# [Maxima] RFC: extracting coefficients of a multivariate polynomial

S. Newhouse sen1 at math.msu.edu
Thu Apr 24 13:04:23 CDT 2008

```andre maute wrote:
> Hi all,
>
> I have to extract the coefficients of a multivariate polynomial.
> The monomials appearing in the multivariate polynomial are given.
>
> For now I'm using the following function,
> which is also the bottleneck of my application.
>
> ---------------------------------------------------------------
> display2d : false;
>
> v : [x,y];
> exps : [[0,2], [0,0], [1,1], [0,1], [1,0], [2,0]];
> poly : a00 + a10*x + a01*y + a20*x^2 + a11*x*y + a02*y^2;
>
> my_coeff(v,exps,poly) := block(
>
>         [c,k,l,h],
>
>         c : [],
>         for k : 1 thru length(exps) do block(
>                 h : poly,
>                 for l : 1 thru length(v) do block(
>                         if exps[k][l] # 0 then block(
>                                 h : coeff(h,v[l],exps[k][l])
>                         )
>                 ),
>                 for l : 1 thru length(v) do block(
>                         h : subst(0,v[l],h)
>                 ),
>                 h : ratsimp(h),
>                 c : append(c,[h])
>         ),
>
>         return(c)
>
> )\$
>
> my_coeff(v,exps,poly);
> ---------------------------------------------------------------------
>
> Does someone know,
> if Maxima does have such a function, a potentially faster one?
>
> The documentation of Maxima revealed nothing for me :-(
>
> Kind Regards,
> Andre
> _______________________________________________
> Maxima mailing list
> Maxima at math.utexas.edu
> http://www.math.utexas.edu/mailman/listinfo/maxima
>
>
You can use the 'coeff' function, perhaps several times. Of course, you
can write a little routine to apply to any polynomial automatically and
do what your my_coeff does. Don't know if it will be faster, but you can
try.

Because my mail program does not easily format the exponents in maxima
screen output, I am sending an example of the manual use of 'coeff' as
an attachment.

HTH,
-sen

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