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Coxeter group is a finitely presented group obtained from an Artin
presentation by imposing the extra relations x<
sup>2</
sup>=1 on all
Artin generators x. The resolution for certain (and conjecturally all)
Artin groups described on the preceding page leads to a resolution for
all Coxeter groups. At present this resolution has only been
implemented in HAP for finite Coxeter groups and only in dimensions
less than or equal to n where n denotes the number of generators in the
Coxeter presentation.<
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following commands compute 7 terms of a free resolution for the
symmetric group on 8 letters, and then use this resolution to construct
a resolution for its alternating subgroup of index 2.<
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D:=[[1,[2,3]],[2,[3,3]],[3,[4,3]],[4,[5,3]],[5,[6,3]],[6,[7,3]]];;<
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gap> R:=ResolutionCoxeterGroup(D,7);;<
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gap> S:=ResolutionFiniteSubgroup(R,AlternatingGroup(8));;<
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gap> Homology(TensorWithIntegers(S),4);<
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[ 2 ]<
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