
D.4.18.6 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.
.
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 be the dimensional torus acting on the polynomial ring
diagonally. Such an action can be described as
follows: there are integers , , , such
that
acts by the substitution
In order to compute the ring of invariants one must specify the matrix
.
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]=x2z
==> _[2]=xyz
==> _[3]=y2z
 See also:
diagInvariants;
finiteDiagInvariants;
intersectionValRingIdeals;
intersectionValRings.
