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D.4.24.10 torusInvariants
Procedure from library normaliz.lib (see normaliz_lib).
- Usage:
- torusInvariants(intmat A);
torusInvariants(intmat A, intvec grading);
- Return:
- Returns an ideal representing the list of monomials generating the ring of
invariants as an algebra over the coefficient field.
1026#1026.
The function returns the ideal given by the input matrix A 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).
- Background:
- Let 1027#1027 be the 299#299-dimensional torus acting on the polynomial ring
1028#1028 diagonally. Such an action can be described as
follows: there are integers 1029#1029, 1030#1030, 1031#1031, such
that
1032#1032 acts by the substitution
1033#1033
In order to compute the ring of invariants 1026#1026 one must specify the matrix
1034#1034.
Example:
| LIB "normaliz.lib";
ring R=0,(x,y,z,w),dp;
intmat E[2][4] = -1,-1,2,0, 1,1,-2,-1;
torusInvariants(E);
==> _[1]=y2z
==> _[2]=xyz
==> _[3]=x2z
| See also:
diagInvariants;
finiteDiagInvariants;
intersectionValRingIdeals;
intersectionValRings.
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