|  |  D.4.20.6 torusInvariants Procedure from librarynormaliz.lib(see  normaliz_lib).
 
Example: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, orhserieshas 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 ![$R = K[X_1 ,\ldots,X_n]$](sing_960.png) 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  . 
 See also:
 diagInvariants;
 finiteDiagInvariants;
 intersectionValRingIdeals;
 intersectionValRings.|  | 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
 | 
 
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