Re: [Axiom-mail] manipulating series not as streams but as sumations

[Ralf Hemmecke]

On 10/21/2014 05:58 AM, Gustavo Goretkin wrote:
> Is it possible to get out of
> 
> series(sin(x),x=0)
> 
> an object that looks more like sum_n=0^n=\infty  (-1)ˆn * x^(2n+1) /
> (2n+1)! than
> 
> x - (1/6)x^3 + (1/120) x^5 ....
> 
> If this is documented somewhere, I'd appreciate a pointer!

I don't exactly understand what you mean. I get the following, and you
certainly get the same.

=================================================================
$ fricas -nosman
Checking for foreign routines
AXIOM="/home/hemmecke/g/fricas-bisect/install/lib/fricas/target/x86_64-unknown-linux"
spad-lib="/home/hemmecke/g/fricas-bisect/install/lib/fricas/target/x86_64-unknown-linux/lib/libspad.so"
foreign routines found
openServer result -2
                       FriCAS Computer Algebra System
          Version: FriCAS d8caf7978e4e8a5775ed13bcc847c8d3a01b2c2e
                  Timestamp: Sun Sep  7 12:43:55 CEST 2014
-----------------------------------------------------------------------------
   Issue )copyright to view copyright notices.
   Issue )summary for a summary of useful system commands.
   Issue )quit to leave FriCAS and return to shell.
-----------------------------------------------------------------------------

(1) -> s := series(sin(x),x=0)

            1  3    1   5     1   7      1    9       1     11      12
   (1)  x - - x  + --- x  - ---- x  + ------ x  - -------- x   + O(x  )
            6      120      5040      362880      39916800
                       Type:
UnivariatePuiseuxSeries(Expression(Integer),x,0)
(2) -> coefficient(s,42)

   (2)  0
                                                    Type:
Expression(Integer)
(3) -> coefficient(s,43)

                                    1
   (3)  - -----------------------------------------------------
          60415263063373835637355132068513997507264512000000000
                                                    Type:
Expression(Integer)

=============================================================

Yes, AXIOM treats a series (in contrast to Maple or Mathematica) as an
infinite object, i.e. the internal structure is such that any
coefficient of this series can be extracted from s.

See for example Chapter 1.11 in the Book.
http://hemmecke.de/fricas/book.pdf
Also Chapter 8.9 might help.

Ralf