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WeylGroups :: poincareSeries(HasseDiagram,RingElement)

poincareSeries(HasseDiagram,RingElement) -- the generating series of a Hasse diagram

Synopsis

Description

i1 : R=rootSystemA(2)

o1 = RootSystem{...8...}

o1 : RootSystem
i2 : H=intervalBruhat(neutralWeylGroupElement R, longestWeylGroupElement R)

o2 = HasseDiagram{{{WeylGroupElement{RootSystem{...8...}, | -1 |}, {{0, | -1 |}, {1, |  2 |}}}}, {{WeylGroupElement{RootSystem{...8...}, |  1 |}, {{0, | 1 |}, {1, |  2 |}}}, {WeylGroupElement{RootSystem{...8...}, | -2 |}, {{0, | -1 |}, {1, | 1 |}}}}, {{WeylGroupElement{RootSystem{...8...}, | -1 |}, {{0, |  2 |}}}, {WeylGroupElement{RootSystem{...8...}, |  2 |}, {{0, | -1 |}}}}, {{WeylGroupElement{RootSystem{...8...}, | 1 |}, {}}}}
                                                          | -1 |        |  2 |       | -1 |                                              | -2 |        | 1 |       | -1 |                                            |  1 |        |  2 |       | 1 |                                              |  2 |        | -1 |                                            | -1 |        |  2 |                                              | 1 |

o2 : HasseDiagram
i3 : ZZ[x]

o3 = ZZ[x]

o3 : PolynomialRing
i4 : poincareSeries(H,x)

      3     2
o4 = x  + 2x  + 2x + 1

o4 : ZZ[x]