}|i=1,\ldots,r> $$
@@ -1735,8 +1735,8 @@
generator $t\cdot x_1\cdot\ldots\cdot x_n -1$ to obtain an ideal $I_2$
in $K[t,x_1,\ldots,x_n]$ from which one computes $I_A$ by elimination of
$t$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 444 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 445 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 444 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 445
-->\Hnewline}
compute $I_A$ without any auxiliary variables, provided that $A$ contains a
vector $w$
with positive coefficients in its row space. This is a real restriction,
i.e., the algorithm will not necessarily work in the general case.
@@ -1762,8 +1762,8 @@
This procedure involves $n$ Groebner basis computations. Actually, this
number can be reduced to at most $n/2$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 445 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 446 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 445 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 446
-->\Hnewline}
to $n/2$ Groebner basis
computations. It needs no auxiliary variables, but a supplementary
precondition; namely, the existence of a vector without zero components
@@ -1794,14 +1794,14 @@
involved in $x^{a_j}$ nor in $x^{b_j}$). Then
$$\{x^{a_j} - x_i^{r_j} x^{b_j} | j\in J \}$$
is a generating set for $I_A$.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 446 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 447 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 446 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 447
-->\Hnewline}
variable $u$ and one supplementary generator $x_1\cdot\ldots\cdot x_n -
u$ (instead of the generator $t\cdot x_1\cdot\ldots\cdot x_n -1$ in
the algorithm of Pottier). The algorithm uses a quite unusual technique to
get rid of the variable $u$ again.
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 447 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 448 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 447 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 448
-->\Hnewline}
Let $A$ be an $m\times n$ matrix with integral coefficients, $b\in
Z\!\!\! Z^m$ and $c\in Z\!\!\! Z^n$. The problem
$$ \min\{c^T x | x\in Z\!\!\! Z^n, Ax=b, x\geq 0\hbox{
@@ -1819,51 +1819,51 @@
First we assume that an initial solution $v$ (i.e., $v\in Z\!\!\!
Z^n, v\geq 0, Av=b$) is already known. We obtain the optimal solution
$v_0$ (i.e., with $c^T v_0$ minimal) by the following procedure:
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 448 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 449 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 448 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 449
-->\Hnewline}
$>_c$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 449 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 450 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 449 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 450
-->\Hnewline}
$x^v$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 450 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 451 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 450 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 451
-->\Hnewline}
$x^(v_0)$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 451 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 452 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 451 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 452
-->\Hnewline}
$v_0$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 452 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 453 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 452 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 453
-->\Hnewline}
$b$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 453 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 454 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 453 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 454
-->\Hnewline}
Faug\`ere,
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 454 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 455 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 454 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 455
-->\Hnewline}
$ 2*genus-2 < deg(G) < size(D) $
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 455 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 456 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 455 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 456
-->\Hnewline}
$\Omega(G-D)$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 456 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 457 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 456 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 457
-->\Hnewline}
$ 2*genus-2 < deg(G) < size(D) $
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 457 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 458 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 457 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 458
-->\Hnewline}
$epsilon$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 458 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 459 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 458 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 459
-->\Hnewline}
$delta$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 459 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 460 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 459 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 460
-->\Hnewline}
$delta$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 460 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 461 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 460 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 461
-->\Hnewline}
$epsilon + genus$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 461 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 462 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 461 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 462
-->\Hnewline}
$epsilon:=[(deg(G)-3*genus+1)/2]$
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 462 -->\Hnewline}
-\HCode{\Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 463 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 462 -->\Hnewline
\Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin sing_tex4ht_tex tex 463
-->\Hnewline}
$ 2*genus-2 < deg(G) < size(D) $
-\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 463 -->\Hnewline}
+\HCode{\Hnewline <!-- tex4ht_end sing_tex4ht_tex tex 463 -->\Hnewline
\Hnewline}
\bye
Index: test/formatting/res/tex_httex_mediawiki/tex
===================================================================
RCS file: test/formatting/res/tex_httex_mediawiki/tex
diff -N test/formatting/res/tex_httex_mediawiki/tex
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res/tex_httex_mediawiki/tex 22 Oct 2009 20:23:20 -0000
1.1
@@ -0,0 +1,40 @@
+<div id="Top"></div>
+<div id="Tests"></div>
+== Tests ==
+
+Now tex on the same line some <!--l. 6-->
+<center class="math-display">[[Image:tex_tex4ht_tex0x.png| N (
)2
+Ï2 = â yi --(a+-bxi)
+i=1 Ïi
+]]</center><!--l. 11-->
+bidule
+Some text one the line following @end tex
+
+Now tex on the following line, valid fot tex (with @end tex on a line).
+some <!--l. 15-->
+tex <span class="TEX">T<span class="E">E</span>X</span>
+
+Same that @html (but empty following line not ignored).
+
+Test of @math
+Here some <math>{x^i}\over{\tan y}</math>.
+
+Maths with protected \:
+<math>a \ b</math>.
+
+Maths with code @-command:
+
+<math><code>math code</code></math>
+
+Maths with code @-command and braces:
+
+<math> \underline{<code>math \hbox{ code }}</code>
\sum_{i}{\underline{f}}</math>
+
address@hidden outside of math
+
address@hidden
+
+
+----
+
+This document was generated on <i>a sunny day</i> using
[http://www.nongnu.org/texi2html/ <i>texi2html</i>].
Index: test/formatting/res/tex_httex_mediawiki/tex.2
===================================================================
RCS file: test/formatting/res/tex_httex_mediawiki/tex.2
diff -N test/formatting/res/tex_httex_mediawiki/tex.2
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res/tex_httex_mediawiki/tex.2 22 Oct 2009 20:23:20
-0000 1.1
@@ -0,0 +1 @@
+dvipng warning: DVI magnification of 1000 over-ridden by user (1400)
tex.texi:42: warning: Unknown command address@hidden'
Index: test/formatting/res/tex_httex_mediawiki/tex_tex4ht_math.texi
===================================================================
RCS file: test/formatting/res/tex_httex_mediawiki/tex_tex4ht_math.texi
diff -N test/formatting/res/tex_httex_mediawiki/tex_tex4ht_math.texi
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res/tex_httex_mediawiki/tex_tex4ht_math.texi 22 Oct
2009 20:23:20 -0000 1.1
@@ -0,0 +1,5 @@
+\input texinfo
address@hidden tex_tex4ht_math.info
address@hidden Automatically generated
+
address@hidden
Index: test/formatting/res/tex_httex_mediawiki/tex_tex4ht_tex.4ct
===================================================================
RCS file: test/formatting/res/tex_httex_mediawiki/tex_tex4ht_tex.4ct
diff -N test/formatting/res/tex_httex_mediawiki/tex_tex4ht_tex.4ct
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res/tex_httex_mediawiki/tex_tex4ht_tex.4ct 22 Oct 2009
