kalmar/Groups.jl
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add exports, remove New module from tests

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Marek Kaluba 2021-06-21 18:45:10 +02:00
parent 26781bad5c
commit 8cd1f09d74
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5 changed files with 76 additions and 75 deletions
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3
src/Groups.jl
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@ -5,7 +5,8 @@ using ThreadsX
import KnuthBendix import KnuthBendix
import OrderedCollections: OrderedSet import OrderedCollections: OrderedSet
export gens, FreeGroup, Aut, SAut export AutomorphismGroup, FreeGroup, FreeGroup, FPGroup, FPGroupElement, SpecialAutomorphismGroup
export alphabet, evaluate, word
include("new_types.jl") include("new_types.jl")
include("new_hashing.jl") include("new_hashing.jl")

90
test/AutFn.jl
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@ -2,30 +2,30 @@
@testset "Transvections" begin @testset "Transvections" begin
@test New.Transvection(:ϱ, 1, 2) isa New.GSymbol @test Groups.Transvection(:ϱ, 1, 2) isa Groups.GSymbol
@test New.Transvection(:ϱ, 1, 2) isa New.Transvection @test Groups.Transvection(:ϱ, 1, 2) isa Groups.Transvection
@test New.Transvection(:λ, 1, 2) isa New.GSymbol @test Groups.Transvection(:λ, 1, 2) isa Groups.GSymbol
@test New.Transvection(:λ, 1, 2) isa New.Transvection @test Groups.Transvection(:λ, 1, 2) isa Groups.Transvection
t = New.Transvection(:ϱ, 1, 2) t = Groups.Transvection(:ϱ, 1, 2)
@test inv(t) isa New.GSymbol @test inv(t) isa Groups.GSymbol
@test inv(t) isa New.Transvection @test inv(t) isa Groups.Transvection
@test t != inv(t) @test t != inv(t)
s = New.Transvection(:ϱ, 1, 2) s = Groups.Transvection(:ϱ, 1, 2)
@test t == s @test t == s
@test hash(t) == hash(s) @test hash(t) == hash(s)
s_ = New.Transvection(:ϱ, 1, 3) s_ = Groups.Transvection(:ϱ, 1, 3)
@test s_ != s @test s_ != s
@test hash(s_) != hash(s) @test hash(s_) != hash(s)
@test New.gersten_alphabet(3) isa Alphabet @test Groups.gersten_alphabet(3) isa Alphabet
A = New.gersten_alphabet(3) A = Groups.gersten_alphabet(3)
@test length(A) == 12 @test length(A) == 12
@test sprint(show, New.ϱ(1, 2)) == "ϱ₁.₂" @test sprint(show, Groups.ϱ(1, 2)) == "ϱ₁.₂"
@test sprint(show, New.λ(3, 2)) == "λ₃.₂" @test sprint(show, Groups.λ(3, 2)) == "λ₃.₂"
end end
A4 = Alphabet( A4 = Alphabet(
@ -38,16 +38,16 @@
[ 2, 1, 4, 3, 6, 5, 8, 7,10, 9] [ 2, 1, 4, 3, 6, 5, 8, 7,10, 9]
) )
F4 = New.FreeGroup([:a, :b, :c, :d], A4) F4 = FreeGroup([:a, :b, :c, :d], A4)
a,b,c,d = gens(F4) a,b,c,d = gens(F4)
D = ntuple(i->gens(F4, i), 4) D = ntuple(i->gens(F4, i), 4)
@testset "Transvection action correctness" begin @testset "Transvection action correctness" begin
i,j = 1,2 i,j = 1,2
r = New.Transvection(:ϱ,i,j) r = Groups.Transvection(:ϱ,i,j)
l = New.Transvection(:λ,i,j) l = Groups.Transvection(:λ,i,j)
(t::New.Transvection)(v::Tuple) = New.evaluate!(v, t, A4) (t::Groups.Transvection)(v::Tuple) = Groups.evaluate!(v, t, A4)
@test r(deepcopy(D)) == (a*b, b, c, d) @test r(deepcopy(D)) == (a*b, b, c, d)
@test inv(r)(deepcopy(D)) == (a*b^-1,b, c, d) @test inv(r)(deepcopy(D)) == (a*b^-1,b, c, d)
@ -55,48 +55,48 @@
@test inv(l)(deepcopy(D)) == (b^-1*a,b, c, d) @test inv(l)(deepcopy(D)) == (b^-1*a,b, c, d)
i,j = 3,1 i,j = 3,1
