CoCoA:HilbertSeriesMultiDeg

HilbertSeriesMultiDeg

the Hilbert-Poincare series wrt a multigrading

Description

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 <ttref>PoincareMultiDeg</ttref> is exacly the same as <ttref>HilbertSeriesMultiDeg</ttref>.

NOTES:

CoCoA-4 has an intrinsic limitation on multigradings (<ttref>Weights Modifier</ttref>)

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 (<ttref>IsPositiveGrading</ttref>).

Example

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

Syntax

HilbertSeriesMultiDeg(TAGGED(<quotes>Quotient</quotes>),WM:MAT):TAGGED(<quotes>$hp.PSeries</quotes>)

HilbertSeries

Weights Modifier

IsPositiveGrading

PositiveGrading4

PoincareMultiDeg

   <type>groebner</type>
   <type>groebner-basic</type>
   <type>hilbert</type>
   <type>quotient</type>
   <type>ring</type>