20:23:20 -0000 1.1
@@ -0,0 +1,2 @@
+\expandafter\ifx\csname doTocEntry\endcsname\relax \expandafter\endinput\fi
+\par
Index: test/formatting/res/tex_httex_mediawiki/tex_tex4ht_tex.4tc
===================================================================
RCS file: test/formatting/res/tex_httex_mediawiki/tex_tex4ht_tex.4tc
diff -N test/formatting/res/tex_httex_mediawiki/tex_tex4ht_tex.4tc
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res/tex_httex_mediawiki/tex_tex4ht_tex.4tc 22 Oct 2009
20:23:20 -0000 1.1
@@ -0,0 +1 @@
+\expandafter\ifx\csname doTocEntry\endcsname\relax \expandafter\endinput\fi
Index: test/formatting/res/tex_httex_mediawiki/tex_tex4ht_tex.css
===================================================================
RCS file: test/formatting/res/tex_httex_mediawiki/tex_tex4ht_tex.css
diff -N test/formatting/res/tex_httex_mediawiki/tex_tex4ht_tex.css
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res/tex_httex_mediawiki/tex_tex4ht_tex.css 22 Oct 2009
20:23:20 -0000 1.1
@@ -0,0 +1,43 @@
+
+/* start css.sty */
+.cmr-7{font-size:70%;}
+.cmmi-10{font-style: italic;}
+.cmmi-7{font-size:70%;font-style: italic;}
+p.noindent { text-indent: 0em }
+td p.noindent { text-indent: 0em; margin-top:0em; }
+p.nopar { text-indent: 0em; }
+p.indent{ text-indent: 1.5em }
address@hidden print {div.crosslinks {visibility:hidden;}}
+a img { border-top: 0; border-left: 0; border-right: 0; }
+center { margin-top:1em; margin-bottom:1em; }
+td center { margin-top:0em; margin-bottom:0em; }
+.Canvas { position:relative; }
+img.math{vertical-align:middle;}
+.obeylines-h,.obeylines-v {white-space: nowrap; }
+div.obeylines-v p { margin-top:0; margin-bottom:0; }
+.overline{ text-decoration:overline; }
+.overline img{ border-top: 1px solid black; }
+td.displaylines {text-align:center; white-space:nowrap;}
+.centerline {text-align:center;}
+.rightline {text-align:right;}
+span.TEX {letter-spacing: -0.125em; }
+span.TEX span.E{ position:relative;top:0.5ex;left:-0.0417em;}
+a span.TEX span.E {text-decoration: none; }
+.underline{ text-decoration:underline; }
+.underline img{ border-bottom: 1px solid black; margin-bottom:1pt; }
+div.proclaim { margin-top: 1em; margin-bottom: 1em; }
+p.item {text-indent:-2em; margin-left:2em;}
+p.itemitem {text-indent:-2em; margin-left:4em;}
+span.item, span.itemitem {width:2em; margin-right:0.4em;}
+td.eqalign3 { text-align:right; margin-left:10em;}
+.eqalign td { white-space: nowrap; }
+div.eqalign {text-align:center;}
+td.eqalignno3, td.leqalignno3 { text-align:right; margin-left:10em;}
+.leqalignno td, .eqalignno td { white-space: nowrap; }
+.leqalignno td.noalign, .eqalignno td.noalign { width:5%; white-space: normal;
}
+table.leqalignno, table.eqalignno {width:100%;}
+img.cdots{vertical-align:middle;}
+div.pmatrix {text-align:center;}
+table.pmatrix {width:100%;}
+/* end css.sty */
+
Index: test/formatting/res/tex_httex_mediawiki/tex_tex4ht_tex.lg
===================================================================
RCS file: test/formatting/res/tex_httex_mediawiki/tex_tex4ht_tex.lg
diff -N test/formatting/res/tex_httex_mediawiki/tex_tex4ht_tex.lg
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res/tex_httex_mediawiki/tex_tex4ht_tex.lg 22 Oct 2009
20:23:20 -0000 1.1
@@ -0,0 +1,55 @@
+htfcss: cmmi font-style: italic;
+htfcss: cmmib font-style: italic; font-weight: bold;
+File: tex_tex4ht_tex.html
+File: tex_tex4ht_tex.css
+File: tex_tex4ht_tex.tmp
+Css: p.noindent { text-indent: 0em }
+Css: td p.noindent { text-indent: 0em; margin-top:0em; }
+Css: p.nopar { text-indent: 0em; }
+Css: p.indent{ text-indent: 1.5em }
+Css: @media print {div.crosslinks {visibility:hidden;}}
+Css: a img { border-top: 0; border-left: 0; border-right: 0; }
+Font_Css("4"): .small-caps{font-variant: small-caps; }
+Font_Css("10"): .htf-cmbx {font-weight: bold; font-style:normal;}
+Font_Css("12"): .htf-calligraphy {font-family:cursive}
+Font_Css("14"): .htf-italic {font-style: italic;}
+Font_Css("16"): .htf-bold {font-weight: bold;}
+Font_Css("12"): .htf-calligraphy-bold {font-family:cursive ; font-weight:
bold; }
+Css: center { margin-top:1em; margin-bottom:1em; }
+Css: td center { margin-top:0em; margin-bottom:0em; }
+Css: .Canvas { position:relative; }
+Css: img.math{vertical-align:middle;}
+Css: .obeylines-h,.obeylines-v {white-space: nowrap; }
+Css: div.obeylines-v p { margin-top:0; margin-bottom:0; }
+Css: .overline{ text-decoration:overline; }
+Css: .overline img{ border-top: 1px solid black; }
+Css: td.displaylines {text-align:center; white-space:nowrap;}
+Css: .centerline {text-align:center;}
+Css: .rightline {text-align:right;}
+Css: span.TEX {letter-spacing: -0.125em; }
+Css: span.TEX span.E{ position:relative;top:0.5ex;left:-0.0417em;}
+Css: a span.TEX span.E {text-decoration: none; }
+Css: .underline{ text-decoration:underline; }
+Css: .underline img{ border-bottom: 1px solid black; margin-bottom:1pt; }
+Css: div.proclaim { margin-top: 1em; margin-bottom: 1em; }
+Css: p.item {text-indent:-2em; margin-left:2em;}
+Css: p.itemitem {text-indent:-2em; margin-left:4em;}
+Css: span.item, span.itemitem {width:2em; margin-right:0.4em;}
+Css: td.eqalign3 { text-align:right; margin-left:10em;}
+Css: .eqalign td { white-space: nowrap; }
+Css: div.eqalign {text-align:center;}
+Css: td.eqalignno3, td.leqalignno3 { text-align:right; margin-left:10em;}
+Css: .leqalignno td, .eqalignno td { white-space: nowrap; }
+Css: .leqalignno td.noalign, .eqalignno td.noalign { width:5%; white-space:
normal; }
+Css: table.leqalignno, table.eqalignno {width:100%;}
+Css: img.cdots{vertical-align:middle;}
+Css: div.pmatrix {text-align:center;}
+Css: table.pmatrix {width:100%;}
+--- needs --- tex_tex4ht_tex.idv[1] ==> tex_tex4ht_tex0x.png ---
+--- characters ---
+Font("cmr","10","10","100")
+Font("cmr","7","7","100")
+Font("cmmi","10","10","100")
+Font("cmmi","7","7","100")
+Font("cmsy","10","10","100")
+Font("cmex","10","10","100")
Index: test/formatting/res/tex_httex_mediawiki/tex_tex4ht_tex.tex
===================================================================
RCS file: test/formatting/res/tex_httex_mediawiki/tex_tex4ht_tex.tex
diff -N test/formatting/res/tex_httex_mediawiki/tex_tex4ht_tex.tex
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res/tex_httex_mediawiki/tex_tex4ht_tex.tex 22 Oct 2009
20:23:20 -0000 1.1
@@ -0,0 +1,18 @@
+% Automatically generated
+\csname tex4ht\endcsname
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin tex_tex4ht_tex tex 1 -->\Hnewline}
+ some
+
+$$ \chi^2 = \sum_{i=1}^N
+ \left(y_i - (a + b x_i)
+ \over \sigma_i\right)^2 $$
+
+
+\HCode{\Hnewline <!-- tex4ht_end tex_tex4ht_tex tex 1 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin tex_tex4ht_tex tex 2 -->\Hnewline}
+ some
+
+tex \TeX
+\HCode{\Hnewline <!-- tex4ht_end tex_tex4ht_tex tex 2 -->\Hnewline \Hnewline}
+
+\bye
Index: test/formatting/res/tex_httex_mediawiki/tex_tex4ht_tex.tmp
===================================================================
RCS file: test/formatting/res/tex_httex_mediawiki/tex_tex4ht_tex.tmp
diff -N test/formatting/res/tex_httex_mediawiki/tex_tex4ht_tex.tmp
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res/tex_httex_mediawiki/tex_tex4ht_tex.tmp 22 Oct 2009
20:23:20 -0000 1.1
@@ -0,0 +1,2 @@
+
+/* css.sty */
\ No newline at end of file
Index: test/formatting/res/tex_httex_mediawiki/tex_tex4ht_tex.xref
===================================================================
RCS file: test/formatting/res/tex_httex_mediawiki/tex_tex4ht_tex.xref
diff -N test/formatting/res/tex_httex_mediawiki/tex_tex4ht_tex.xref
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res/tex_httex_mediawiki/tex_tex4ht_tex.xref 22 Oct 2009
20:23:20 -0000 1.1
@@ -0,0 +1 @@
+\:CrossWord{)F1F-}{tex_tex4ht_tex.html}{1}%
Index: test/formatting/res/tex_l2h_mediawiki/tex
===================================================================
RCS file: test/formatting/res/tex_l2h_mediawiki/tex
diff -N test/formatting/res/tex_l2h_mediawiki/tex
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res/tex_l2h_mediawiki/tex 22 Oct 2009 20:23:20 -0000
1.1
@@ -0,0 +1,47 @@
+<div id="Top"></div>
+<div id="Tests"></div>
+== Tests ==
+
+Now tex on the same line
+some
+<br />
+<div class="mathdisplay" align="CENTER"><!-- MATH
+\begin{displaymath}
+\chi^2 = \sum_{i=1}^N
+\left(y_i - (a + b x_i)
+\over \sigma_i\right)^2
+\end{displaymath}
+-->[[Image:tex_1.png|179px|\begin{displaymath}\chi^2 = \sum_{i=1}^N
+\left(y_i - (a + b x_i)
+\over \sigma_i\right)^2 \end{displaymath}]]</div>
+<br clear="ALL" /> bidule
+Some text one the line following @end tex
+
+Now tex on the following line, valid fot tex (with @end tex on a line).
+some
+tex <span class="logo-TeX">T<small>E</small>X</span>
+
+Same that @html (but empty following line not ignored).
+
+Test of @math
+Here some <math>{x^i}\over{\tan y}</math>.
+
+Maths with protected \:
+<math>a \ b</math>.
+
+Maths with code @-command:
+
+<math><code>math code</code></math>
+
+Maths with code @-command and braces:
+
+<math> \underline{<code>math \hbox{ code }}</code>
\sum_{i}{\underline{f}}</math>
+
address@hidden outside of math
+
address@hidden
+
+
+----
+
+This document was generated on <i>a sunny day</i> using
[http://www.nongnu.org/texi2html/ <i>texi2html</i>].
