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# hasseDiagramToGraph(HasseDiagram) -- turning a hasse diagram into a graph (intended for graphic representation)

## Description

By default, the HasseGraph will have vertices with empty labels.

 i1 : R=rootSystemA(3) o1 = RootSystem{...8...} o1 : RootSystem i2 : w1 = reduce(R,{2}) o2 = WeylGroupElement{RootSystem{...8...}, | 2 |} | -1 | | 2 | o2 : WeylGroupElement i3 : w2 = reduce(R,{1,2,1,3,2}) o3 = WeylGroupElement{RootSystem{...8...}, | -1 |} | -2 | | 1 | o3 : WeylGroupElement i4 : myInterval=intervalBruhat(w1,w2) o4 = HasseDiagram{{{WeylGroupElement{RootSystem{...8...}, | -1 |}, {{0, | 0 |}, {1, | 1 |}, {2, | -1 |}}}}, {{WeylGroupElement{RootSystem{...8...}, | 1 |}, {{0, | -1 |}, {1, | 1 |}, {3, | 1 |}, {4, | -1 |}}}, {WeylGroupElement{RootSystem{...8...}, | -3 |}, {{1, | 1 |}, {2, | -1 |}, {3, | 0 |}}}, {WeylGroupElement{RootSystem{...8...}, | -2 |}, {{0, | -1 |}, {2, | 2 |}, {4, | 0 |}}}}, {{WeylGroupElement{RootSystem{...8...}, | 2 |}, {{0, | 0 |}, {2, | 2 |}}}, {WeylGroupElement{RootSystem{...8...}, | 3 |}, {{1, | 0 |}, {2, | -1 |}}}, {WeylGroupElement{RootSystem{...8...}, | -3 |}, {{2, | 1 |}, {3, | 0 |}}}, {WeylGroupElement{RootSystem{...8...}, | -2 |}, {{1, | 1 |}, {3, | -1 |}}}, {WeylGroupElement{RootSystem{...8...}, | -1 |}, {{0, | -1 |}, {3, | 2 |}}}}, {{WeylGroupElement{RootSystem{...8...}, | 1 |}, {{0, | 2 |}}}, {WeylGroupElement{RootSystem{...8...}, | 2 |}, {{0, | -1 |}}}, {WeylGroupElement{RootSystem{...8...}, | 3 |}, {{0, | 0 |}}}, {WeylGroupElement{RootSystem{...8...}, | -2 |}, {{0, | 1 |}}}}, {{WeylGroupElement{RootSystem{...8...}, | 2 |}, {}}}} | -2 | | -1 | | 1 | | 2 | | -3 | | 2 | | 1 | | 0 | | 1 | | 2 | | 0 | | 2 | | -1 | | -1 | | 1 | | -1 | | -1 | | -3 | | -1 | | -1 | | -1 | | -1 | | 2 | | 1 | | 0 | | -1 | | 3 | | 1 | | 1 | | -1 | | 2 | | -1 | | -2 | | -1 | | 1 | | 1 | | -2 | | -1 | | 1 | | 1 | | -1 | | 1 | | 2 | | -1 | | -1 | | 1 | | -1 | | -1 | | 1 | | 1 | | -1 | | 1 | | -1 | | 2 | | 2 | | 1 | | 0 | | 2 | | 2 | | 2 | | 0 | | -1 | | 2 | | -1 | | 1 | | 1 | | 2 | | -2 | | -1 | | 1 | | 3 | | -1 | | 0 | | 3 | | 0 | | -2 | | 1 | | 1 | | 2 | | 2 | | -1 | | 2 | o4 : HasseDiagram i5 : hasseDiagramToGraph(myInterval) o5 = HasseGraph{{{, {{, 0}, {, 1}, {, 2}}}}, {{, {{, 0}, {, 1}, {, 3}, {, 4}}}, {, {{, 1}, {, 2}, {, 3}}}, {, {{, 0}, {, 2}, {, 4}}}}, {{, {{, 0}, {, 2}}}, {, {{, 1}, {, 2}}}, {, {{, 2}, {, 3}}}, {, {{, 1}, {, 3}}}, {, {{, 0}, {, 3}}}}, {{, {{, 0}}}, {, {{, 0}}}, {, {{, 0}}}, {, {{, 0}}}}, {{, {}}}} o5 : HasseGraph

It is also possible to ask for reduced decompositions as labels by changing the option "labels" as below.

 i6 : hasseDiagramToGraph(myInterval,"labels"=>"reduced decomposition") o6 = HasseGraph{{{12132, {{3, 0}, {121, 1}, {2, 2}}}}, {{2132, {{2, 0}, {121, 1}, {12321, 3}, {232, 4}}}, {1232, {{12321, 1}, {2, 2}, {3, 3}}}, {1213, {{232, 0}, {1, 2}, {3, 4}}}}, {{213, {{3, 0}, {1, 2}}}, {232, {{3, 1}, {2, 2}}}, {123, {{12321, 2}, {3, 3}}}, {132, {{121, 1}, {232, 3}}}, {121, {{2, 0}, {1, 3}}}}, {{21, {{1, 0}}}, {32, {{232, 0}}}, {23, {{3, 0}}}, {12, {{121, 0}}}}, {{2, {}}}} o6 : HasseGraph