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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.
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