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D.4.26.7 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
acting diagonally on the surrounding polynomial ring
. The
group is the direct product of cyclic groups generated by finitely many
elements . The element acts on the indeterminate by
where is a primitive root of
unity of order equal to . The ring of invariants is generated by all
monomials satisfying the system
mod ord, .
The input to the function is the matrix with rows
ord, . The output is a monomial ideal
listing the algebra generators of the subalgebra of invariants
for all
.
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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