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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.
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