Singular Manual: finiteDiagInvariants

| #### D.4.25.11 finiteDiagInvariants Procedure from library `normaliz.lib` (see normaliz_lib). Usage: finiteDiagInvariants(intmat U); finiteDiagInvariants(intmat U, intvec grading); Return: This function computes the ring of invariants of a finite abelian group 190#190 acting diagonally on the surrounding polynomial ring 1037#1037. The group is the direct product of cyclic groups generated by finitely many elements 1038#1038. The element 995#995 acts on the indeterminate 1039#1039 by 1040#1040 where 1041#1041 is a primitive root of unity of order equal to 1042#1042. The ring of invariants is generated by all monomials satisfying the system 1043#1043 mod ord1044#1044, 1045#1045. The input to the function is the 1046#1046 matrix 1047#1047 with rows 1048#1048 ord1049#1049, 1045#1045. The output is a monomial ideal listing the algebra generators of the subalgebra of invariants 1050#1050 for all 1051#1051. The function returns the ideal given by the input matrix C 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). Note: Example:
    LIB "normaliz.lib";
    ring R = 0,(x,y,z,w),dp;
    intmat C[2][5] = 1,1,1,1,5, 1,0,2,0,7;
    finiteDiagInvariants(C);
    ==> _[1]=w5
    ==> _[2]=z7w3
    ==> _[3]=z14w
    ==> _[4]=z35
    ==> _[5]=yw4
    ==> _[6]=yz7w2
    ==> _[7]=yz14
    ==> _[8]=y2w3
    ==> _[9]=y2z7w
    ==> _[10]=y3w2
    ==> _[11]=y3z7
    ==> _[12]=y4w
    ==> _[13]=y5
    ==> _[14]=xz3w
    ==> _[15]=xz24
    ==> _[16]=xyz3
    ==> _[17]=x2z13
    ==> _[18]=x3z2
    ==> _[19]=x5zw4
    ==> _[20]=x5yzw3
    ==> _[21]=x5y2zw2
    ==> _[22]=x5y3zw
    ==> _[23]=x5y4z
    ==> _[24]=x7w3
    ==> _[25]=x7yw2
    ==> _[26]=x7y2w
    ==> _[27]=x7y3
    ==> _[28]=x12zw2
    ==> _[29]=x12yzw
    ==> _[30]=x12y2z
    ==> _[31]=x14w
    ==> _[32]=x14y
    ==> _[33]=x19z
    ==> _[34]=x35
See also: diagInvariants; intersectionValRingIdeals; intersectionValRings; torusInvariants.

User manual for Singular version 4.4.1, 2025, generated by texi2html.