CoCoA:HVector

HVector

the h-vector of a module or quotient object

Description

This function returns the h-vector of M, i.e., the

coefficients of the numerator of the simplified Poincare series for M.

M can be a module or a quotient.

The weights of the indeterminates of the polynomial ring of M must all be 1,

and the coefficient ring must be a field.

If the input is not homogeneous, the Hilbert function of the

corresponding leading term (initial) ideal or module is calculated.

Example

  Use R ::= Q[t,x,y,z];
  HVector(R/Ideal(x,y,z)^5);
[1, 3, 6, 10, 15]
-------------------------------
  Poincare(R/Ideal(x,y,z)^5);
(1 + 3t + 6t^2 + 10t^3 + 15t^4) / (1-t)
-------------------------------

Syntax

HVector(R:RING or TAGGED(<quotes>Quotient</quotes>)):LIST

Hilbert

HilbertSeries

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