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

Synopsis

• Function: poincareSeries

• Usage:

  poincareSeries(R,x)

• Inputs:
  • R, an instance of the type RootSystem
  • x, a ring element
• Outputs:
  • a ring element, 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]