|
|
D.4.16.8 diagInvariants
Procedure from library normaliz.lib (see normaliz_lib).
- Usage:
- diagInvariants(intmat A, intmat U);
- Return:
- @tex
This function computes the ring of invariants of a diagonalizable group
$D = T\times G$ where $T$ is a torus and $G$ is a finite abelian group, both
acting diagonally on the polynomial ring $K[X_1,\ldots,X_n]$. The group
actions are specified by the input matrices A and U. The first matrix specifies
the torus action, the second the action of the finite group. See
torusInvariants and finiteDiagInvariants for more detail. The output is a
monomial ideal listing the algebra generators of the subalgebra of invariants.
@end tex
The function returns the ideal given by the input matrix A if one of
the options supp, triang, or hvect 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.
Example:
| | LIB "normaliz.lib";
ring R=0,(x,y,z,w),dp;
intmat E[2][4] = -1,-1,2,0, 1,1,-2,-1;
intmat C[2][5] = 1,1,1,1,5, 1,0,2,0,7;
diagInvariants(E,C);
==> _[1]=y70z35
==> _[2]=xy19z10
==> _[3]=x70z35
==> _[4]=x59yz30
==> _[5]=x48y2z25
==> _[6]=x37y3z20
==> _[7]=x26y4z15
==> _[8]=x15y5z10
==> _[9]=x4y6z5
|
See also:
exportNuminvs;
finiteDiagInvariants;
intersectionValRingIdeals;
intersectionValRings;
showNuminvs;
torusInvariants.
|
