up previous next
AffHilbertSeries

the affine Hilbert-Poincare series

Syntax
AffHilbertSeries(TAGGED("Quotient")):TAGGED("$hp.PSeries")

Description
This function computes the affine Hilbert-Poincare series of M. The grading must be a positive Z^1-grading (i.e. GradingMat must have a single row with positive entries), and the ordering must be degree compatible. In the standard case, i.e. the weights of all indeterminates are 1, the result is simplified so that the power appearing in the denominator is the dimension of M + 1.

It used to be called AffPoincare [OBSOLESCENT] .

NOTES:

(i) the coefficient ring must be a field.

(ii) these functions produce tagged objects: they cannot safely be (non-)equality to other values.

For further details on affine Hilbert functions see the book: Kreuzer, Robbiano "Computer Commutative Algebra II", Section 5.6.

Example
/**/  use R ::= QQ[x,y,z];
/**/  AffHilbertSeries(R/ideal(z^4-1, x*z^4-y-3));
(1 +x +x^2 +x^3) / (1-x)^2

See Also