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the Hilbert-Poincare series wrt a multigrading

HilbertSeriesMultiDeg(TAGGED("Quotient"), WM:MAT):TAGGED("$hp.PSeries")

This function computes the Hilbert-Poincare series of M. The input, M, must be homogeneous with respect to the grading defined by the second argument.

The function PoincareMultiDeg is exacly the same as HilbertSeriesMultiDeg .

NOTES: CoCoA-4 has an intrinsic limitation on multigradings ( Weights Modifier ) which does not allow zero-entries in the first row of the defining matrix. This function performs all the appropriate conversions for computing the HilbertSeries wrt any positive grading ( IsPositiveGrading ).

  Use R ::= QQ[x,y,z];
  WM := Mat([[1,0,0],[1,-1,0]]);
  HilbertSeriesMultiDeg(R/Ideal(Indets())^2, WM);

See Also