134 lines
4.5 KiB
Julia
134 lines
4.5 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, rationalize
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export GroupAlgebraElement
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immutable GroupAlgebraElement{T<:Number}
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coefficients::AbstractVector{T}
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product_matrix::Array{Int,2}
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# basis::Array{Any,1}
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function GroupAlgebraElement(coefficients::AbstractVector,
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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(coefficients, 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::AbstractVector{T},pm) = GroupAlgebraElement{T}(c,pm)
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convert{T<:Number}(::Type{T}, X::GroupAlgebraElement) =
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GroupAlgebraElement(convert(AbstractVector{T}, X.coefficients), 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 $T of length $(length(X)):\n $(X.coefficients)")
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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.coefficients == Y.coefficients || 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<:Number}(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.coefficients+Y.coefficients, X.product_matrix)
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end
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function add{T<:Number, S<:Number}(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.coefficients, Y.coefficients)...),
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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.coefficients, X.product_matrix)
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(-)(X::GroupAlgebraElement, Y::GroupAlgebraElement) = add(X,-Y)
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function algebra_multiplication{T<:Number}(X::AbstractVector{T}, Y::AbstractVector{T}, pm::Array{Int,2})
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result = zeros(X)
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for (j,y) in enumerate(Y)
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if y != zero(T)
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for (i, index) in enumerate(pm[:,j])
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if X[i] != zero(T)
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index == 0 && throw(ArgumentError("The product don't seem to belong to the span of basis!"))
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result[index] += X[i]*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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return result
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end
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function group_star_multiplication{T<:Number}(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 = algebra_multiplication(X.coefficients, Y.coefficients, X.product_matrix)
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return GroupAlgebraElement(result, X.product_matrix)
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end
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function group_star_multiplication{T<:Number, S<:Number}(
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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<:Number, S<:Number}(X::GroupAlgebraElement{T},
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Y::GroupAlgebraElement{S}) = group_star_multiplication(X,Y);
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(*){T<:Number}(a::T, X::GroupAlgebraElement{T}) = GroupAlgebraElement(
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a*X.coefficients, X.product_matrix)
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function scalar_multiplication{T<:Number, S<:Number}(a::T,
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X::GroupAlgebraElement{S})
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promote_type(T,S) == S || warn("Scalar and coefficients are in different rings! Promoting result to $(promote_type(T,S))")
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return GroupAlgebraElement(a*X.coefficients, X.product_matrix)
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end
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(*){T<:Number}(a::T,X::GroupAlgebraElement) = scalar_multiplication(a, X)
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//{T<:Rational, S<:Rational}(X::GroupAlgebraElement{T}, a::S) =
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GroupAlgebraElement(X.coefficients//a, X.product_matrix)
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//{T<:Rational, S<:Integer}(X::GroupAlgebraElement{T}, a::S) =
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X//convert(T,a)
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length(X::GroupAlgebraElement) = length(X.coefficients)
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size(X::GroupAlgebraElement) = size(X.coefficients)
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function norm(X::GroupAlgebraElement, p=2)
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if p == 1
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return sum(abs(X.coefficients))
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elseif p == Inf
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return max(abs(X.coefficients))
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else
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return norm(X.coefficients, p)
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end
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end
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ɛ(X::GroupAlgebraElement) = sum(X.coefficients)
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function rationalize{T<:Integer, S<:Number}(
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::Type{T}, X::GroupAlgebraElement{S}; tol=eps(S))
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v = rationalize(T, X.coefficients, tol=tol)
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return GroupAlgebraElement(v, X.product_matrix)
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end
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end
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