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ring of invariants of a diagonalizable group action

NmzDiagInvariants(M: MAT, N: MAT, R: Ring): LIST of RINGELEM

This function computes the ring of invariants of a diagonalizable group D = T x G where T is a torus and G is a finite abelian group, both acting diagonally on the polynomial ring K[X_1,...,X_n].

The group actions are specified by the input matrices M and N . The first matrix specifies the torus action, the second the action of the finite group. See NmzTorusInvariants or NmzFiniteDiagInvariants for more detail. The output is the monomial subalgebra of invariants in R .

/**/     use R::=QQ[x,y,z,w];
/**/     T := matrix([[-1,-1,2,0],[1,1,-2,-1]]);
/**/     U := matrix([[1,1,1,1,5],[1,0,2,0,7]]);
/**/     NmzDiagInvariants(T,U,R);
[x^4*y^6*z^5, x^15*y^5*z^10, x*y^19*z^10, x^26*y^4*z^15, x^37*y^3*z^20, x^48*y^2*z^25, x^59*y*z^30, x^70*z^35, y^70*z^35]

See Also