r = New.Transvection(:ϱ,i,j) r = Groups.Transvection(:ϱ,i,j)
l = New.Transvection(:λ,i,j) l = Groups.Transvection(:λ,i,j)
@test r(deepcopy(D)) == (a, b, c*a, d) @test r(deepcopy(D)) == (a, b, c*a, d)
@test inv(r)(deepcopy(D)) == (a, b, c*a^-1,d) @test inv(r)(deepcopy(D)) == (a, b, c*a^-1,d)
@test l(deepcopy(D)) == (a, b, a*c, d) @test l(deepcopy(D)) == (a, b, a*c, d)
@test inv(l)(deepcopy(D)) == (a, b, a^-1*c,d) @test inv(l)(deepcopy(D)) == (a, b, a^-1*c,d)
i,j = 4,3 i,j = 4,3
r = New.Transvection(:ϱ,i,j) r = Groups.Transvection(:ϱ,i,j)
l = New.Transvection(:λ,i,j) l = Groups.Transvection(:λ,i,j)
@test r(deepcopy(D)) == (a, b, c, d*c) @test r(deepcopy(D)) == (a, b, c, d*c)
@test inv(r)(deepcopy(D)) == (a, b, c, d*c^-1) @test inv(r)(deepcopy(D)) == (a, b, c, d*c^-1)
@test l(deepcopy(D)) == (a, b, c, c*d) @test l(deepcopy(D)) == (a, b, c, c*d)
@test inv(l)(deepcopy(D)) == (a, b, c, c^-1*d) @test inv(l)(deepcopy(D)) == (a, b, c, c^-1*d)
i,j = 2,4 i,j = 2,4
r = New.Transvection(:ϱ,i,j) r = Groups.Transvection(:ϱ,i,j)
l = New.Transvection(:λ,i,j) l = Groups.Transvection(:λ,i,j)
@test r(deepcopy(D)) == (a, b*d, c, d) @test r(deepcopy(D)) == (a, b*d, c, d)
@test inv(r)(deepcopy(D)) == (a, b*d^-1,c, d) @test inv(r)(deepcopy(D)) == (a, b*d^-1,c, d)
@test l(deepcopy(D)) == (a, d*b, c, d) @test l(deepcopy(D)) == (a, d*b, c, d)
@test inv(l)(deepcopy(D)) == (a, d^-1*b,c, d) @test inv(l)(deepcopy(D)) == (a, d^-1*b,c, d)
end end
A = New.SpecialAutomorphismGroup(F4, maxrules=1000) A = SpecialAutomorphismGroup(F4, maxrules=1000)
@testset "AutomorphismGroup constructors" begin @testset "AutomorphismGroup constructors" begin
@test A isa New.AbstractFPGroup @test A isa Groups.AbstractFPGroup
@test A isa New.AutomorphismGroup @test A isa AutomorphismGroup
@test KnuthBendix.alphabet(A) isa Alphabet @test alphabet(A) isa Alphabet
@test New.relations(A) isa Vector{<:Pair} @test Groups.relations(A) isa Vector{<:Pair}
@test sprint(show, A) == "automorphism group of free group on 4 generators" @test sprint(show, A) == "automorphism group of free group on 4 generators"
end end
@testset "Automorphisms: hash and evaluate" begin @testset "Automorphisms: hash and evaluate" begin
@test New.domain(gens(A, 1)) == D @test Groups.domain(gens(A, 1)) == D
g, h = gens(A, 1), gens(A, 8) g, h = gens(A, 1), gens(A, 8)
@test New.evaluate(g*h) == New.evaluate(h*g) @test evaluate(g*h) == evaluate(h*g)
@test (g*h).savedhash == zero(UInt) @test (g*h).savedhash == zero(UInt)
@test sprint(show, typeof(g)) == "Automorphism{Groups.New.FreeGroup{Symbol},…}" @test sprint(show, typeof(g)) == "Automorphism{FreeGroup{Symbol},…}"
a = g*h a = g*h
b = h*g b = h*g
@ -111,22 +111,22 @@
# ϱ₁₂*ϱ₂₁⁻¹*λ₁₂*ε₂ == σ₂₁₃₄ # ϱ₁₂*ϱ₂₁⁻¹*λ₁₂*ε₂ == σ₂₁₃₄
g = gens(A, 1) g = gens(A, 1)
x1, x2, x3, x4 = New.domain(g) x1, x2, x3, x4 = Groups.domain(g)
@test New.evaluate(g) == (x1*x2, x2, x3, x4) @test evaluate(g) == (x1*x2, x2, x3, x4)
g = g*inv(gens(A, 4)) # ϱ₂₁ g = g*inv(gens(A, 4)) # ϱ₂₁
@test New.evaluate(g) == (x1*x2, x1^-1, x3, x4) @test evaluate(g) == (x1*x2, x1^-1, x3, x4)
g = g*gens(A, 13) g = g*gens(A, 13)
@test New.evaluate(g) == (x2, x1^-1, x3, x4) @test evaluate(g) == (x2, x1^-1, x3, x4)
end end
@testset "Automorphisms: SAut(F₄)" begin @testset "Automorphisms: SAut(F₄)" begin
N = 4 N = 4
G = New.SpecialAutomorphismGroup(New.FreeGroup(N)) G = SpecialAutomorphismGroup(FreeGroup(N))
