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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.
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