new, simple arithmetic + tests
This commit is contained in:
parent
1151ac7bd3
commit
6fac166a04
|
|
@ -575,6 +575,7 @@ include("mtables.jl")
|
|||
|
||||
include("types.jl")
|
||||
include("algebra_elts.jl")
|
||||
include("arithmetic.jl")
|
||||
include("show.jl")
|
||||
|
||||
end
|
||||
|
|
|
|||
|
|
@ -0,0 +1,104 @@
|
|||
# module structure:
|
||||
Base.:*(a::Number, X::AlgebraElement) =
|
||||
mul!(similar(X, promote_type(eltype(X), typeof(a))), X, a)
|
||||
Base.:*(X::AlgebraElement, a::Number) = a * X
|
||||
Base.:(/)(X::AlgebraElement, a::Number) = inv(a) * X
|
||||
|
||||
# TODO: handle this through mul!?
|
||||
Base.:(//)(X::AlgebraElement, a::Number) = AlgebraElement(coeffs(X) .// a, parent(X))
|
||||
|
||||
# ring structure:
|
||||
Base.:-(X::AlgebraElement) = neg!(similar(X), X)
|
||||
Base.:+(X::AlgebraElement, Y::AlgebraElement) =
|
||||
add!(similar(X, promote_type(eltype(X), eltype(Y))), X, Y)
|
||||
Base.:-(X::AlgebraElement, Y::AlgebraElement) =
|
||||
sub!(similar(X, promote_type(eltype(X), eltype(Y))), X, Y)
|
||||
Base.:*(X::AlgebraElement, Y::AlgebraElement) =
|
||||
mul!(similar(X, promote_type(eltype(X), eltype(Y))), X, Y)
|
||||
|
||||
Base.:^(a::AlgebraElement, p::Integer) = Base.power_by_squaring(a, p)
|
||||
|
||||
# mutable API; TODO: replace with MutableArithmetic
|
||||
|
||||
zero!(v::AbstractVector{T}) where T = (v .= zero(T); v)
|
||||
|
||||
function zero!(a::AlgebraElement)
|
||||
a.coeffs .= zero(first(coeffs(a)))
|
||||
return a
|
||||
end
|
||||
|
||||
function neg!(res::AlgebraElement, X::AlgebraElement)
|
||||
@assert parent(res) === parent(X)
|
||||
res.coeffs .= -coeffs(X)
|
||||
return res
|
||||
end
|
||||
|
||||
function add!(res::AlgebraElement, X::AlgebraElement, Y::AlgebraElement)
|
||||
@assert parent(res) === parent(X) == parent(Y)
|
||||
# res = (res === X || res === Y) ? similar(res) : res
|
||||
res.coeffs .= coeffs(X) .+ coeffs(Y)
|
||||
return res
|
||||
end
|
||||
|
||||
function sub!(res::AlgebraElement, X::AlgebraElement, Y::AlgebraElement)
|
||||
@assert parent(res) === parent(X) == parent(Y)
|
||||
# res = (res === X || res === Y) ? similar(res) : res
|
||||
res.coeffs .= coeffs(X) .- coeffs(Y)
|
||||
return res
|
||||
end
|
||||
|
||||
function mul!(res::AlgebraElement, X::AlgebraElement, a::Number)
|
||||
@assert parent(res) === parent(X)
|
||||
# res = (res === X || res === Y) ? similar(res) : res
|
||||
res.coeffs .= a .* coeffs(X)
|
||||
return res
|
||||
end
|
||||
|
||||
function mul!(
|
||||
res::AbstractVector,
|
||||
X::AbstractVector,
|
||||
Y::AbstractVector,
|
||||
ms::MultiplicativeStructure,
|
||||
)
|
||||
res = (res === X || res === Y) ? zero(res) : zero!(res)
|
||||
return fmac!(res, X, Y, ms)
|
||||
end
|
||||
|
||||
function mul!(res::AlgebraElement, X::AlgebraElement, Y::AlgebraElement)
|
||||
res = (res === X || res === Y) ? zero(res) : zero!(res)
|
||||
return fmac!(res, X, Y)
|
||||
end
