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Normaliz :: finiteDiagInvariants

finiteDiagInvariants -- ring of invariants of a finite group action

Synopsis

Description

This function computes the ring of invariants of a finite abelian group G acting diagonally on the surrounding polynomial ring K[X1,...,Xn]. The group is the direct product of cyclic groups generated by finitely many elements g1,...,gw. The element gi acts on the indeterminate Xj by gi(Xj)= λiuijXjwhere λi is a primitive root of unity of order equal to ord(gi). The ring of invariants is generated by all monomials satisfying the system ui1a1+...+uin an ≡ 0 mod ord(gi), i=1,...,w. The input to the function is the w×(n+1) matrix U with rows ui1 ...uin ord(gi), i=1,...,w. The output is the monomial subalgebra of invariants RG={f∈R : gi f= f for all i=1,...,w}.

This method can be used with the options allComputations and grading.

R=QQ[x,y,z,w];
U=matrix{{1,1,1,1,5},{1,0,2,0,7}}
finiteDiagInvariants(U,R)

See also

Ways to use finiteDiagInvariants :