# poincare(Ring) -- assemble degrees of an ring into a polynomial

## Synopsis

• Function: poincare
• Usage:
poincare R
• Inputs:
• Outputs:
• , in the Laurent polynomial ring whose variables correspond to the degrees of the ring

## Description

We compute the Poincare polynomial of a ring.
 i1 : R=ZZ/101[x]/ideal(x^2); i2 : poincare R 2 o2 = 1 - T o2 : ZZ[T] i3 : numerator hilbertSeries R 2 o3 = 1 - T o3 : ZZ[T]
Recall that the variables of the polynomial are the variables of the degrees ring.
 i4 : R=ZZ/101[x, Degrees => {{1,1}}]/ideal(x^2); i5 : poincare R 2 2 o5 = 1 - T T 0 1 o5 : ZZ[T ..T ] 0 1 i6 : numerator hilbertSeries R 2 2 o6 = 1 - T T 0 1 o6 : ZZ[T ..T ] 0 1