|
||||
|
||||
function fmac!(res::AlgebraElement, X::AlgebraElement, Y::AlgebraElement)
|
||||
A = parent(res)
|
||||
fmac!(coeffs(res), coeffs(X), coeffs(Y), A.mstructure)
|
||||
return res
|
||||
end
|
||||
|
||||
function fmac!(
|
||||
res::AbstractVector,
|
||||
X::SparseVector,
|
||||
Y::SparseVector,
|
||||
mstr::MultiplicativeStructure,
|
||||
)
|
||||
for j in Y.nzind
|
||||
for i in X.nzind
|
||||
res[mstr[i, j]] += X[i] * Y[j]
|
||||
end
|
||||
end
|
||||
return res
|
||||
end
|
||||
|
||||
function fmac!(
|
||||
res::AbstractVector,
|
||||
X::AbstractVector,
|
||||
Y::AbstractVector,
|
||||
mstr::MultiplicativeStructure,
|
||||
)
|
||||
for j in eachindex(Y)
|
||||
for i in eachindex(X)
|
||||
res[mstr[i, j]] += X[i] * Y[j]
|
||||
end
|
||||
end
|
||||
return res
|
||||
end
|
||||
|
|
@ -0,0 +1,159 @@
|
|||
@testset "Arithmetic" begin
|
||||
G = SymmetricGroup(3)
|
||||
b = New.Basis{UInt8}(collect(G))
|
||||
l = length(b)
|
||||
RG = New.StarAlgebra(G, b, (l,l))
|
||||
|
||||
@testset "Module structure" begin
|
||||
a = New.AlgebraElement(ones(Int, order(G)), RG)
|
||||
|
||||
@test -a isa New.AlgebraElement
|
||||
@test New.coeffs(-a) == -New.coeffs(a)
|
||||
|
||||
@test 2*a isa New.AlgebraElement
|
||||
@test eltype(2*a) == typeof(2)
|
||||
@test New.coeffs(2*a) == 2New.coeffs(a)
|
||||
|
||||
@test 2.0*a isa New.AlgebraElement
|
||||
@test eltype(2.0*a) == typeof(2.0)
|
||||
@test New.coeffs(2.0*a) == 2.0*New.coeffs(a)
|
||||
|
||||
@test New.coeffs(a/2) == New.coeffs(a)/2
|
||||
b = a/2
|
||||
@test b isa New.AlgebraElement
|
||||
@test eltype(b) == typeof(1/2)
|
||||
@test New.coeffs(b/2) == 0.25*New.coeffs(a)
|
||||
|
||||
c = a//1
|
||||
|
||||
@test eltype(c) == Rational{Int}
|
||||
@test c//4 isa New.AlgebraElement
|
||||
@test c//big(4) isa New.AlgebraElement
|
||||
@test eltype(c//(big(4)//1)) == Rational{BigInt}
|
||||
|
||||
@test (1.0a)*1//2 == (0.5a) == c//2
|
||||
end
|
||||
|
||||
@testset "Additive structure" begin
|
||||
a = New.AlgebraElement(ones(Int, order(G)), RG)
|
||||
b = sum(sign(g)*RG(g) for g in G)
|
||||
|
||||
@test a == New.AlgebraElement(ones(Int, order(G)), RG) == sum(RG(g) for g in G)
|
||||
|
||||
@test 1/2*(a+b).coeffs == [1.0, 0.0, 1.0, 0.0, 1.0, 0.0]
|
||||
|
||||
a = RG(1) + RG(perm"(2,3)") + RG(perm"(1,2,3)")
|
||||
b = RG(1) - RG(perm"(1,2)(3)") - RG(perm"(1,2,3)")
|
||||
|
||||
@test a - b == RG(perm"(2,3)") + RG(perm"(1,2)(3)") + 2RG(perm"(1,2,3)")
|
||||
|
||||
@test a + b - 2a == b - a
|
||||
|
||||
@test 1//2*2a == a
|
||||
@test a + 2a == (3//1)*a
|
||||
@test 2a - (1//1)*a == a
|
||||
end
|
||||
|
||||
@testset "Multiplicative structure" begin
|
||||
for g in G, h in G
|
||||
a = RG(g)
|
||||
b = RG(h)
|
||||
@test a*b == RG(g*h)
|
||||
@test (a+b)*(a+b) == a*a + a*b + b*a + b*b
|
||||
end
|
||||
|
||||
for g in G
|
||||
@test New.star(RG(g)) == RG(inv(g))
|
||||
@test (one(RG)-RG(g))*New.star(one(RG)-RG(g)) ==
