Singular Manual: finiteDiagInvariants

| #### D.4.24.11 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 189#189 acting diagonally on the surrounding polynomial ring 1035#1035. The group is the direct product of cyclic groups generated by finitely many elements 1036#1036. The element 993#993 acts on the indeterminate 1037#1037 by 1038#1038 where 1039#1039 is a primitive root of unity of order equal to 1040#1040. The ring of invariants is generated by all monomials satisfying the system 1041#1041 mod ord1042#1042, 1043#1043. The input to the function is the 1044#1044 matrix 1045#1045 with rows 1046#1046 ord1047#1047, 1043#1043. The output is a monomial ideal listing the algebra generators of the subalgebra of invariants 1048#1048 for all 1049#1049. 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 4.4.0, 2024, generated by texi2html.