Singular Manual: torusInvariants

| #### 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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