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D.4.25.10 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.
1028#1028.
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 1029#1029 be the 301#301-dimensional torus acting on the polynomial ring
1030#1030 diagonally. Such an action can be described as
follows: there are integers 1031#1031, 1032#1032, 1033#1033, such
that
1034#1034 acts by the substitution
1035#1035
In order to compute the ring of invariants 1028#1028 one must specify the matrix
1036#1036.
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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