S = gens(G) S = gens(G)
@test S isa Vector{<:New.FPGroupElement{<:New.AutomorphismGroup{<:New.FreeGroup}}} @test S isa Vector{<:FPGroupElement{<:AutomorphismGroup{<:FreeGroup}}}
@test length(S) == 2*N*(N-1) @test length(S) == 2*N*(N-1)
@test length(unique(S)) == length(S) @test length(unique(S)) == length(S)
@ -157,7 +157,7 @@ end
# using Random # using Random
# using GroupsCore # using GroupsCore
# #
# A = New.SpecialAutomorphismGroup(New.FreeGroup(4), maxrules=2000, ordering=KnuthBendix.RecursivePathOrder) # A = New.SpecialAutomorphismGroup(FreeGroup(4), maxrules=2000, ordering=KnuthBendix.RecursivePathOrder)
# #
# # for seed in 1:1000 # # for seed in 1:1000
# let seed = 68 # let seed = 68
@ -168,22 +168,22 @@ end
# @info "seed=$seed" g h # @info "seed=$seed" g h
# @time isone(g*inv(g)) # @time isone(g*inv(g))
# @time isone(inv(g)*g) # @time isone(inv(g)*g)
# @info "" length(New.word(New.normalform!(g*inv(g)))) length(New.word(New.normalform!(inv(g)*g))) # @info "" length(word(New.normalform!(g*inv(g)))) length(word(New.normalform!(inv(g)*g)))
# a = commutator(g, h, g) # a = commutator(g, h, g)
# b = conj(inv(g), h) * conj(conj(g, h), g) # b = conj(inv(g), h) * conj(conj(g, h), g)
# #
# @info length(New.word(a)) # @info length(word(a))
# @info length(New.word(b)) # @info length(word(b))
# #
# w = a*inv(b) # w = a*inv(b)
# @info length(New.word(w)) # @info length(word(w))
# New.normalform!(w) # New.normalform!(w)
# @info length(New.word(w)) # @info length(word(w))
# #
# #
# # # #
# # @time ima = New.evaluate(a) # # @time ima = evaluate(a)
# # @time imb = New.evaluate(b) # # @time imb = evaluate(b)
# # @info "" a b ima imb # # @info "" a b ima imb
# # @time a == b # # @time a == b
# end # end

6
test/benchmarks.jl
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@ -6,7 +6,7 @@ using Groups.New
function wl_ball(F; radius::Integer) function wl_ball(F; radius::Integer)
g, state = iterate(F) g, state = iterate(F)
while length(New.word(g)) <= radius while length(word(g)) <= radius
res = iterate(F, state) res = iterate(F, state)
isnothing(res) && break isnothing(res) && break
g, state = res g, state = res
@ -20,7 +20,7 @@ end
N = 4 N = 4
@testset "iteration: FreeGroup" begin @testset "iteration: FreeGroup" begin
FN = New.FreeGroup(N) FN = FreeGroup(N)
R = 8 R = 8
let G = FN let G = FN
@ -46,7 +46,7 @@ end
@testset "iteration: SAut(F_n)" begin @testset "iteration: SAut(F_n)" begin
R = 4 R = 4
FN = New.FreeGroup(N) FN = FreeGroup(N)
SAutFN = New.SpecialAutomorphismGroup(FN) SAutFN = New.SpecialAutomorphismGroup(FN)
let G = SAutFN let G = SAutFN

36
test/fp_groups.jl
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@ -1,38 +1,38 @@
@testset "FPGroups" begin @testset "FPGroups" begin
A = Alphabet([:a, :A, :b, :B, :c, :C], [2,1,4,3,6,5]) A = Alphabet([:a, :A, :b, :B, :c, :C], [2,1,4,3,6,5])
@test New.FreeGroup(A) isa New.FreeGroup @test FreeGroup(A) isa FreeGroup
@test sprint(show, New.FreeGroup(A)) == "free group on 3 generators" @test sprint(show, FreeGroup(A)) == "free group on 3 generators"
F = New.FreeGroup([:a, :b, :c], A) F = FreeGroup([:a, :b, :c], A)
@test sprint(show, F) == "free group on 3 generators" @test sprint(show, F) == "free group on 3 generators"
a,b,c = gens(F) a,b,c = gens(F)
@test c*b*a isa New.FPGroupElement @test c*b*a isa FPGroupElement
