Re: [Axiom-developer] RE: [xml-litprog-l] Re: noweb, pamphlets, and TeXmacs

[Mike Dewar]

On Mon, Nov 25, 2002 at 01:16:07PM -0500, Bill Page wrote:
<snip>
> LaTex is a defacto standard notation for mathematical
> markup but MATH/ML is rapidly evolving as a more
> "modern" alternative. Should one attempt to adopt such
> a radially different (and some say exceedingly verbose)
> approach as MATH/ML in the design of a new user
> interface for Axiom? How advanced are the graphical
> rendering packages? (More open source?) Could MATH/ML
> be integrated with a tool like Leo? The alternative
> of a LaTex-like interface is already available in
> TeXmacs. But the use of XML as a standard visible
> "internal" representation format strikes me as very
> very desirable. And of course by design MATH/ML is
> much more compatible with XML than is LaTex encoding.

LaTeX is fine as a rendering language but it does not have a regular
syntax and is very hard to manipulate.  I've just spent several months
working with XML documents with embedded fragments of LaTeX for
mathematics and the upshot is that we're removing the LaTeX and
replacing it with MathML.  Also, once you translate to LaTeX, it is
very hard to have any degree of interactivity such as cut-and-paste
since the structure of the rendered version may have little or no
relationship to the underlying data structures.  With MathML/XML you can
annotate the presentation form with the content form (and vice-versa) or
use xref to link related parts of different structures.  In addition you
have access to tools based on XSLT etc.  There is no reason why you
cannot use XSLT to render MathML - and indeed there is a SourceForge
project to do just that (http://sourceforge.net/projects/xsltml).

As far as rendering goes, Mozilla based its MathML rendering on TeX and
is really quite good.  The same code also found its way into Netscape 7.
There are also various plugins available for IE, you can find my
colleague David Carlisle's "universal stylesheet" at the MathML home
page (http://www.w3c.org/Math) which allows you to produce documents
which are portable across several browsers.  By the way David is bot
only a member of the MathMl committee but also one of the authors of
LaTeX2e so we aren't biased!

Having said all that you need to be careful when using MathML for
content markup - the defined symbols are fairly trivial (US high-school
maths) and you need to use one of the extension mechanisms such as
csymbol to extend the namespace for more interesting things.  You can
use OpenMath (http://monet.nag.co.uk/openmath) for this, i.e. make the
definitionURL attribute point to an appropriate OpenMath Content
Dictionary, or do what Maple and Mathematica do and use system-specific
URIs.  

Regards, Mike.

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