
D.4.27 symodstd_lib
 Library:
 symodstd.lib
 Purpose:
 Procedures for computing Groebner basis of ideals
being invariant under certain variable permutations.
 Author:
 Stefan Steidel, steidel@mathematik.unikl.de
 Overview:
 A library for computing the Groebner basis of an ideal in the polynomial
ring over the rational numbers, that is invariant under certain permutations
of the variables, using the symmetry and modular methods.
More precisely let I = <f1,...,fr> be an ideal in Q[x(1),...,x(n)] and
sigma a permutation of order k in Sym(n) such that sigma(I) = I.
We assume that sigma({f1,...,fr}) = {f1,...,fr}. This can always be obtained
by adding sigma(fi) to {f1,...,fr}.
To compute a standard basis of I we apply a modification of the modular
version of the standard basis algorithm (improving the calculations in
positive characteristic). Therefore we only allow primes p such that p1 is
divisible by k. This guarantees the existance of a kth primitive root of
unity in Z/pZ.
Procedures:
