Description
The Poincare polynomial is the numerator of the
Hilbert series. It encodes information about the degrees of basis elements of given object. The polynomial has terms
(-1)^i T_0^(d_0) ... T_(n-1)^(d_(n-1)) in it for each basis element of
C_i with multi-degree
{d_0,...,d_(n-1)}. When the multi-degree has a single component, the term is
(-1)^i T^(d_0).
This polynomial is an element of the degrees ring. Notice that the monomial ordering used in the degrees ring is RevLex, so the polynomials in it will be displayed with the smallest exponents first.