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Macaulay2Doc :: poincare

poincare -- assemble degrees into polynomial

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.

See also

Ways to use poincare :

For the programmer

The object poincare is a method function.