Index: test/formatting/res/tex_l2h_mediawiki/tex-l2h_cache.pm
===================================================================
RCS file: test/formatting/res/tex_l2h_mediawiki/tex-l2h_cache.pm
diff -N test/formatting/res/tex_l2h_mediawiki/tex-l2h_cache.pm
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res/tex_l2h_mediawiki/tex-l2h_cache.pm 22 Oct 2009
20:23:20 -0000 1.1
@@ -0,0 +1,31 @@
+
+$l2h_cache_key = q/ some
+
+$$ \chi^2 = \sum_{i=1}^N
+ \left(y_i - (a + b x_i)
+ \over \sigma_i\right)^2 $$/;
+$l2h_cache{$l2h_cache_key} = q|
+some
+
+<br />
+
+<div class="mathdisplay" align="CENTER"><!-- MATH
+ \begin{displaymath}
+\chi^2 = \sum_{i=1}^N
+ \left(y_i - (a + b x_i)
+ \over \sigma_i\right)^2
+\end{displaymath}
+ -->[[Image:tex_1.png\|179px\|\begin{displaymath}\chi^2 = \sum_{i=1}^N
+\left(y_i - (a + b x_i)
+\over \sigma_i\right)^2 \end{displaymath}]]</div>
+
+<br clear="ALL" />|;
+
+$l2h_cache_key = q/ some
+
+tex \TeX/;
+$l2h_cache{$l2h_cache_key} = q|
+some
+
+tex <span class="logo-TeX">T<small>E</small>X</span>|;
+1;
\ No newline at end of file
Index: test/formatting/res/tex_l2h_mediawiki/tex.2
===================================================================
RCS file: test/formatting/res/tex_l2h_mediawiki/tex.2
diff -N test/formatting/res/tex_l2h_mediawiki/tex.2
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res/tex_l2h_mediawiki/tex.2 22 Oct 2009 20:23:20 -0000
1.1
@@ -0,0 +1,2 @@
+texexpand
+tex.texi:42: warning: Unknown command address@hidden'
Index: test/formatting/res/tex_l2h_mediawiki/tex_l2h.html
===================================================================
RCS file: test/formatting/res/tex_l2h_mediawiki/tex_l2h.html
diff -N test/formatting/res/tex_l2h_mediawiki/tex_l2h.html
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res/tex_l2h_mediawiki/tex_l2h.html 22 Oct 2009 20:23:20
-0000 1.1
@@ -0,0 +1,39 @@
+tex_l2h<!-- l2h_begin tex_l2h 1 -->
+
+some
+
+<br />
+
+<div class="mathdisplay" align="CENTER"><!-- MATH
+ \begin{displaymath}
+\chi^2 = \sum_{i=1}^N
+ \left(y_i - (a + b x_i)
+ \over \sigma_i\right)^2
+\end{displaymath}
+ -->[[Image:tex_1.png|179px|\begin{displaymath}\chi^2 = \sum_{i=1}^N
+\left(y_i - (a + b x_i)
+\over \sigma_i\right)^2 \end{displaymath}]]</div>
+
+<br clear="ALL" />
+
+<!-- l2h_end tex_l2h 1 -->
+
+intersticiae
+
+<!-- l2h_begin tex_l2h 2 -->
+
+some
+
+tex <span class="logo-TeX">T<small>E</small>X</span>
+<!-- l2h_end tex_l2h 2 -->
+
+intersticiae
+
+<br />
+
+----
+<!--Converted with LaTeX2HTML
+original version by: Nikos Drakos, CBLU, University of Leeds
+* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
+* with significant contributions from:
+ Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
Index: test/formatting/res/tex_l2h_mediawiki/tex_l2h.tex
===================================================================
RCS file: test/formatting/res/tex_l2h_mediawiki/tex_l2h.tex
diff -N test/formatting/res/tex_l2h_mediawiki/tex_l2h.tex
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res/tex_l2h_mediawiki/tex_l2h.tex 22 Oct 2009 20:23:20
-0000 1.1
@@ -0,0 +1,30 @@
+% This document was automatically generated by the l2h extenstion of texi2html
+% DO NOT EDIT !!!
+\documentclass{article}
+\usepackage{html}
+\begin{document}
+\begin{rawhtml}
+
+<!-- l2h_begin tex_l2h 1 -->
+\end{rawhtml}
+ some
+
+$$ \chi^2 = \sum_{i=1}^N
+ \left(y_i - (a + b x_i)
+ \over \sigma_i\right)^2 $$
+\begin{rawhtml}
+<!-- l2h_end tex_l2h 1 -->
+
+\end{rawhtml}
+\begin{rawhtml}
+
+<!-- l2h_begin tex_l2h 2 -->
+\end{rawhtml}
+ some
+
+tex \TeX
+\begin{rawhtml}
+<!-- l2h_end tex_l2h 2 -->
+
+\end{rawhtml}
+\end{document}
Index: test/formatting/res/tex_l2h_mediawiki/tex_l2h_images.pl
===================================================================
RCS file: test/formatting/res/tex_l2h_mediawiki/tex_l2h_images.pl
diff -N test/formatting/res/tex_l2h_mediawiki/tex_l2h_images.pl
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res/tex_l2h_mediawiki/tex_l2h_images.pl 22 Oct 2009
20:23:20 -0000 1.1
@@ -0,0 +1,14 @@
+# LaTeX2HTML
+# Associate images original text with physical files.
+
+
+$key =
q/{displaymath}chi^2=sum_{i=1}^Nleft(y_i-(a+bx_i)oversigma_iright)^2{displaymath};MSF=1.5;AAT/;
+$cached_env_img{$key} = q|<IMG
+ WIDTH="179" HEIGHT="52" BORDER="0"
+ SRC="|."$dir".q|tex_l2h_img1.png"
+ ALT="\begin{displaymath}\chi^2 = \sum_{i=1}^N
+\left(y_i - (a + b x_i)
+\over \sigma_i\right)^2 \end{displaymath}">|;
+
+1;
+
Index: test/formatting/res/tex_l2h_mediawiki/tex_l2h_images.tex
===================================================================
RCS file: test/formatting/res/tex_l2h_mediawiki/tex_l2h_images.tex
diff -N test/formatting/res/tex_l2h_mediawiki/tex_l2h_images.tex
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res/tex_l2h_mediawiki/tex_l2h_images.tex 22 Oct 2009
20:23:20 -0000 1.1
@@ -0,0 +1,147 @@
+\batchmode
+
+\documentclass{article}
+\RequirePackage{ifthen}
+
+
+\usepackage{html}
+
+
+\usepackage[dvips]{color}
+
+
+\pagecolor[gray]{.7}
+
+\usepackage[]{inputenc}
+
+
+
+\makeatletter
+
+\makeatletter
address@hidden \catcode`\_=8
+\newenvironment{tex2html_wrap}{}{}%
+\catcode`\<=12\catcode`\_=\count@
+\newcommand{\providedcommand}[1]{\expandafter\providecommand\csname
#1\endcsname}%
+\newcommand{\renewedcommand}[1]{\expandafter\providecommand\csname
#1\endcsname{}%
+ \expandafter\renewcommand\csname #1\endcsname}%
+\newcommand{\newedenvironment}[1]{\newenvironment{#1}{}{}\renewenvironment{#1}}%
+\let\newedcommand\renewedcommand
+\let\renewedenvironment\newedenvironment
+\makeatother
+\let\mathon=$
+\let\mathoff=$
+\ifx\AtBeginDocument\undefined \newcommand{\AtBeginDocument}[1]{}\fi
+\newbox\sizebox
+\setlength{\hoffset}{0pt}\setlength{\voffset}{0pt}
+\addtolength{\textheight}{\footskip}\setlength{\footskip}{0pt}
+\addtolength{\textheight}{\topmargin}\setlength{\topmargin}{0pt}
+\addtolength{\textheight}{\headheight}\setlength{\headheight}{0pt}
+\addtolength{\textheight}{\headsep}\setlength{\headsep}{0pt}
+\setlength{\textwidth}{451pt}
+\setlength{\textheight}{554pt}
+\newwrite\lthtmlwrite
+\makeatletter
+\let\realnormalsize=\normalsize
+\global\topskip=2sp
address@hidden@float address@hidden@float
address@hidden@address@hidden@float}
address@hidden@math\fi}
address@hidden@address@hidden@savefreelist}
address@hidden@dbflt address@hidden@float
address@hidden
address@hidden
address@hidden@address@hidden@dbflt}
+\def\adjustnormalsize{\def\normalsize{\mathsurround=0pt \realnormalsize
+ \parindent=0pt\abovedisplayskip=0pt\belowdisplayskip=0pt}%
+ \def\phantompar{\csname par\endcsname}\normalsize}%
+\def\lthtmltypeout#1{{\let\protect\string \immediate\write\lthtmlwrite{#1}}}%
+\newcommand\lthtmlhboxmathA{\adjustnormalsize\setbox\sizebox=\hbox\bgroup\kern.05em
}%
+\newcommand\lthtmlhboxmathB{\adjustnormalsize\setbox\sizebox=\hbox
to\hsize\bgroup\hfill }%
+\newcommand\lthtmlvboxmathA{\adjustnormalsize\setbox\sizebox=\vbox\bgroup %
+ \let\ifinner=\iffalse \let\)address@hidden }%
address@hidden@address@hidden
+ \expandafter\box\next\egroup}%
+\newcommand\lthtmlmathtype[1]{\gdef\lthtmlmathenv{#1}}%
+\newcommand\lthtmllogmath{\dimen0\ht\sizebox \advance\dimen0\dp\sizebox
+ \ifdim\dimen0>.95\vsize
+ \lthtmltypeout{%
+*** image for \lthtmlmathenv\space is too tall at \the\dimen0, reducing to .95
vsize ***}%
+ \ht\sizebox.95\vsize \dp\sizebox\z@ \fi
+ \lthtmltypeout{l2hSize %
+:\lthtmlmathenv:\the\ht\sizebox::\the\dp\sizebox::\the\wd\sizebox.\preveqno}}%
address@hidden@freelist
+ \lthtmlmathtype{#1}\lthtmlvboxmathA}%
+\newcommand\lthtmlpictureA{\bgroup\catcode`\_=8 \lthtmlpictureB}%
+\newcommand\lthtmlpictureB[1]{\lthtmlmathtype{#1}\egroup
+ address@hidden@freelist \lthtmlhboxmathB}%
+\newcommand\lthtmlpictureZ[1]{\hfill\lthtmlfigureZ}%
+\newcommand\lthtmlfigureZ{\lthtmlboxmathZ\lthtmllogmath\copy\sizebox
+ address@hidden@savefreelist}%
+\newcommand\lthtmldisplayA{\bgroup\catcode`\_=8 \lthtmldisplayAi}%
