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. 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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