next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
Posets :: poincarePolynomial

poincarePolynomial -- computes the Poincare polynomial of a ranked poset with a unique minimal element

Synopsis

Description

The Poincare polynomial of P is the polynomial in a single variable t derived from the rankFunction and the moebiusFunction of P.

The Poincare polynomial of the n booleanLattice is (1+t)n.
i1 : n = 5;
i2 : factor poincarePolynomial booleanLattice n

            5
o2 = (t + 1)

o2 : Expression of class Product
The Poincare polynomial of the B3 arrangement is (1+t)(1+3t)(1+5t).
i3 : R = QQ[x,y,z];
i4 : A = {x,y,z,x+y,x+z,y+z,x-y,x-z,y-z};
i5 : LA = intersectionLattice(A, R);
i6 : factor poincarePolynomial LA

o6 = (t + 1)(3t + 1)(5t + 1)

o6 : Expression of class Product

See also

Ways to use poincarePolynomial :