up previous next
the affine HilbertPoincare series
AffHilbertSeries(TAGGED("Quotient")):TAGGED("$hp.PSeries")

This function computes the affine HilbertPoincare series of M.
The grading must be a positive
Z^1grading (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.
/**/ Use R ::= QQ[x,y,z];
/**/ AffHilbertSeries(R/ideal(z^41, x*z^4y3));
(1 +x +x^2 +x^3) / (1x)^2