|
||||
2*one(RG) - RG(g) - RG(inv(g))
|
||||
@test New.aug(one(RG) - RG(g)) == 0
|
||||
end
|
||||
|
||||
a = RG(1) + RG(perm"(2,3)") + RG(perm"(1,2,3)")
|
||||
b = RG(1) - RG(perm"(1,2)(3)") - RG(perm"(1,2,3)")
|
||||
|
||||
@test a*b == New.mul!(a,a,b)
|
||||
|
||||
@test New.aug(a) == 3
|
||||
@test New.aug(b) == -1
|
||||
@test New.aug(a)*New.aug(b) == New.aug(a*b) == New.aug(b*a)
|
||||
|
||||
z = sum((one(RG)-RG(g))*New.star(one(RG)-RG(g)) for g in G)
|
||||
@test New.aug(z) == 0
|
||||
|
||||
@test New.supp(z) == New.basis(parent(z))
|
||||
@test New.supp(RG(1) + RG(perm"(2,3)")) == [one(G), perm"(2,3)"]
|
||||
@test New.supp(a) == [perm"(3)", perm"(2,3)", perm"(1,2,3)"]
|
||||
|
||||
@testset "Projections in Symm(3)" begin
|
||||
G = SymmetricGroup(3)
|
||||
b = New.Basis{UInt8}(collect(G))
|
||||
l = length(b)
|
||||
|
||||
RG = New.StarAlgebra(G, b)
|
||||
@test RG isa New.StarAlgebra
|
||||
|
||||
P = sum(RG(g) for g in b) // l
|
||||
@test P * P == P
|
||||
|
||||
P3 = 2 * sum(RG(g) for g in b if sign(g) > 0) // l
|
||||
@test P3 * P3 == P3
|
||||
|
||||
PAlt = sum(sign(g) * RG(g) for g in b) // l
|
||||
@test PAlt * PAlt == PAlt
|
||||
|
||||
@test P3 * PAlt == PAlt * P3
|
||||
|
||||
P2 = (RG(1) + RG(b[2])) // 2
|
||||
@test P2 * P2 == P2
|
||||
|
||||
@test P2 * P3 == P3 * P2 == P
|
||||
|
||||
P2m = (RG(1) - RG(b[2])) // 2
|
||||
@test P2m * P2m == P2m
|
||||
|
||||
@test P2m * P3 == P3 * P2m == PAlt
|
||||
@test iszero(P2m * P2)
|
||||
end
|
||||
end
|
||||
|
||||
@testset "Mutable API and trivial mstructure" begin
|
||||
|
||||
G = SymmetricGroup(5)
|
||||
b = New.Basis{UInt8}(collect(G))
|
||||
|
||||
RG = New.StarAlgebra(G, b)
|
||||
l = order(Int, G)
|
||||
RGc = New.StarAlgebra(G, b, (l, l))
|
||||
|
||||
@test all(RG.mstructure .== RGc.mstructure)
|
||||
|
||||
Z = zero(RGc)
|
||||
W = zero(RGc)
|
||||
|
||||
for g in [rand(G) for _ in 1:30]
|
||||
X = RG(g)
|
||||
Y = -RG(inv(g))
|
||||
for i in 1:10
|
||||
X[rand(G)] += rand(1:3)
|
||||
Y[rand(G)] -= rand(1:3)
|
||||
end
|
||||
|
||||
Xc = New.AlgebraElement(New.coeffs(X), RGc)
|
||||
Yc = New.AlgebraElement(New.coeffs(Y), RGc)
|
||||
|
||||
@test New.coeffs(X*Y) ==
|
||||
New.coeffs(Xc*Yc) == New.coeffs(New.mul!(Z, X, Y))
|
||||
|
||||
@test Z.coeffs == New.mul!(W.coeffs, X.coeffs, Y.coeffs, RG.mstructure)
|
||||
@test Z.coeffs == W.coeffs
|
||||
@test Z.coeffs == New.mul!(W.coeffs, X.coeffs, Y.coeffs, RGc.mstructure)
|
||||
@test Z.coeffs == W.coeffs
|
||||
|
||||
New.zero!(W)
|
||||
|
||||
@test New.coeffs((2*X*Y)) ==
|
||||
(New.fmac!(W.coeffs, X.coeffs, Y.coeffs, RG.mstructure); New.coeffs(New.mul!(W, W, 2)))
|
||||
end
|
||||
end
|
||||
end
|
||||
|
|
@ -12,6 +12,7 @@ using GroupRings.New
|
|||
|
||||
include("constructors.jl")
|
||||
include("cachedmtables.jl")
|
||||
include("arithmetic.jl")
|
||||
end
|
||||
|
||||
@testset "GroupRings" begin
|
||||
|
|
|
|||
Loading…
Reference in New Issue