+\newcommand\lthtmldisplayAi[1]{\lthtmlmathtype{#1}\egroup\lthtmlvboxmathA}%
+\newcommand\lthtmldisplayB[1]{\edef\preveqno{(\theequation)}%
+ address@hidden
+\newcommand\lthtmldisplayZ{\lthtmlboxmathZ\lthtmllogmath\lthtmlsetmath}%
+\newcommand\lthtmlinlinemathA{\bgroup\catcode`\_=8 \lthtmlinlinemathB}
+\newcommand\lthtmlinlinemathB[1]{\lthtmlmathtype{#1}\egroup\lthtmlhboxmathA
+ \vrule height1.5ex width0pt }%
+\newcommand\lthtmlinlineA{\bgroup\catcode`\_=8 \lthtmlinlineB}%
+\newcommand\lthtmlinlineB[1]{\lthtmlmathtype{#1}\egroup\lthtmlhboxmathA}%
+\newcommand\lthtmlinlineZ{\egroup\expandafter\ifdim\dp\sizebox>0pt %
+ \expandafter\centerinlinemath\fi\lthtmllogmath\lthtmlsetinline}
+\newcommand\lthtmlinlinemathZ{\egroup\expandafter\ifdim\dp\sizebox>0pt %
+ \expandafter\centerinlinemath\fi\lthtmllogmath\lthtmlsetmath}
+\newcommand\lthtmlindisplaymathZ{\egroup %
+ \centerinlinemath\lthtmllogmath\lthtmlsetmath}
+\def\lthtmlsetinline{\hbox{\vrule width.1em \vtop{\vbox{%
+ \kern.1em\copy\sizebox}\ifdim\dp\sizebox>0pt\kern.1em\else\kern.3pt\fi
+ \ifdim\hsize>\wd\sizebox \hrule depth1pt\fi}}}
+\def\lthtmlsetmath{\hbox{\vrule width.1em\kern-.05em\vtop{\vbox{%
+ \kern.1em\kern0.75 pt\hbox{\hglue.17em\copy\sizebox\hglue0.75 pt}}\kern.3pt%
+ \ifdim\dp\sizebox>0pt\kern.1em\fi \kern0.75 pt%
+ \ifdim\hsize>\wd\sizebox \hrule depth1pt\fi}}}
+\def\centerinlinemath{%
+ \dimen1=\ifdim\ht\sizebox<\dp\sizebox \dp\sizebox\else\ht\sizebox\fi
+ \advance\dimen1by.5pt \vrule width0pt height\dimen1 depth\dimen1
+ \dp\sizebox=\dimen1\ht\sizebox=\dimen1\relax}
+
+\def\lthtmlcheckvsize{\ifdim\ht\sizebox<\vsize
+ \ifdim\wd\sizebox<\hsize\expandafter\hfill\fi \expandafter\vfill
+ \else\expandafter\vss\fi}%
+\providecommand{\selectlanguage}[1]{}%
+\makeatletter \tracingstats = 1
+
+
+\begin{document}
+\pagestyle{empty}\thispagestyle{empty}\lthtmltypeout{}%
+\lthtmltypeout{latex2htmlLength hsize=\the\hsize}\lthtmltypeout{}%
+\lthtmltypeout{latex2htmlLength vsize=\the\vsize}\lthtmltypeout{}%
+\lthtmltypeout{latex2htmlLength hoffset=\the\hoffset}\lthtmltypeout{}%
+\lthtmltypeout{latex2htmlLength voffset=\the\voffset}\lthtmltypeout{}%
+\lthtmltypeout{latex2htmlLength topmargin=\the\topmargin}\lthtmltypeout{}%
+\lthtmltypeout{latex2htmlLength topskip=\the\topskip}\lthtmltypeout{}%
+\lthtmltypeout{latex2htmlLength headheight=\the\headheight}\lthtmltypeout{}%
+\lthtmltypeout{latex2htmlLength headsep=\the\headsep}\lthtmltypeout{}%
+\lthtmltypeout{latex2htmlLength parskip=\the\parskip}\lthtmltypeout{}%
+\lthtmltypeout{latex2htmlLength
oddsidemargin=\the\oddsidemargin}\lthtmltypeout{}%
+\makeatletter
address@hidden evensidemargin=\the\evensidemargin}%
+\else\lthtmltypeout{latex2htmlLength evensidemargin=\the\oddsidemargin}\fi%
+\lthtmltypeout{}%
+\makeatother
+\setcounter{page}{1}
+\onecolumn
+
+% !!! IMAGES START HERE !!!
+
+{\newpage\clearpage
+\lthtmldisplayA{displaymath6}%
+\begin{displaymath} \chi^2 = \sum_{i=1}^N
+ \left(y_i - (a + b x_i)
+ \over \sigma_i\right)^2 \end{displaymath}%
+\lthtmldisplayZ
+\lthtmlcheckvsize\clearpage}
+
+
+\end{document}
Index: test/formatting/res/tex_l2h_mediawiki/tex_l2h_labels.pl
===================================================================
RCS file: test/formatting/res/tex_l2h_mediawiki/tex_l2h_labels.pl
diff -N test/formatting/res/tex_l2h_mediawiki/tex_l2h_labels.pl
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res/tex_l2h_mediawiki/tex_l2h_labels.pl 22 Oct 2009
20:23:20 -0000 1.1
@@ -0,0 +1,13 @@
+# LaTeX2HTML
+# Associate labels original text with physical files.
+
+
+1;
+
+
+# LaTeX2HTML
+# labels from external_latex_labels array.
+
+
+1;
+
Index: test/formatting/res_all/tex_httex_mediawiki/tex
===================================================================
RCS file: test/formatting/res_all/tex_httex_mediawiki/tex
diff -N test/formatting/res_all/tex_httex_mediawiki/tex
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res_all/tex_httex_mediawiki/tex 22 Oct 2009 20:23:20
-0000 1.1
@@ -0,0 +1,40 @@
+<div id="Top"></div>
+<div id="Tests"></div>
+== Tests ==
+
+Now tex on the same line some <!--l. 6-->
+<center class="math-display">[[Image:tex_tex4ht_tex0x.png| N (
)2
+Ï2 = â yi --(a+-bxi)
+i=1 Ïi
+]]</center><!--l. 11-->
+bidule
+Some text one the line following @end tex
+
+Now tex on the following line, valid fot tex (with @end tex on a line).
+some <!--l. 15-->
+tex <span class="TEX">T<span class="E">E</span>X</span>
+
+Same that @html (but empty following line not ignored).
+
+Test of @math
+Here some <math>{x^i}\over{\tan y}</math>.
+
+Maths with protected \:
+<math>a \ b</math>.
+
+Maths with code @-command:
+
+<math><code>math code</code></math>
+
+Maths with code @-command and braces:
+
+<math> \underline{<code>math \hbox{ code }}</code>
\sum_{i}{\underline{f}}</math>
+
address@hidden outside of math
+
address@hidden
+
+
+----
+
+This document was generated on <i>a sunny day</i> using
[http://www.nongnu.org/texi2html/ <i>texi2html</i>].
Index: test/formatting/res_all/tex_httex_mediawiki/tex.2
===================================================================
RCS file: test/formatting/res_all/tex_httex_mediawiki/tex.2
diff -N test/formatting/res_all/tex_httex_mediawiki/tex.2
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res_all/tex_httex_mediawiki/tex.2 22 Oct 2009 20:23:20
-0000 1.1
@@ -0,0 +1 @@
+dvipng warning: DVI magnification of 1000 over-ridden by user (1400)
tex.texi:42: warning: Unknown command address@hidden'
Index: test/formatting/res_all/tex_httex_mediawiki/tex_tex4ht_math.texi
===================================================================
RCS file: test/formatting/res_all/tex_httex_mediawiki/tex_tex4ht_math.texi
diff -N test/formatting/res_all/tex_httex_mediawiki/tex_tex4ht_math.texi
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res_all/tex_httex_mediawiki/tex_tex4ht_math.texi 22 Oct
2009 20:23:20 -0000 1.1
@@ -0,0 +1,5 @@
+\input texinfo
address@hidden tex_tex4ht_math.info
address@hidden Automatically generated
+
address@hidden
Index: test/formatting/res_all/tex_httex_mediawiki/tex_tex4ht_tex.4ct
===================================================================
RCS file: test/formatting/res_all/tex_httex_mediawiki/tex_tex4ht_tex.4ct
diff -N test/formatting/res_all/tex_httex_mediawiki/tex_tex4ht_tex.4ct
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res_all/tex_httex_mediawiki/tex_tex4ht_tex.4ct 22 Oct
2009 20:23:20 -0000 1.1
@@ -0,0 +1,2 @@
+\expandafter\ifx\csname doTocEntry\endcsname\relax \expandafter\endinput\fi
+\par
Index: test/formatting/res_all/tex_httex_mediawiki/tex_tex4ht_tex.4tc
===================================================================
RCS file: test/formatting/res_all/tex_httex_mediawiki/tex_tex4ht_tex.4tc
diff -N test/formatting/res_all/tex_httex_mediawiki/tex_tex4ht_tex.4tc
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res_all/tex_httex_mediawiki/tex_tex4ht_tex.4tc 22 Oct
2009 20:23:20 -0000 1.1
@@ -0,0 +1 @@
+\expandafter\ifx\csname doTocEntry\endcsname\relax \expandafter\endinput\fi
Index: test/formatting/res_all/tex_httex_mediawiki/tex_tex4ht_tex.css
===================================================================
RCS file: test/formatting/res_all/tex_httex_mediawiki/tex_tex4ht_tex.css
diff -N test/formatting/res_all/tex_httex_mediawiki/tex_tex4ht_tex.css
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res_all/tex_httex_mediawiki/tex_tex4ht_tex.css 22 Oct
2009 20:23:20 -0000 1.1
@@ -0,0 +1,43 @@
+
+/* start css.sty */
+.cmr-7{font-size:70%;}
+.cmmi-10{font-style: italic;}
+.cmmi-7{font-size:70%;font-style: italic;}
+p.noindent { text-indent: 0em }
+td p.noindent { text-indent: 0em; margin-top:0em; }
+p.nopar { text-indent: 0em; }
+p.indent{ text-indent: 1.5em }
address@hidden print {div.crosslinks {visibility:hidden;}}
+a img { border-top: 0; border-left: 0; border-right: 0; }
+center { margin-top:1em; margin-bottom:1em; }
