Initial Commit

src/GroupAlgebras.jl

@@ -1,5 +1,133 @@
 module GroupAlgebras
 
-# package code goes here
+import Base: convert, show, isequal, ==
+import Base: +, -, *, //
+import Base: size, length, norm, rationalize
 
-end # module
+export GroupAlgebraElement
+
+
+immutable GroupAlgebraElement{T<:Number}
+    coefficients::AbstractVector{T}
+    product_matrix::Array{Int,2}
+    # basis::Array{Any,1}
+
+    function GroupAlgebraElement(coefficients::AbstractVector,
+        product_matrix::Array{Int,2})
+
+        size(product_matrix, 1) == size(product_matrix, 2) ||
+            throw(ArgumentError("Product matrix has to be square"))
+        new(coefficients, product_matrix)
+    end
+end
+
+# GroupAlgebraElement(c,pm,b) = GroupAlgebraElement(c,pm)
+GroupAlgebraElement{T}(c::AbstractVector{T},pm) = GroupAlgebraElement{T}(c,pm)
+
+convert{T<:Number}(::Type{T}, X::GroupAlgebraElement) =
+    GroupAlgebraElement(convert(AbstractVector{T}, X.coefficients), X.product_matrix)
+
+show{T}(io::IO, X::GroupAlgebraElement{T}) = print(io,
+    "Element of Group Algebra over $T of length $(length(X)):\n $(X.coefficients)")
+
+
+function isequal{T, S}(X::GroupAlgebraElement{T}, Y::GroupAlgebraElement{S})
+    if T != S
+        warn("Comparing elements with different coefficients Rings!")
+    end
+    X.product_matrix == Y.product_matrix || return false
+    X.coefficients == Y.coefficients || return false
+    return true
+end
+
+(==)(X::GroupAlgebraElement, Y::GroupAlgebraElement) = isequal(X,Y)
+
+function add{T<:Number}(X::GroupAlgebraElement{T}, Y::GroupAlgebraElement{T})
+    X.product_matrix == Y.product_matrix || throw(ArgumentError(
+    "Elements don't seem to belong to the same Group Algebra!"))
+    return GroupAlgebraElement(X.coefficients+Y.coefficients, X.product_matrix)
+end
+
+function add{T<:Number, S<:Number}(X::GroupAlgebraElement{T},
+    Y::GroupAlgebraElement{S})
+    warn("Adding elements with different base rings!")
+    return GroupAlgebraElement(+(promote(X.coefficients, Y.coefficients)...),
+    X.product_matrix)
+end
+
+(+)(X::GroupAlgebraElement, Y::GroupAlgebraElement) = add(X,Y)
+(-)(X::GroupAlgebraElement) = GroupAlgebraElement(-X.coefficients, X.product_matrix)
+(-)(X::GroupAlgebraElement, Y::GroupAlgebraElement) = add(X,-Y)
+
+function algebra_multiplication{T<:Number}(X::AbstractVector{T}, Y::AbstractVector{T}, pm::Array{Int,2})
+    result = zeros(X)
+    for (j,y) in enumerate(Y)
+        if y != zero(T)
+            for (i, index) in enumerate(pm[:,j])
+                if X[i] != zero(T)
+                    index == 0 && throw(ArgumentError("The product don't seem to belong to the span of basis!"))
+                    result[index] += X[i]*y
+                end
+            end
+        end
+    end
+    return result
+end
+
+function group_star_multiplication{T<:Number}(X::GroupAlgebraElement{T},
+    Y::GroupAlgebraElement{T})
+    X.product_matrix == Y.product_matrix || ArgumentError(
+    "Elements don't seem to belong to the same Group Algebra!")
+    result = algebra_multiplication(X.coefficients, Y.coefficients, X.product_matrix)
+    return GroupAlgebraElement(result, X.product_matrix)
+end
+
+function group_star_multiplication{T<:Number, S<:Number}(
+    X::GroupAlgebraElement{T},
+    Y::GroupAlgebraElement{S})
+    S == T || warn("Multiplying elements with different base rings!")
+    return group_star_multiplication(promote(X,Y)...)
+end
+
+(*){T<:Number, S<:Number}(X::GroupAlgebraElement{T},
+    Y::GroupAlgebraElement{S}) = group_star_multiplication(X,Y);
+
+(*){T<:Number}(a::T, X::GroupAlgebraElement{T}) = GroupAlgebraElement(
+    a*X.coefficients, X.product_matrix)
+
+function scalar_multiplication{T<:Number, S<:Number}(a::T,
+    X::GroupAlgebraElement{S})
+    promote_type(T,S) == S || warn("Scalar and coefficients are in different rings! Promoting result to $(promote_type(T,S))")
+    return GroupAlgebraElement(a*X.coefficients, X.product_matrix)
+end
+
+(*){T<:Number}(a::T,X::GroupAlgebraElement) = scalar_multiplication(a, X)
+
+//{T<:Rational, S<:Rational}(X::GroupAlgebraElement{T}, a::S) =
+    GroupAlgebraElement(X.coefficients//a, X.product_matrix)
+
+//{T<:Rational, S<:Integer}(X::GroupAlgebraElement{T}, a::S) =
+    X//convert(T,a)
+
+length(X::GroupAlgebraElement) = length(X.coefficients)
+size(X::GroupAlgebraElement) = size(X.coefficients)
+
+function norm(X::GroupAlgebraElement, p=2)
+    if p == 1
+        return sum(abs(X.coefficients))
+    elseif p == Inf
+        return max(abs(X.coefficients))
+    else
+        return norm(X.coefficients, p)
+    end
+end
+
+ɛ(X::GroupAlgebraElement) = sum(X.coefficients)
+
+function rationalize{T<:Integer, S<:Number}(
+    ::Type{T}, X::GroupAlgebraElement{S}; tol=eps(S))
+    v = rationalize(T, X.coefficients, tol=tol)
+    return GroupAlgebraElement(v, X.product_matrix)
+end
+
+end