Manipulating Polynomials

[done-with-fish]

I would like to use polymake to compute coefficients of certain generating functions. For example, the script

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use application 'polytope'; sub hStarPoly { my ($p) = @_; my $h = $p -> H_STAR_VECTOR; my $d = $h -> dim(); my $R = new Ring("t"); $d -= 1; my $exps = new Matrix<Int>( map { "$_" } (0..$d) ); my $poly = new Polynomial($exps,$h,$R); return $poly; }

can be used to compute the h* polynomial of a polytope. So running

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$h = hStarPoly(cube(3));

defines a polynomial $h. I'd like to be able to do stuff with $h. For example, I'd like to evaluate $h at 1 or evaluate $h at u^(-1)*v where u and v are indeterminants. Is it possible to this sort of algebra within polymake?

[blorenz]

The polynomials in polymake are rather primitive and do not support this.
But you could create the \( h^* \)-polynomial directly with \( uv^{-1} \) instead of \( t \) by using a slightly bigger exponent matrix with two columns and a ring with u and v as variables.

For more advanced operations with polynomials you could also use the interface to singular (e.g. via singular_eval), but there is currently no direct way to retrieve polynomials back from singular.

Benjamin

[done-with-fish]

Your first suggestion is what I've ended up using. Thanks for the help!