Merge remote-tracking branch 'origin/AutFn' into enh/julia-v0.7
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commit
ecc44a8da6
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@ -340,8 +340,43 @@ function -(X::GroupRingElem{S}, Y::GroupRingElem{T}) where {S, T}
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addeq!((-Y), X)
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end
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@doc doc"""
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mul!(result::AbstractArray{T},
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doc"""
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fmac!(result::AbstractVector{T},
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X::AbstractVector,
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Y::AbstractVector,
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pm::Array{Int,2}) where {T<:Number}
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> Fused multiply-add for group ring coeffs using multiplication table `pm`.
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> The result of X*Y in GroupRing is added in-place to `result`.
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> Notes:
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> * this method will silently produce false results if `X[k]` is non-zero for
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> `k > size(pm,1)`.
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> * This method will fail if any zeros (i.e. uninitialised entries) are present
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> in `pm`.
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> Use with extreme care!
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"""
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function fmac!(result::AbstractVector{T},
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X::AbstractVector,
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Y::AbstractVector,
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pm::Array{Int,2}) where {T<:Number}
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z = zero(T)
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s1 = size(pm,1)
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s2 = size(pm,2)
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@inbounds for j in 1:s2
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if Y[j] != z
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for i in 1:s1
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if X[i] != z
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result[pm[i,j]] += X[i]*Y[j]
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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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doc"""
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mul!(result::AbstractVector{T},
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X::AbstractVector,
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Y::AbstractVector,
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pm::Array{Int,2}) where {T<:Number}
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@ -360,24 +395,12 @@ function mul!(result::AbstractVector{T},
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pm::Array{Int,2}) where {T<:Number}
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z = zero(T)
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result .= z
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lY = length(Y)
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s = size(pm,1)
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@inbounds for j in 1:lY
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if Y[j] != z
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for i in 1:s
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if X[i] != z
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pm[i,j] == 0 && throw(ArgumentError("The product don't seem to be supported on basis!"))
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result[pm[i,j]] += X[i]*Y[j]
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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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return fmac!(result, X, Y, pm)
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end
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@doc doc"""
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mul!(result::GroupRingElem{T},
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doc"""
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mul!{T}(result::GroupRingElem{T},
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X::GroupRingElem,
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Y::GroupRingElem)
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> In-place multiplication for `GroupRingElem`s `X` and `Y`.
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@ -211,4 +211,92 @@ using SparseArrays
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end
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end
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@testset "SumOfSquares in group rings" begin
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∗ = star
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G = FreeGroup(["g", "h", "k", "l"])
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S = G.(G.gens)
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S = [S; inv.(S)]
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ID = G()
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RADIUS=3
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@time E_R, sizes = Groups.generate_balls(S, ID, radius=2*RADIUS);
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@test sizes == [9, 65, 457, 3201, 22409, 156865]
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E_rdict = GroupRings.reverse_dict(E_R)
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pm = GroupRings.create_pm(E_R, E_rdict, sizes[RADIUS]; twisted=true);
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RG = GroupRing(G, E_R, E_rdict, pm)
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g = RG.basis[2]
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h = RG.basis[3]
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k = RG.basis[4]
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l = RG.basis[5]
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G = (1-RG(g))
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@test G^2 == 2 - RG(g) - ∗(RG(g))
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G = (1-RG(g))
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H = (1-RG(h))
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K = (1-RG(k))
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L = (1-RG(l))
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GH = (1-RG(g*h))
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KL = (1-RG(k*l))
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X = (2 - ∗(RG(g)) - RG(h))
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Y = (2 - ∗(RG(g*h)) - RG(k))
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@test -(2 - RG(g*h) - ∗(RG(g*h))) + 2G^2 + 2H^2 == X^2
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@test (2 - RG(g*h) - ∗(RG(g*h))) == GH^2
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@test -(2 - RG(g*h*k) - ∗(RG(g*h*k))) + 2GH^2 + 2K^2 == Y^2
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@test -(2 - RG(g*h*k) - ∗(RG(g*h*k))) +
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2(GH^2 - 2G^2 - 2H^2) +
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4G^2 + 4H^2 + 2K^2 ==
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Y^2
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@test GH^2 - 2G^2 - 2H^2 == - X^2
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@test -(2 - RG(g*h*k) - ∗(RG(g*h*k))) + 4G^2 + 4H^2 + 2K^2 == 2X^2 + Y^2
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@test GH^2 == 2G^2 + 2H^2 - (2 - ∗(RG(g)) - RG(h))^2
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@test KL^2 == 2K^2 + 2L^2 - (2 - ∗(RG(k)) - RG(l))^2
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@test -(2 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) + 2*GH^2 + 2*KL^2 ==
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(2 - ∗(RG(g*h)) - RG(k*l))^2
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@test -(2 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) +
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2(2G^2 + 2H^2 - (2 - ∗(RG(g)) - RG(h))^2) +
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2(2K^2 + 2L^2 - (2 - ∗(RG(k)) - RG(l))^2) ==
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(2 - ∗(RG(g*h)) - RG(k*l))^2
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@test -(2 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) +
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2(2G^2 + 2H^2) +
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2(2K^2 + 2L^2) ==
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(2 - ∗(RG(g*h)) - RG(k*l))^2 +
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2(2 - ∗(RG(g)) - RG(h))^2 +
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2(2 - ∗(RG(k)) - RG(l))^2
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@test -(2 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) +
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2(2 - ∗(RG(g*h*k)) - RG(g*h*k)) + 2L^2 ==
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(2 - ∗(RG(g*h*k)) - RG(l))^2
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@test 2 - ∗(RG(g*h*k)) - RG(g*h*k) ==
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2GH^2 + 2K^2 - (2 - ∗(RG(g*h)) - RG(k))^2
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@test -(2 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) +
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2(2GH^2 + 2K^2 - (2 - ∗(RG(g*h)) - RG(k))^2) + 2L^2 ==
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(2 - ∗(RG(g*h*k)) - RG(l))^2
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@test -(2 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) +
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2(2GH^2 + 2K^2) + 2L^2 ==
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(2 - ∗(RG(g*h*k)) - RG(l))^2 +
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2(2 - ∗(RG(g*h)) - RG(k))^2
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@test -(2 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) +
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8G^2 + 8H^2 + 4K^2 + 2L^2 ==
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(2 - ∗(RG(g*h*k)) - RG(l))^2 + 2(2 - ∗(RG(g*h)) - RG(k))^2 + 4(2 - ∗(RG(g)) - RG(h))^2
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@test -(2 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) +
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2GH^2 + 2KL^2 == (2 - ∗(RG(g*h)) - RG(k*l))^2
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@test -(2 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) + 2(2G^2 + 2H^2) + 2(2K^2 + 2L^2) ==
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(2 - ∗(RG(g*h)) - RG(k*l))^2 + 2(2 - ∗(RG(k)) - RG(l))^2 + 2(2 - ∗(RG(g)) - RG(h))^2
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end
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end
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