# quotient of F: # quotient of F:
G = New.FPGroup(F, [a*b=>b*a, a*c=>c*a, b*c=>c*b]) G = FPGroup(F, [a*b=>b*a, a*c=>c*a, b*c=>c*b])
@test G isa New.FPGroup @test G isa FPGroup
@test sprint(show, G) == "⟨a, b, c | a*b => b*a, a*c => c*a, b*c => c*b⟩" @test sprint(show, G) == "⟨a, b, c | a*b => b*a, a*c => c*a, b*c => c*b⟩"
@test rand(G) isa New.FPGroupElement @test rand(G) isa FPGroupElement
f = a*c*b f = a*c*b
@test New.word(f) isa Word{UInt8} @test word(f) isa Word{UInt8}
aG,bG,cG = gens(G) aG,bG,cG = gens(G)
@test aG isa New.FPGroupElement @test aG isa FPGroupElement
@test_throws AssertionError aG == a @test_throws AssertionError aG == a
@test New.word(aG) == New.word(a) @test word(aG) == word(a)
g = aG*cG*bG g = aG*cG*bG
@test_throws AssertionError f == g @test_throws AssertionError f == g
@test New.word(f) == New.word(g) @test word(f) == word(g)
@test New.word(g) == [1, 5, 3] @test word(g) == [1, 5, 3]
New.normalform!(g) Groups.normalform!(g)
@test New.word(g) == [1, 3, 5] @test word(g) == [1, 3, 5]
let g = aG*cG*bG let g = aG*cG*bG
# test that we normalize g before printing # test that we normalize g before printing
@ -40,15 +40,15 @@
end end
# quotient of G # quotient of G
H = New.FPGroup(G, [aG^2=>cG, bG*cG=>aG], maxrules=200) H = FPGroup(G, [aG^2=>cG, bG*cG=>aG], maxrules=200)
h = H(New.word(g)) h = H(word(g))
@test h isa New.FPGroupElement @test h isa FPGroupElement
@test_throws AssertionError h == g @test_throws AssertionError h == g
@test_throws AssertionError h*g @test_throws AssertionError h*g
New.normalform!(h) Groups.normalform!(h)
@test h == H([5]) @test h == H([5])
@testset "GroupsCore conformance: H" begin @testset "GroupsCore conformance: H" begin

16
test/free_groups.jl
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@ -1,12 +1,12 @@
@testset "New.FreeGroup" begin @testset "FreeGroup" begin
A3 = Alphabet([:a, :b, :c, :A, :B, :C], [4,5,6,1,2,3]) A3 = Alphabet([:a, :b, :c, :A, :B, :C], [4,5,6,1,2,3])
F3 = New.FreeGroup([:a, :b, :c], A3) F3 = FreeGroup([:a, :b, :c], A3)
@test F3 isa New.FreeGroup @test F3 isa FreeGroup
@test gens(F3) isa Vector @test gens(F3) isa Vector
@test eltype(F3) <: New.FPGroupElement{<:New.FreeGroup} @test eltype(F3) <: FPGroupElement{<:FreeGroup}
w = F3([1,2,3,4]) w = F3([1,2,3,4])
W = inv(w) W = inv(w)
@ -15,7 +15,7 @@
@test isone(w*W) @test isone(w*W)
@test New.alphabet(w) == A3 @test alphabet(w) == A3
@testset "generic iteration" begin @testset "generic iteration" begin
w, s = iterate(F3) w, s = iterate(F3)
@ -43,7 +43,7 @@
@testset "wl_ball" begin @testset "wl_ball" begin
function wl_ball(F; radius::Integer) function wl_ball(F; radius::Integer)
g, state = iterate(F) g, state = iterate(F)
while length(New.word(g)) <= radius while length(word(g)) <= radius
res = iterate(F, state) res = iterate(F, state)
isnothing(res) && break isnothing(res) && break
g, state = res g, state = res
@ -55,11 +55,11 @@
E4 = wl_ball(F3, radius=4) E4 = wl_ball(F3, radius=4)
@test length(E4) == 937 @test length(E4) == 937
@test New.word(last(E4)) == Word([6])^4 @test word(last(E4)) == Word([6])^4
E8, t, _ = @timed wl_ball(F3, radius=8) E8, t, _ = @timed wl_ball(F3, radius=8)
@test length(E8) == 585937 @test length(E8) == 585937
@test New.word(last(E8)) == Word([6])^8 @test word(last(E8)) == Word([6])^8
@test t/10^9 < 1 @test t/10^9 < 1
end end