Building maxima / mailing lists / sym package

On Tue, 10 Dec 2002, lp wrote:

> Martin RUBEY wrote:
> 
> > > > In a different vein, I offer to translate the (french)
> documentation
> > > > of sym, if there is no translation yet and if there is somebody
> > > > interested...
> > >
> > > Yes!  Interested!
> 
> I'm interested in the sym package and the documentation also.
> I've been using the Google translator and trial and error to find
> out what the commands do.

Well, the documentation issue has nearly vanished, as I found an English 
doc on the web, here is the link to the links:
http://www.ma.utexas.edu/pipermail/maxima/2002/003111.html

and here is the link:
http://www.mathe2.uni-bayreuth.de/axel/htmlpapers/valibouze.html
> 
> I used Martin's suggestions for the sym1.mac file and
> load("sym") works fine with gcl/maxima on RH 7.3. Thanks for that.
> 
> I'm picking my way through Harold Edward's book on Galois
> Theory and I'm trying to use some relevant Maxima
> commands as I go along.

I don't know anything about Galois Theory, but I'm interested!

> First I'd like to do some simple things with symmetric polynomials
> like compute the representation for a symmetric polynomial
> in terms of elementary symmetric polynomials.
> 
> (eg. (x - y)^2 = (x + y)^2 - 4xy = (e1)^2 - 4(e2) )
> 
This is very easy:

(C11) elem:2;

(D11)                                  2
(C12) elem([],(x - y)^2,[x,y]);

                                    2
(D12)                             E1  - 4 E2

The reason why it looks a little complicated is the following: the 
function elem comes in three flavors, if elem=2 as I did here, it accepts 
a symmetric polynomial. if elem=1 (default) it accepts a contracted form 
of a symmetric polynomial, which you can get via

(C13) contract((x - y)^2,[x,y]);

                                   2
(D13)                             x  - 2 x y

Contracted form means: keep only one monomial for each orbit.

if elem=3, it uses the partition form of the polynomial.

The first argument of elem is a possibly empty list of integers, the first 
specifying the size of the alphabet (i.e., n if e1=x1+x2+...+xn),

the others can be used to substitute values for the ei after doing the 
basis transformation.

> Does anyone have any suggestions or references for that
> sort of thing? I'm looking at the examples for the sym
> commands in the Maxima  (french) documentation.
> I may start looking at GAP also, but I wanted to see what
> I could do with Maxima first.

Use the english doc, or learn french :-)

All the best,

Martin