+td center { margin-top:0em; margin-bottom:0em; }
+.Canvas { position:relative; }
+img.math{vertical-align:middle;}
+.obeylines-h,.obeylines-v {white-space: nowrap; }
+div.obeylines-v p { margin-top:0; margin-bottom:0; }
+.overline{ text-decoration:overline; }
+.overline img{ border-top: 1px solid black; }
+td.displaylines {text-align:center; white-space:nowrap;}
+.centerline {text-align:center;}
+.rightline {text-align:right;}
+span.TEX {letter-spacing: -0.125em; }
+span.TEX span.E{ position:relative;top:0.5ex;left:-0.0417em;}
+a span.TEX span.E {text-decoration: none; }
+.underline{ text-decoration:underline; }
+.underline img{ border-bottom: 1px solid black; margin-bottom:1pt; }
+div.proclaim { margin-top: 1em; margin-bottom: 1em; }
+p.item {text-indent:-2em; margin-left:2em;}
+p.itemitem {text-indent:-2em; margin-left:4em;}
+span.item, span.itemitem {width:2em; margin-right:0.4em;}
+td.eqalign3 { text-align:right; margin-left:10em;}
+.eqalign td { white-space: nowrap; }
+div.eqalign {text-align:center;}
+td.eqalignno3, td.leqalignno3 { text-align:right; margin-left:10em;}
+.leqalignno td, .eqalignno td { white-space: nowrap; }
+.leqalignno td.noalign, .eqalignno td.noalign { width:5%; white-space: normal;
}
+table.leqalignno, table.eqalignno {width:100%;}
+img.cdots{vertical-align:middle;}
+div.pmatrix {text-align:center;}
+table.pmatrix {width:100%;}
+/* end css.sty */
+
Index: test/formatting/res_all/tex_httex_mediawiki/tex_tex4ht_tex.lg
===================================================================
RCS file: test/formatting/res_all/tex_httex_mediawiki/tex_tex4ht_tex.lg
diff -N test/formatting/res_all/tex_httex_mediawiki/tex_tex4ht_tex.lg
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res_all/tex_httex_mediawiki/tex_tex4ht_tex.lg 22 Oct
2009 20:23:20 -0000 1.1
@@ -0,0 +1,55 @@
+htfcss: cmmi font-style: italic;
+htfcss: cmmib font-style: italic; font-weight: bold;
+File: tex_tex4ht_tex.html
+File: tex_tex4ht_tex.css
+File: tex_tex4ht_tex.tmp
+Css: p.noindent { text-indent: 0em }
+Css: td p.noindent { text-indent: 0em; margin-top:0em; }
+Css: p.nopar { text-indent: 0em; }
+Css: p.indent{ text-indent: 1.5em }
+Css: @media print {div.crosslinks {visibility:hidden;}}
+Css: a img { border-top: 0; border-left: 0; border-right: 0; }
+Font_Css("4"): .small-caps{font-variant: small-caps; }
+Font_Css("10"): .htf-cmbx {font-weight: bold; font-style:normal;}
+Font_Css("12"): .htf-calligraphy {font-family:cursive}
+Font_Css("14"): .htf-italic {font-style: italic;}
+Font_Css("16"): .htf-bold {font-weight: bold;}
+Font_Css("12"): .htf-calligraphy-bold {font-family:cursive ; font-weight:
bold; }
+Css: center { margin-top:1em; margin-bottom:1em; }
+Css: td center { margin-top:0em; margin-bottom:0em; }
+Css: .Canvas { position:relative; }
+Css: img.math{vertical-align:middle;}
+Css: .obeylines-h,.obeylines-v {white-space: nowrap; }
+Css: div.obeylines-v p { margin-top:0; margin-bottom:0; }
+Css: .overline{ text-decoration:overline; }
+Css: .overline img{ border-top: 1px solid black; }
+Css: td.displaylines {text-align:center; white-space:nowrap;}
+Css: .centerline {text-align:center;}
+Css: .rightline {text-align:right;}
+Css: span.TEX {letter-spacing: -0.125em; }
+Css: span.TEX span.E{ position:relative;top:0.5ex;left:-0.0417em;}
+Css: a span.TEX span.E {text-decoration: none; }
+Css: .underline{ text-decoration:underline; }
+Css: .underline img{ border-bottom: 1px solid black; margin-bottom:1pt; }
+Css: div.proclaim { margin-top: 1em; margin-bottom: 1em; }
+Css: p.item {text-indent:-2em; margin-left:2em;}
+Css: p.itemitem {text-indent:-2em; margin-left:4em;}
+Css: span.item, span.itemitem {width:2em; margin-right:0.4em;}
+Css: td.eqalign3 { text-align:right; margin-left:10em;}
+Css: .eqalign td { white-space: nowrap; }
+Css: div.eqalign {text-align:center;}
+Css: td.eqalignno3, td.leqalignno3 { text-align:right; margin-left:10em;}
+Css: .leqalignno td, .eqalignno td { white-space: nowrap; }
+Css: .leqalignno td.noalign, .eqalignno td.noalign { width:5%; white-space:
normal; }
+Css: table.leqalignno, table.eqalignno {width:100%;}
+Css: img.cdots{vertical-align:middle;}
+Css: div.pmatrix {text-align:center;}
+Css: table.pmatrix {width:100%;}
+--- needs --- tex_tex4ht_tex.idv[1] ==> tex_tex4ht_tex0x.png ---
+--- characters ---
+Font("cmr","10","10","100")
+Font("cmr","7","7","100")
+Font("cmmi","10","10","100")
+Font("cmmi","7","7","100")
+Font("cmsy","10","10","100")
+Font("cmex","10","10","100")
Index: test/formatting/res_all/tex_httex_mediawiki/tex_tex4ht_tex.tex
===================================================================
RCS file: test/formatting/res_all/tex_httex_mediawiki/tex_tex4ht_tex.tex
diff -N test/formatting/res_all/tex_httex_mediawiki/tex_tex4ht_tex.tex
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res_all/tex_httex_mediawiki/tex_tex4ht_tex.tex 22 Oct
2009 20:23:21 -0000 1.1
@@ -0,0 +1,18 @@
+% Automatically generated
+\csname tex4ht\endcsname
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin tex_tex4ht_tex tex 1 -->\Hnewline}
+ some
+
+$$ \chi^2 = \sum_{i=1}^N
+ \left(y_i - (a + b x_i)
+ \over \sigma_i\right)^2 $$
+
+
+\HCode{\Hnewline <!-- tex4ht_end tex_tex4ht_tex tex 1 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin tex_tex4ht_tex tex 2 -->\Hnewline}
+ some
+
+tex \TeX
+\HCode{\Hnewline <!-- tex4ht_end tex_tex4ht_tex tex 2 -->\Hnewline \Hnewline}
+
+\bye
Index: test/formatting/res_all/tex_httex_mediawiki/tex_tex4ht_tex.tmp
===================================================================
RCS file: test/formatting/res_all/tex_httex_mediawiki/tex_tex4ht_tex.tmp
diff -N test/formatting/res_all/tex_httex_mediawiki/tex_tex4ht_tex.tmp
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res_all/tex_httex_mediawiki/tex_tex4ht_tex.tmp 22 Oct
2009 20:23:21 -0000 1.1
@@ -0,0 +1,2 @@
+
+/* css.sty */
\ No newline at end of file
Index: test/formatting/res_all/tex_httex_mediawiki/tex_tex4ht_tex.xref
===================================================================
RCS file: test/formatting/res_all/tex_httex_mediawiki/tex_tex4ht_tex.xref
diff -N test/formatting/res_all/tex_httex_mediawiki/tex_tex4ht_tex.xref
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res_all/tex_httex_mediawiki/tex_tex4ht_tex.xref 22 Oct
2009 20:23:21 -0000 1.1
@@ -0,0 +1 @@
+\:CrossWord{)F1F-}{tex_tex4ht_tex.html}{1}%
Index: test/formatting/res_all/tex_l2h_mediawiki/tex
===================================================================
RCS file: test/formatting/res_all/tex_l2h_mediawiki/tex
diff -N test/formatting/res_all/tex_l2h_mediawiki/tex
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res_all/tex_l2h_mediawiki/tex 22 Oct 2009 20:23:21
-0000 1.1
@@ -0,0 +1,47 @@
+<div id="Top"></div>
+<div id="Tests"></div>
+== Tests ==
+
+Now tex on the same line
+some
+<br />
+<div class="mathdisplay" align="CENTER"><!-- MATH
+\begin{displaymath}
+\chi^2 = \sum_{i=1}^N
+\left(y_i - (a + b x_i)
+\over \sigma_i\right)^2
+\end{displaymath}
+-->[[Image:tex_1.png|179px|\begin{displaymath}\chi^2 = \sum_{i=1}^N
+\left(y_i - (a + b x_i)
+\over \sigma_i\right)^2 \end{displaymath}]]</div>
+<br clear="ALL" /> bidule
+Some text one the line following @end tex
+
+Now tex on the following line, valid fot tex (with @end tex on a line).
+some
+tex <span class="logo-TeX">T<small>E</small>X</span>
+
+Same that @html (but empty following line not ignored).
+
+Test of @math
+Here some <math>{x^i}\over{\tan y}</math>.
+
+Maths with protected \:
+<math>a \ b</math>.
+
+Maths with code @-command:
+
+<math><code>math code</code></math>
+
+Maths with code @-command and braces:
+
+<math> \underline{<code>math \hbox{ code }}</code>
\sum_{i}{\underline{f}}</math>
+
address@hidden outside of math
+
address@hidden
+
+
+----
+
+This document was generated on <i>a sunny day</i> using
[http://www.nongnu.org/texi2html/ <i>texi2html</i>].
