On the Reduction of G-invariant Polynomials for Arbitrary Permutation Groups G
Manfred Göbel · Birkhäuser Basel eBooks · 1998
Let R be a commutative ring with 1, let R[X 1…,X n ] be the polynomial ring in X 1,…, X n over R, let G be a permutation group acting on the indeterminates and let σ1, …, σ n be the elementary symmetric polynomials. This paper presents a detailed analysis and implementation issues of an algorithm for computing a representation of an arbitrary G-invariant polynomial in R[X 1…,X n ] as a finite R[σ1, …, σ n ]-linear combination of G-invariant polynomials with a total degree of at most max{n,n(n - 1)/2}. In addition, we show how the degree bounds can be improved for a certain class of permutation groups.