i1 : R=rootSystemA(3) o1 = RootSystem{...8...} o1 : RootSystem |
i2 : P=parabolic(R,set {3}) o2 = set {3} o2 : Parabolic |
i3 : w1 = reduce(R,{2}) o3 = WeylGroupElement{RootSystem{...8...}, | 2 |} | -1 | | 2 | o3 : WeylGroupElement |
i4 : w2 = reduce(R,{1,2,1,3,2}) o4 = WeylGroupElement{RootSystem{...8...}, | -1 |} | -2 | | 1 | o4 : WeylGroupElement |
i5 : myInterval=intervalBruhat(w1 % P,w2 % P) o5 = HasseDiagram{{{WeylGroupElement{RootSystem{...8...}, | 1 |}, {{0, | 1 |}, {1, | -1 |}}}}, {{WeylGroupElement{RootSystem{...8...}, | -2 |}, {{0, | 1 |}, {1, | -1 |}}}, {WeylGroupElement{RootSystem{...8...}, | -1 |}, {{1, | 2 |}, {2, | -1 |}}}}, {{WeylGroupElement{RootSystem{...8...}, | 2 |}, {{0, | -1 |}}}, {WeylGroupElement{RootSystem{...8...}, | -2 |}, {{0, | 1 |}}}, {WeylGroupElement{RootSystem{...8...}, | 1 |}, {{0, | 2 |}}}}, {{WeylGroupElement{RootSystem{...8...}, | 2 |}, {}}}} | -3 | | 0 | | 1 | | 3 | | 1 | | 1 | | -1 | | -1 | | 2 | | 1 | | 1 | | 1 | | 1 | | -2 | | -1 | | -1 | | 1 | | 1 | | 1 | | -2 | | -1 | | 1 | | 3 | | 0 | | -1 | | -2 | | 1 | | 2 | | -1 | | 3 | | 0 | | 2 | o5 : HasseDiagram |
Each row of the Hasse diagram contains the elements of a certain length together with their links to the next row.
i6 : myInterval#1 o6 = {{WeylGroupElement{RootSystem{...8...}, | -2 |}, {{0, | 1 |}, {1, | -1 | 3 | | 1 | | 1 | -2 | | -1 | | 1 ------------------------------------------------------------------------ |}}}, {WeylGroupElement{RootSystem{...8...}, | -1 |}, {{1, | 2 |}, {2, | | -1 | | -1 | | | 3 | | 0 | ------------------------------------------------------------------------ | -1 |}}}} | 2 | | -1 | o6 : List |