Index: test/formatting/res_all/tex_l2h_mediawiki/tex-l2h_cache.pm
===================================================================
RCS file: test/formatting/res_all/tex_l2h_mediawiki/tex-l2h_cache.pm
diff -N test/formatting/res_all/tex_l2h_mediawiki/tex-l2h_cache.pm
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res_all/tex_l2h_mediawiki/tex-l2h_cache.pm 22 Oct 2009
20:23:21 -0000 1.1
@@ -0,0 +1,31 @@
+
+$l2h_cache_key = q/ some
+
+$$ \chi^2 = \sum_{i=1}^N
+ \left(y_i - (a + b x_i)
+ \over \sigma_i\right)^2 $$/;
+$l2h_cache{$l2h_cache_key} = q|
+some
+
+<br />
+
+<div class="mathdisplay" align="CENTER"><!-- MATH
+ \begin{displaymath}
+\chi^2 = \sum_{i=1}^N
+ \left(y_i - (a + b x_i)
+ \over \sigma_i\right)^2
+\end{displaymath}
+ -->[[Image:tex_1.png\|179px\|\begin{displaymath}\chi^2 = \sum_{i=1}^N
+\left(y_i - (a + b x_i)
+\over \sigma_i\right)^2 \end{displaymath}]]</div>
+
+<br clear="ALL" />|;
+
+$l2h_cache_key = q/ some
+
+tex \TeX/;
+$l2h_cache{$l2h_cache_key} = q|
+some
+
+tex <span class="logo-TeX">T<small>E</small>X</span>|;
+1;
\ No newline at end of file
Index: test/formatting/res_all/tex_l2h_mediawiki/tex.2
===================================================================
RCS file: test/formatting/res_all/tex_l2h_mediawiki/tex.2
diff -N test/formatting/res_all/tex_l2h_mediawiki/tex.2
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res_all/tex_l2h_mediawiki/tex.2 22 Oct 2009 20:23:21
-0000 1.1
@@ -0,0 +1,2 @@
+texexpand
+tex.texi:42: warning: Unknown command address@hidden'
Index: test/formatting/res_all/tex_l2h_mediawiki/tex_l2h.html
===================================================================
RCS file: test/formatting/res_all/tex_l2h_mediawiki/tex_l2h.html
diff -N test/formatting/res_all/tex_l2h_mediawiki/tex_l2h.html
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res_all/tex_l2h_mediawiki/tex_l2h.html 22 Oct 2009
20:23:21 -0000 1.1
@@ -0,0 +1,39 @@
+tex_l2h<!-- l2h_begin tex_l2h 1 -->
+
+some
+
+<br />
+
+<div class="mathdisplay" align="CENTER"><!-- MATH
+ \begin{displaymath}
+\chi^2 = \sum_{i=1}^N
+ \left(y_i - (a + b x_i)
+ \over \sigma_i\right)^2
+\end{displaymath}
+ -->[[Image:tex_1.png|179px|\begin{displaymath}\chi^2 = \sum_{i=1}^N
+\left(y_i - (a + b x_i)
+\over \sigma_i\right)^2 \end{displaymath}]]</div>
+
+<br clear="ALL" />
+
+<!-- l2h_end tex_l2h 1 -->
+
+intersticiae
+
+<!-- l2h_begin tex_l2h 2 -->
+
+some
+
+tex <span class="logo-TeX">T<small>E</small>X</span>
+<!-- l2h_end tex_l2h 2 -->
+
+intersticiae
+
+<br />
+
+----
+<!--Converted with LaTeX2HTML
+original version by: Nikos Drakos, CBLU, University of Leeds
+* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
+* with significant contributions from:
+ Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
Index: test/formatting/res_all/tex_l2h_mediawiki/tex_l2h.tex
===================================================================
RCS file: test/formatting/res_all/tex_l2h_mediawiki/tex_l2h.tex
diff -N test/formatting/res_all/tex_l2h_mediawiki/tex_l2h.tex
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res_all/tex_l2h_mediawiki/tex_l2h.tex 22 Oct 2009
20:23:21 -0000 1.1
@@ -0,0 +1,30 @@
+% This document was automatically generated by the l2h extenstion of texi2html
+% DO NOT EDIT !!!
+\documentclass{article}
+\usepackage{html}
+\begin{document}
+\begin{rawhtml}
+
+<!-- l2h_begin tex_l2h 1 -->
+\end{rawhtml}
+ some
+
+$$ \chi^2 = \sum_{i=1}^N
+ \left(y_i - (a + b x_i)
+ \over \sigma_i\right)^2 $$
+\begin{rawhtml}
+<!-- l2h_end tex_l2h 1 -->
+
+\end{rawhtml}
+\begin{rawhtml}
+
+<!-- l2h_begin tex_l2h 2 -->
+\end{rawhtml}
+ some
+
+tex \TeX
+\begin{rawhtml}
+<!-- l2h_end tex_l2h 2 -->
+
+\end{rawhtml}
+\end{document}
Index: test/formatting/res_all/tex_l2h_mediawiki/tex_l2h_images.pl
===================================================================
RCS file: test/formatting/res_all/tex_l2h_mediawiki/tex_l2h_images.pl
diff -N test/formatting/res_all/tex_l2h_mediawiki/tex_l2h_images.pl
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res_all/tex_l2h_mediawiki/tex_l2h_images.pl 22 Oct 2009
20:23:21 -0000 1.1
@@ -0,0 +1,14 @@
+# LaTeX2HTML
+# Associate images original text with physical files.
+
+
+$key =
q/{displaymath}chi^2=sum_{i=1}^Nleft(y_i-(a+bx_i)oversigma_iright)^2{displaymath};MSF=1.5;AAT/;
+$cached_env_img{$key} = q|<IMG
+ WIDTH="179" HEIGHT="52" BORDER="0"
+ SRC="|."$dir".q|tex_l2h_img1.png"
+ ALT="\begin{displaymath}\chi^2 = \sum_{i=1}^N
+\left(y_i - (a + b x_i)
+\over \sigma_i\right)^2 \end{displaymath}">|;
+
+1;
+
Index: test/formatting/res_all/tex_l2h_mediawiki/tex_l2h_images.tex
===================================================================
RCS file: test/formatting/res_all/tex_l2h_mediawiki/tex_l2h_images.tex
diff -N test/formatting/res_all/tex_l2h_mediawiki/tex_l2h_images.tex
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res_all/tex_l2h_mediawiki/tex_l2h_images.tex 22 Oct
2009 20:23:21 -0000 1.1
@@ -0,0 +1,147 @@
+\batchmode
+
+\documentclass{article}
+\RequirePackage{ifthen}
+
+
+\usepackage{html}
+
+
+\usepackage[dvips]{color}
+
+
+\pagecolor[gray]{.7}
+
+\usepackage[]{inputenc}
+
+
+
+\makeatletter
+
+\makeatletter
address@hidden \catcode`\_=8
+\newenvironment{tex2html_wrap}{}{}%
+\catcode`\<=12\catcode`\_=\count@
+\newcommand{\providedcommand}[1]{\expandafter\providecommand\csname
#1\endcsname}%
+\newcommand{\renewedcommand}[1]{\expandafter\providecommand\csname
#1\endcsname{}%
+ \expandafter\renewcommand\csname #1\endcsname}%
+\newcommand{\newedenvironment}[1]{\newenvironment{#1}{}{}\renewenvironment{#1}}%
+\let\newedcommand\renewedcommand
+\let\renewedenvironment\newedenvironment
+\makeatother
+\let\mathon=$
+\let\mathoff=$
+\ifx\AtBeginDocument\undefined \newcommand{\AtBeginDocument}[1]{}\fi
+\newbox\sizebox
+\setlength{\hoffset}{0pt}\setlength{\voffset}{0pt}
+\addtolength{\textheight}{\footskip}\setlength{\footskip}{0pt}
+\addtolength{\textheight}{\topmargin}\setlength{\topmargin}{0pt}
+\addtolength{\textheight}{\headheight}\setlength{\headheight}{0pt}
+\addtolength{\textheight}{\headsep}\setlength{\headsep}{0pt}
+\setlength{\textwidth}{451pt}
+\setlength{\textheight}{554pt}
+\newwrite\lthtmlwrite
+\makeatletter
+\let\realnormalsize=\normalsize
+\global\topskip=2sp
address@hidden@float address@hidden@float
address@hidden@address@hidden@float}
address@hidden@math\fi}
address@hidden@address@hidden@savefreelist}
address@hidden@dbflt address@hidden@float
address@hidden
address@hidden
address@hidden@address@hidden@dbflt}
+\def\adjustnormalsize{\def\normalsize{\mathsurround=0pt \realnormalsize
+ \parindent=0pt\abovedisplayskip=0pt\belowdisplayskip=0pt}%
+ \def\phantompar{\csname par\endcsname}\normalsize}%
+\def\lthtmltypeout#1{{\let\protect\string \immediate\write\lthtmlwrite{#1}}}%
+\newcommand\lthtmlhboxmathA{\adjustnormalsize\setbox\sizebox=\hbox\bgroup\kern.05em
}%
+\newcommand\lthtmlhboxmathB{\adjustnormalsize\setbox\sizebox=\hbox
to\hsize\bgroup\hfill }%
+\newcommand\lthtmlvboxmathA{\adjustnormalsize\setbox\sizebox=\vbox\bgroup %
+ \let\ifinner=\iffalse \let\)address@hidden }%
address@hidden@address@hidden
+ \expandafter\box\next\egroup}%
+\newcommand\lthtmlmathtype[1]{\gdef\lthtmlmathenv{#1}}%
+\newcommand\lthtmllogmath{\dimen0\ht\sizebox \advance\dimen0\dp\sizebox
+ \ifdim\dimen0>.95\vsize
+ \lthtmltypeout{%
+*** image for \lthtmlmathenv\space is too tall at \the\dimen0, reducing to .95
vsize ***}%
+ \ht\sizebox.95\vsize \dp\sizebox\z@ \fi
+ \lthtmltypeout{l2hSize %
+:\lthtmlmathenv:\the\ht\sizebox::\the\dp\sizebox::\the\wd\sizebox.\preveqno}}%
address@hidden@freelist
+ \lthtmlmathtype{#1}\lthtmlvboxmathA}%
+\newcommand\lthtmlpictureA{\bgroup\catcode`\_=8 \lthtmlpictureB}%
+\newcommand\lthtmlpictureB[1]{\lthtmlmathtype{#1}\egroup
+ address@hidden@freelist \lthtmlhboxmathB}%
+\newcommand\lthtmlpictureZ[1]{\hfill\lthtmlfigureZ}%
+\newcommand\lthtmlfigureZ{\lthtmlboxmathZ\lthtmllogmath\copy\sizebox
+ address@hidden@savefreelist}%
+\newcommand\lthtmldisplayA{\bgroup\catcode`\_=8 \lthtmldisplayAi}%
