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poincare(Ideal) -- assemble degrees of the quotient of the ambient ring by an ideal into a polynomial

Synopsis

Description

We compute the Poincare polynomial of the quotient of the ambient ring by an ideal.
R = ZZ/101[w..z];
I = monomialCurveIdeal(R,{1,3,4});
poincare I
numerator reduceHilbert hilbertSeries I
Recall that the variables of the polynomial are the variables of the degrees ring.
R=ZZ/101[x, Degrees => {{1,1}}];
I = ideal x^2;
poincare I
numerator reduceHilbert hilbertSeries I

Caveat

As is often the case, calling this function on an ideal I actually computes it for R/I where R is the ring of I.