122 lines
4.4 KiB
Julia
122 lines
4.4 KiB
Julia
module GroupAlgebras
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import Base: convert, show, isequal, ==
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import Base: +, -, *, //
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import Base: size, length, norm
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export GroupAlgebraElement
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typealias CoordinateVector{T<:Number} AbstractVector{T}
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immutable GroupAlgebraElement{T<:CoordinateVector}
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coordinates::T
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product_matrix::Array{Int,2}
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# basis::Array{Any,1}
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function GroupAlgebraElement(coordinates::T,
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product_matrix::Array{Int,2})
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size(product_matrix, 1) == size(product_matrix, 2) ||
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throw(ArgumentError("Product matrix has to be square"))
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new(coordinates, product_matrix)
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end
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end
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# GroupAlgebraElement(c,pm,b) = GroupAlgebraElement(c,pm)
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GroupAlgebraElement{T}(c::T,pm) = GroupAlgebraElement{T}(c,pm)
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convert{T<:Number}(::Type{T}, X::GroupAlgebraElement) =
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GroupAlgebraElement(convert(CoordinateVector{T}, X.coordinates), X.product_matrix)
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show{T}(io::IO, X::GroupAlgebraElement{T}) = print(io,
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"Element of Group Algebra over $(typeofelt(X)), of length $(length(X)):\n", X.coordinates)
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function isequal{T, S}(X::GroupAlgebraElement{T}, Y::GroupAlgebraElement{S})
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if T != S
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warn("Comparing elements with different coefficients Rings!")
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end
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X.product_matrix == Y.product_matrix || return false
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X.coordinates == Y.coordinates || return false
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return true
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end
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(==)(X::GroupAlgebraElement, Y::GroupAlgebraElement) = isequal(X,Y)
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function add{T<:CoordinateVector}(X::GroupAlgebraElement{T}, Y::GroupAlgebraElement{T})
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X.product_matrix == Y.product_matrix || throw(ArgumentError(
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"Elements don't seem to belong to the same Group Algebra!"))
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return GroupAlgebraElement(X.coordinates+Y.coordinates, X.product_matrix)
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end
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function add{T<:CoordinateVector, S<:CoordinateVector}(X::GroupAlgebraElement{T},
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Y::GroupAlgebraElement{S})
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warn("Adding elements with different base rings!")
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return GroupAlgebraElement(+(promote(X.coordinates, Y.coordinates)...),
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X.product_matrix)
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end
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(+)(X::GroupAlgebraElement, Y::GroupAlgebraElement) = add(X,Y)
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(-)(X::GroupAlgebraElement) = GroupAlgebraElement(-X.coordinates, X.product_matrix)
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(-)(X::GroupAlgebraElement, Y::GroupAlgebraElement) = add(X,-Y)
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function group_star_multiplication{T<:CoordinateVector}(X::GroupAlgebraElement{T},
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Y::GroupAlgebraElement{T})
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X.product_matrix == Y.product_matrix || ArgumentError(
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"Elements don't seem to belong to the same Group Algebra!")
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result = zeros(X.coordinates)
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for (i,x) in enumerate(X.coordinates)
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if x != 0
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for (j,y) in enumerate(Y.coordinates)
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if y != 0
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index = X.product_matrix[i,j]
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if index == 0
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throw(ArgumentError("The product don't seem to belong to the span of basis!"))
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else
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result[index]+= x*y
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end
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end
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end
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end
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end
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return GroupAlgebraElement(result, X.product_matrix)
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end
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function group_star_multiplication{T<:CoordinateVector, S<:CoordinateVector}(
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X::GroupAlgebraElement{T},
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Y::GroupAlgebraElement{S})
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S == T || warn("Multiplying elements with different base rings!")
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return group_star_multiplication(promote(X,Y)...)
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end
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(*){T<:CoordinateVector, S<:CoordinateVector}(X::GroupAlgebraElement{T},
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Y::GroupAlgebraElement{S}) = group_star_multiplication(X,Y);
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typeofelt{T<:Number}(X::AbstractVector{T}) = T
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typeofelt{S<:CoordinateVector}(X::GroupAlgebraElement{S}) = typeofelt(X.coordinates)
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function (*){T<:Number, S<:CoordinateVector}(a::T, X::GroupAlgebraElement{S})
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W = typeofelt(X)
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promote_type(T,W) == W || warn("Scalar and coordinates are in different rings! Promoting result to $(promote_type(T,W))")
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return GroupAlgebraElement(a*X.coordinates, X.product_matrix)
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end
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(*){T<:Number, S<:CoordinateVector}(X::GroupAlgebraElement{S}, a::T) = (*)(a, X)
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function rational_division{T<:CoordinateVector, S<:Rational}(X::GroupAlgebraElement{T}, a::S)
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if typeofelt(X) <: Rational
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return GroupAlgebraElement(X.coordinates//a, X.product_matrix)
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else
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throw(ArgumentError("Rational division attempt on a GroupAlgebraElement of non-rational coefficients!"))
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end
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end
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(//)(X,a) = rational_division(X,a)
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(//){S<:Integer}(X::GroupAlgebraElement, a::S) = //(X, Rational{S}(a))
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length(X::GroupAlgebraElement) = length(X.coordinates)
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size(X::GroupAlgebraElement) = size(X.coordinates)
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norm(X::GroupAlgebraElement, p=2) = norm(X.coordinates, p)
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end
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