+\newcommand\lthtmldisplayAi[1]{\lthtmlmathtype{#1}\egroup\lthtmlvboxmathA}%
+\newcommand\lthtmldisplayB[1]{\edef\preveqno{(\theequation)}%
+ address@hidden
+\newcommand\lthtmldisplayZ{\lthtmlboxmathZ\lthtmllogmath\lthtmlsetmath}%
+\newcommand\lthtmlinlinemathA{\bgroup\catcode`\_=8 \lthtmlinlinemathB}
+\newcommand\lthtmlinlinemathB[1]{\lthtmlmathtype{#1}\egroup\lthtmlhboxmathA
+ \vrule height1.5ex width0pt }%
+\newcommand\lthtmlinlineA{\bgroup\catcode`\_=8 \lthtmlinlineB}%
+\newcommand\lthtmlinlineB[1]{\lthtmlmathtype{#1}\egroup\lthtmlhboxmathA}%
+\newcommand\lthtmlinlineZ{\egroup\expandafter\ifdim\dp\sizebox>0pt %
+ \expandafter\centerinlinemath\fi\lthtmllogmath\lthtmlsetinline}
+\newcommand\lthtmlinlinemathZ{\egroup\expandafter\ifdim\dp\sizebox>0pt %
+ \expandafter\centerinlinemath\fi\lthtmllogmath\lthtmlsetmath}
+\newcommand\lthtmlindisplaymathZ{\egroup %
+ \centerinlinemath\lthtmllogmath\lthtmlsetmath}
+\def\lthtmlsetinline{\hbox{\vrule width.1em \vtop{\vbox{%
+ \kern.1em\copy\sizebox}\ifdim\dp\sizebox>0pt\kern.1em\else\kern.3pt\fi
+ \ifdim\hsize>\wd\sizebox \hrule depth1pt\fi}}}
+\def\lthtmlsetmath{\hbox{\vrule width.1em\kern-.05em\vtop{\vbox{%
+ \kern.1em\kern0.75 pt\hbox{\hglue.17em\copy\sizebox\hglue0.75 pt}}\kern.3pt%
+ \ifdim\dp\sizebox>0pt\kern.1em\fi \kern0.75 pt%
+ \ifdim\hsize>\wd\sizebox \hrule depth1pt\fi}}}
+\def\centerinlinemath{%
+ \dimen1=\ifdim\ht\sizebox<\dp\sizebox \dp\sizebox\else\ht\sizebox\fi
+ \advance\dimen1by.5pt \vrule width0pt height\dimen1 depth\dimen1
+ \dp\sizebox=\dimen1\ht\sizebox=\dimen1\relax}
+
+\def\lthtmlcheckvsize{\ifdim\ht\sizebox<\vsize
+ \ifdim\wd\sizebox<\hsize\expandafter\hfill\fi \expandafter\vfill
+ \else\expandafter\vss\fi}%
+\providecommand{\selectlanguage}[1]{}%
+\makeatletter \tracingstats = 1
+
+
+\begin{document}
+\pagestyle{empty}\thispagestyle{empty}\lthtmltypeout{}%
+\lthtmltypeout{latex2htmlLength hsize=\the\hsize}\lthtmltypeout{}%
+\lthtmltypeout{latex2htmlLength vsize=\the\vsize}\lthtmltypeout{}%
+\lthtmltypeout{latex2htmlLength hoffset=\the\hoffset}\lthtmltypeout{}%
+\lthtmltypeout{latex2htmlLength voffset=\the\voffset}\lthtmltypeout{}%
+\lthtmltypeout{latex2htmlLength topmargin=\the\topmargin}\lthtmltypeout{}%
+\lthtmltypeout{latex2htmlLength topskip=\the\topskip}\lthtmltypeout{}%
+\lthtmltypeout{latex2htmlLength headheight=\the\headheight}\lthtmltypeout{}%
+\lthtmltypeout{latex2htmlLength headsep=\the\headsep}\lthtmltypeout{}%
+\lthtmltypeout{latex2htmlLength parskip=\the\parskip}\lthtmltypeout{}%
+\lthtmltypeout{latex2htmlLength
oddsidemargin=\the\oddsidemargin}\lthtmltypeout{}%
+\makeatletter
address@hidden evensidemargin=\the\evensidemargin}%
+\else\lthtmltypeout{latex2htmlLength evensidemargin=\the\oddsidemargin}\fi%
+\lthtmltypeout{}%
+\makeatother
+\setcounter{page}{1}
+\onecolumn
+
+% !!! IMAGES START HERE !!!
+
+{\newpage\clearpage
+\lthtmldisplayA{displaymath6}%
+\begin{displaymath} \chi^2 = \sum_{i=1}^N
+ \left(y_i - (a + b x_i)
+ \over \sigma_i\right)^2 \end{displaymath}%
+\lthtmldisplayZ
+\lthtmlcheckvsize\clearpage}
+
+
+\end{document}
Index: test/formatting/res_all/tex_l2h_mediawiki/tex_l2h_labels.pl
===================================================================
RCS file: test/formatting/res_all/tex_l2h_mediawiki/tex_l2h_labels.pl
diff -N test/formatting/res_all/tex_l2h_mediawiki/tex_l2h_labels.pl
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res_all/tex_l2h_mediawiki/tex_l2h_labels.pl 22 Oct 2009
20:23:21 -0000 1.1
@@ -0,0 +1,13 @@
+# LaTeX2HTML
+# Associate labels original text with physical files.
+
+
+1;
+
+
+# LaTeX2HTML
+# labels from external_latex_labels array.
+
+
+1;
+
Index: test/formatting/res_info/tex_httex_mediawiki/tex
===================================================================
RCS file: test/formatting/res_info/tex_httex_mediawiki/tex
diff -N test/formatting/res_info/tex_httex_mediawiki/tex
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res_info/tex_httex_mediawiki/tex 22 Oct 2009 20:23:21
-0000 1.1
@@ -0,0 +1,40 @@
+<div id="Top"></div>
+<div id="Tests"></div>
+== Tests ==
+
+Now tex on the same line some <!--l. 6-->
+<center class="math-display">[[Image:tex_tex4ht_tex0x.png| N (
)2
+Ï2 = â yi --(a+-bxi)
+i=1 Ïi
+]]</center><!--l. 11-->
+bidule
+Some text one the line following @end tex
+
+Now tex on the following line, valid fot tex (with @end tex on a line).
+some <!--l. 15-->
+tex <span class="TEX">T<span class="E">E</span>X</span>
+
+Same that @html (but empty following line not ignored).
+
+Test of @math
+Here some <math>{x^i}\over{\tan y}</math>.
+
+Maths with protected \:
+<math>a \ b</math>.
+
+Maths with code @-command:
+
+<math><code>math code</code></math>
+
+Maths with code @-command and braces:
+
+<math> \underline{<code>math \hbox{ code }}</code>
\sum_{i}{\underline{f}}</math>
+
address@hidden outside of math
+
address@hidden
+
+
+----
+
+This document was generated on <i>a sunny day</i> using
[http://www.nongnu.org/texi2html/ <i>texi2html</i>].
Index: test/formatting/res_info/tex_httex_mediawiki/tex.2
===================================================================
RCS file: test/formatting/res_info/tex_httex_mediawiki/tex.2
diff -N test/formatting/res_info/tex_httex_mediawiki/tex.2
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res_info/tex_httex_mediawiki/tex.2 22 Oct 2009 20:23:21
-0000 1.1
@@ -0,0 +1 @@
+dvipng warning: DVI magnification of 1000 over-ridden by user (1400)
tex.texi:42: warning: Unknown command address@hidden'
Index: test/formatting/res_info/tex_httex_mediawiki/tex_tex4ht_math.texi
===================================================================
RCS file: test/formatting/res_info/tex_httex_mediawiki/tex_tex4ht_math.texi
diff -N test/formatting/res_info/tex_httex_mediawiki/tex_tex4ht_math.texi
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res_info/tex_httex_mediawiki/tex_tex4ht_math.texi 22 Oct
2009 20:23:21 -0000 1.1
@@ -0,0 +1,5 @@
+\input texinfo
address@hidden tex_tex4ht_math.info
address@hidden Automatically generated
+
address@hidden
Index: test/formatting/res_info/tex_httex_mediawiki/tex_tex4ht_tex.4ct
===================================================================
RCS file: test/formatting/res_info/tex_httex_mediawiki/tex_tex4ht_tex.4ct
diff -N test/formatting/res_info/tex_httex_mediawiki/tex_tex4ht_tex.4ct
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res_info/tex_httex_mediawiki/tex_tex4ht_tex.4ct 22 Oct
2009 20:23:21 -0000 1.1
@@ -0,0 +1,2 @@
+\expandafter\ifx\csname doTocEntry\endcsname\relax \expandafter\endinput\fi
+\par
Index: test/formatting/res_info/tex_httex_mediawiki/tex_tex4ht_tex.4tc
===================================================================
RCS file: test/formatting/res_info/tex_httex_mediawiki/tex_tex4ht_tex.4tc
diff -N test/formatting/res_info/tex_httex_mediawiki/tex_tex4ht_tex.4tc
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res_info/tex_httex_mediawiki/tex_tex4ht_tex.4tc 22 Oct
2009 20:23:21 -0000 1.1
@@ -0,0 +1 @@
+\expandafter\ifx\csname doTocEntry\endcsname\relax \expandafter\endinput\fi
Index: test/formatting/res_info/tex_httex_mediawiki/tex_tex4ht_tex.css
===================================================================
RCS file: test/formatting/res_info/tex_httex_mediawiki/tex_tex4ht_tex.css
diff -N test/formatting/res_info/tex_httex_mediawiki/tex_tex4ht_tex.css
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res_info/tex_httex_mediawiki/tex_tex4ht_tex.css 22 Oct
2009 20:23:21 -0000 1.1
@@ -0,0 +1,43 @@
+
+/* start css.sty */
+.cmr-7{font-size:70%;}
+.cmmi-10{font-style: italic;}
+.cmmi-7{font-size:70%;font-style: italic;}
+p.noindent { text-indent: 0em }
+td p.noindent { text-indent: 0em; margin-top:0em; }
+p.nopar { text-indent: 0em; }
+p.indent{ text-indent: 1.5em }
address@hidden print {div.crosslinks {visibility:hidden;}}
+a img { border-top: 0; border-left: 0; border-right: 0; }
+center { margin-top:1em; margin-bottom:1em; }
+td center { margin-top:0em; margin-bottom:0em; }
+.Canvas { position:relative; }
+img.math{vertical-align:middle;}
