Singular

D.4.19.8 diagInvariants

Procedure from library normaliz.lib (see normaliz_lib).

Usage:
diagInvariants(intmat A, intmat U);
diagInvariants(intmat A, intmat U, intvec grading);

Return:
This function computes the ring of invariants of a diagonalizable group where is a torus and is a finite abelian group, both acting diagonally on the polynomial ring . The group actions are specified by the input matrices A and U. The first matrix specifies the torus action, the second the action of the finite group. See torusInvariants and finiteDiagInvariants for more detail. The output is a monomial ideal listing the algebra generators of the subalgebra of invariants.

The function returns the ideal given by the input matrix A if one of the options supp, triang, volume, or hseries has been activated. However, in this case some numerical invariants are computed, and some other data may be contained in files that you can read into Singular (see showNuminvs, exportNuminvs).

Example:
 LIB "normaliz.lib"; ring R=0,(x,y,z,w),dp; intmat E[2][4] = -1,-1,2,0, 1,1,-2,-1; intmat C[2][5] = 1,1,1,1,5, 1,0,2,0,7; diagInvariants(E,C); ==> _[1]=y70z35 ==> _[2]=xy19z10 ==> _[3]=x4y6z5 ==> _[4]=x15y5z10 ==> _[5]=x26y4z15 ==> _[6]=x37y3z20 ==> _[7]=x48y2z25 ==> _[8]=x59yz30 ==> _[9]=x70z35