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Introduce {Perm,DirectProd}Character <: AbstractCharacter <: Function
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###############################################################################
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#
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# Character of DirectProducts
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# Characters of Symmetric Group and DirectProduct
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#
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###############################################################################
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function epsilon(i, g::DirectProductGroupElem)
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return reduce(*, 1, ((-1)^isone(g.elts[j]) for j in 1:i))
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abstract AbstractCharacter <: Function
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immutable PermCharacter <: AbstractCharacter
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p::Partition
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end
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immutable DirectProdCharacter <: AbstractCharacter
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i::Int
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end
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function (chi::PermCharacter)(g::Nemo.perm)
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R = Nemo.partitionseq(chi.p)
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p = Partition(Nemo.permtype(g))
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return Int(Nemo.MN1inner(R, p, 1, Nemo._charvalsTable))
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end
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## NOTE: this works only for Z/2!!!!
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function (chi::DirectProdCharacter)(g::DirectProductGroupElem)
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return reduce(*, 1, ((-1)^isone(g.elts[j]) for j in 1:chi.i))
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end
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###############################################################################
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