+.obeylines-h,.obeylines-v {white-space: nowrap; }
+div.obeylines-v p { margin-top:0; margin-bottom:0; }
+.overline{ text-decoration:overline; }
+.overline img{ border-top: 1px solid black; }
+td.displaylines {text-align:center; white-space:nowrap;}
+.centerline {text-align:center;}
+.rightline {text-align:right;}
+span.TEX {letter-spacing: -0.125em; }
+span.TEX span.E{ position:relative;top:0.5ex;left:-0.0417em;}
+a span.TEX span.E {text-decoration: none; }
+.underline{ text-decoration:underline; }
+.underline img{ border-bottom: 1px solid black; margin-bottom:1pt; }
+div.proclaim { margin-top: 1em; margin-bottom: 1em; }
+p.item {text-indent:-2em; margin-left:2em;}
+p.itemitem {text-indent:-2em; margin-left:4em;}
+span.item, span.itemitem {width:2em; margin-right:0.4em;}
+td.eqalign3 { text-align:right; margin-left:10em;}
+.eqalign td { white-space: nowrap; }
+div.eqalign {text-align:center;}
+td.eqalignno3, td.leqalignno3 { text-align:right; margin-left:10em;}
+.leqalignno td, .eqalignno td { white-space: nowrap; }
+.leqalignno td.noalign, .eqalignno td.noalign { width:5%; white-space: normal;
}
+table.leqalignno, table.eqalignno {width:100%;}
+img.cdots{vertical-align:middle;}
+div.pmatrix {text-align:center;}
+table.pmatrix {width:100%;}
+/* end css.sty */
+
Index: test/formatting/res_info/tex_httex_mediawiki/tex_tex4ht_tex.lg
===================================================================
RCS file: test/formatting/res_info/tex_httex_mediawiki/tex_tex4ht_tex.lg
diff -N test/formatting/res_info/tex_httex_mediawiki/tex_tex4ht_tex.lg
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res_info/tex_httex_mediawiki/tex_tex4ht_tex.lg 22 Oct
2009 20:23:21 -0000 1.1
@@ -0,0 +1,55 @@
+htfcss: cmmi font-style: italic;
+htfcss: cmmib font-style: italic; font-weight: bold;
+File: tex_tex4ht_tex.html
+File: tex_tex4ht_tex.css
+File: tex_tex4ht_tex.tmp
+Css: p.noindent { text-indent: 0em }
+Css: td p.noindent { text-indent: 0em; margin-top:0em; }
+Css: p.nopar { text-indent: 0em; }
+Css: p.indent{ text-indent: 1.5em }
+Css: @media print {div.crosslinks {visibility:hidden;}}
+Css: a img { border-top: 0; border-left: 0; border-right: 0; }
+Font_Css("4"): .small-caps{font-variant: small-caps; }
+Font_Css("10"): .htf-cmbx {font-weight: bold; font-style:normal;}
+Font_Css("12"): .htf-calligraphy {font-family:cursive}
+Font_Css("14"): .htf-italic {font-style: italic;}
+Font_Css("16"): .htf-bold {font-weight: bold;}
+Font_Css("12"): .htf-calligraphy-bold {font-family:cursive ; font-weight:
bold; }
+Css: center { margin-top:1em; margin-bottom:1em; }
+Css: td center { margin-top:0em; margin-bottom:0em; }
+Css: .Canvas { position:relative; }
+Css: img.math{vertical-align:middle;}
+Css: .obeylines-h,.obeylines-v {white-space: nowrap; }
+Css: div.obeylines-v p { margin-top:0; margin-bottom:0; }
+Css: .overline{ text-decoration:overline; }
+Css: .overline img{ border-top: 1px solid black; }
+Css: td.displaylines {text-align:center; white-space:nowrap;}
+Css: .centerline {text-align:center;}
+Css: .rightline {text-align:right;}
+Css: span.TEX {letter-spacing: -0.125em; }
+Css: span.TEX span.E{ position:relative;top:0.5ex;left:-0.0417em;}
+Css: a span.TEX span.E {text-decoration: none; }
+Css: .underline{ text-decoration:underline; }
+Css: .underline img{ border-bottom: 1px solid black; margin-bottom:1pt; }
+Css: div.proclaim { margin-top: 1em; margin-bottom: 1em; }
+Css: p.item {text-indent:-2em; margin-left:2em;}
+Css: p.itemitem {text-indent:-2em; margin-left:4em;}
+Css: span.item, span.itemitem {width:2em; margin-right:0.4em;}
+Css: td.eqalign3 { text-align:right; margin-left:10em;}
+Css: .eqalign td { white-space: nowrap; }
+Css: div.eqalign {text-align:center;}
+Css: td.eqalignno3, td.leqalignno3 { text-align:right; margin-left:10em;}
+Css: .leqalignno td, .eqalignno td { white-space: nowrap; }
+Css: .leqalignno td.noalign, .eqalignno td.noalign { width:5%; white-space:
normal; }
+Css: table.leqalignno, table.eqalignno {width:100%;}
+Css: img.cdots{vertical-align:middle;}
+Css: div.pmatrix {text-align:center;}
+Css: table.pmatrix {width:100%;}
+--- needs --- tex_tex4ht_tex.idv[1] ==> tex_tex4ht_tex0x.png ---
+--- characters ---
+Font("cmr","10","10","100")
+Font("cmr","7","7","100")
+Font("cmmi","10","10","100")
+Font("cmmi","7","7","100")
+Font("cmsy","10","10","100")
+Font("cmex","10","10","100")
Index: test/formatting/res_info/tex_httex_mediawiki/tex_tex4ht_tex.tex
===================================================================
RCS file: test/formatting/res_info/tex_httex_mediawiki/tex_tex4ht_tex.tex
diff -N test/formatting/res_info/tex_httex_mediawiki/tex_tex4ht_tex.tex
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res_info/tex_httex_mediawiki/tex_tex4ht_tex.tex 22 Oct
2009 20:23:21 -0000 1.1
@@ -0,0 +1,18 @@
+% Automatically generated
+\csname tex4ht\endcsname
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin tex_tex4ht_tex tex 1 -->\Hnewline}
+ some
+
+$$ \chi^2 = \sum_{i=1}^N
+ \left(y_i - (a + b x_i)
+ \over \sigma_i\right)^2 $$
+
+
+\HCode{\Hnewline <!-- tex4ht_end tex_tex4ht_tex tex 1 -->\Hnewline \Hnewline}
+\HCode{\Hnewline \Hnewline <!-- tex4ht_begin tex_tex4ht_tex tex 2 -->\Hnewline}
+ some
+
+tex \TeX
+\HCode{\Hnewline <!-- tex4ht_end tex_tex4ht_tex tex 2 -->\Hnewline \Hnewline}
+
+\bye
Index: test/formatting/res_info/tex_httex_mediawiki/tex_tex4ht_tex.tmp
===================================================================
RCS file: test/formatting/res_info/tex_httex_mediawiki/tex_tex4ht_tex.tmp
diff -N test/formatting/res_info/tex_httex_mediawiki/tex_tex4ht_tex.tmp
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res_info/tex_httex_mediawiki/tex_tex4ht_tex.tmp 22 Oct
2009 20:23:21 -0000 1.1
@@ -0,0 +1,2 @@
+
+/* css.sty */
\ No newline at end of file
Index: test/formatting/res_info/tex_httex_mediawiki/tex_tex4ht_tex.xref
===================================================================
RCS file: test/formatting/res_info/tex_httex_mediawiki/tex_tex4ht_tex.xref
diff -N test/formatting/res_info/tex_httex_mediawiki/tex_tex4ht_tex.xref
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res_info/tex_httex_mediawiki/tex_tex4ht_tex.xref 22 Oct
2009 20:23:21 -0000 1.1
@@ -0,0 +1 @@
+\:CrossWord{)F1F-}{tex_tex4ht_tex.html}{1}%
Index: test/formatting/res_info/tex_l2h_mediawiki/tex
===================================================================
RCS file: test/formatting/res_info/tex_l2h_mediawiki/tex
diff -N test/formatting/res_info/tex_l2h_mediawiki/tex
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res_info/tex_l2h_mediawiki/tex 22 Oct 2009 20:23:21
-0000 1.1
@@ -0,0 +1,39 @@
+<div id="Top"></div>
+<div id="Tests"></div>
+== Tests ==
+
+Now tex on the same line <pre class="tex"> some
+$$ \chi^2 = \sum_{i=1}^N
+\left(y_i - (a + b x_i)
+\over \sigma_i\right)^2 $$
+</pre> bidule
+Some text one the line following @end tex
+
+Now tex on the following line, valid fot tex (with @end tex on a line).
+<pre class="tex"> some
+tex \TeX
+</pre>
+Same that @html (but empty following line not ignored).
+
+Test of @math
+Here some <math>{x^i}\over{\tan y}</math>.
+
+Maths with protected \:
+<math>a \ b</math>.
+
+Maths with code @-command:
+
+<math><code>math code</code></math>
+
+Maths with code @-command and braces:
+
+<math> \underline{<code>math \hbox{ code }}</code>
\sum_{i}{\underline{f}}</math>
+
address@hidden outside of math
+
address@hidden
+
+
+----
+
+This document was generated on <i>a sunny day</i> using
[http://www.nongnu.org/texi2html/ <i>texi2html</i>].
Index: test/formatting/res_info/tex_l2h_mediawiki/tex.2
===================================================================
RCS file: test/formatting/res_info/tex_l2h_mediawiki/tex.2
diff -N test/formatting/res_info/tex_l2h_mediawiki/tex.2
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ test/formatting/res_info/tex_l2h_mediawiki/tex.2 22 Oct 2009 20:23:21
-0000 1.1
@@ -0,0 +1,2 @@
+Unknown option: l2h
+tex.texi:42: warning: Unknown command address@hidden'