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

## Synopsis

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

## Description

 i1 : R=rootSystemA(3) o1 = RootSystem{...8...} o1 : RootSystem i2 : P=parabolic(R,set{1,2}) o2 = set {1, 2} o2 : Parabolic i3 : ZZ[x] o3 = ZZ[x] o3 : PolynomialRing i4 : poincareSeries(R,P,x) 3 2 o4 = x + x + x + 1 o4 : ZZ[x]