# poincareSeries(RootSystem,RingElement) -- the generating series of the Weyl group by length

## Synopsis

• Function: poincareSeries
• Usage:
poincareSeries(R,x)
• Inputs:
• Outputs:
• , a polynomial in the variable x where the coefficient in front of x^i is the number of elements in the Weyl group of R of length i.

## Description

 i1 : R=rootSystemA(2) o1 = RootSystem{...8...} o1 : RootSystem i2 : ZZ[x] o2 = ZZ[x] o2 : PolynomialRing i3 : poincareSeries(R,x) 3 2 o3 = x + 2x + 2x + 1 o3 : ZZ[x]