kalmar/Groups.jl
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remapping the functionality of AutSymbols

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This commit is contained in:
kalmar 2017-02-09 21:06:10 +01:00
parent a745090d0c
commit f88d59e7e9
1 changed files with 29 additions and 34 deletions
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63
src/automorphism_groups.jl
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@ -7,26 +7,23 @@ immutable AutSymbol <: GSymbol
gen::String
pow::Int
ex::Expr
fmap::Function
imap::Function
func::Function
end
function (f::AutSymbol){T}(v::Vector{GWord{T}})
if f.pow > 0
map = f.fmap
if f.pow == 0
return v
else
map = f.imap
return f.func(v)
# else
# throw(ArgumentError("Check that Symbol $f is properly defined!\n $(dump(f))"))
end
for i in 1:abs(f.pow)
v::Vector{GWord{T}} = map(v)
end
return v
end
(==)(s::AutSymbol, t::AutSymbol) = s.gen == t.gen && s.pow == t.pow
hash(s::AutSymbol, h::UInt) = hash(s.gen, hash(s.pow, hash(:AutSymbol, h)))
IdSymbol(::Type{AutSymbol}) = AutSymbol("(id)", 0, :(Id(N)), v -> Vector{GWord}(v), v -> Vector{GWord}(v))
IdSymbol(::Type{AutSymbol}) = AutSymbol("(id)", 0, :(id()), id)
function change_pow(s::AutSymbol, n::Int)
if n == 0
@ -41,58 +38,56 @@ function change_pow(s::AutSymbol, n::Int)
return rmul_AutSymbol(s.ex.args[2], s.ex.args[3], pow=n)
elseif symbol == :λ
return lmul_AutSymbol(s.ex.args[2], s.ex.args[3], pow=n)
elseif symbol == :Id
elseif symbol == :id
return s
else
warn("Changing an unknown type of symbol! $s")
return AutSymbol(s.gen, n, s.ex, s.fmap, s.imap)
return AutSymbol(s.gen, n, s.ex, s.func)
end
end
inv(f::AutSymbol) = change_pow(f, -f.pow)
function ϱ(i,j)
# @assert i ≠ j
return v -> [(k!=i ? GWord(v[k]) : v[i]*v[j]) for k in eachindex(v)]
function id()
return v -> v
end
function ϱ_inv(i,j)
function ϱ(i,j, pow=1)
# @assert i ≠ j
return v -> [(k!=i ? GWord(v[k]) : v[i]*v[j]^-1) for k in eachindex(v)]
return v -> [(k==i ? v[i]*v[j]^pow : v[k]) for k in eachindex(v)]
end
function λ(i,j)
function λ(i,j, pow=1)
# @assert i ≠ j
return v -> ([(k!=i ? GWord(v[k]) : v[j]*v[i]) for k in eachindex(v)])
return v -> [(k==i ? v[j]^pow*v[i] : v[k]) for k in eachindex(v)]
end
function λ_inv(i,j)
# @assert i ≠ j
return v -> ([(k!=i ? GWord(v[k]) : v[j]^-1*v[i]) for k in eachindex(v)])
end
ɛ(i) = v -> [(k!=i ? GWord(v[k]) : v[k]^-1) for k in eachindex(v)]
function σ(perm)
function σ(perm, pow=1)
# @assert sort(perm) == collect(1:length(perm))
return v -> [GWord(v[perm[k]]) for k in eachindex(v)]
if pow == 1
return v -> [v[perm[k]] for k in eachindex(v)]
else
p = Permutations.Permutation(perm)
perm = array(p^pow)
return v -> [v[perm[k]] for k in eachindex(v)]
end
end
ɛ(i, pow=1) = v -> [(k==i ? v[k]^(-1*(pow % 2)) : v[k]) for k in eachindex(v)]
function rmul_AutSymbol(i,j; pow::Int=1)
gen = string('ϱ',Char(8320+i), Char(8320+j)...)
return AutSymbol(gen, pow, :(ϱ($i,$j)), ϱ(i,j), ϱ_inv(i,j))
return AutSymbol(gen, pow, :(ϱ($i,$j, $pow)), ϱ(i,j, pow))
end
function lmul_AutSymbol(i,j; pow::Int=1)
gen = string('λ',Char(8320+i), Char(8320+j)...)
return AutSymbol(gen, pow, :(λ($i,$j)), λ(i,j), λ_inv(i,j))
return AutSymbol(gen, pow, :(λ($i,$j, $pow)), λ(i,j, pow))
end
function flip_AutSymbol(j; pow::Int=1)
gen = string('ɛ', Char(8320 + j))
return AutSymbol(gen, (2+ pow%2)%2, :(ɛ($j)), ɛ(j), ɛ(j))
return AutSymbol(gen, (2+pow%2)%2, :(ɛ($j, $pow)), ɛ(j,pow))
end
function symmetric_AutSymbol(perm::Vector{Int}; pow::Int=1)
@ -105,7 +100,7 @@ function symmetric_AutSymbol(perm::Vector{Int}; pow::Int=1)
return one(AutSymbol)
else
gen = string('σ', [Char(8320 + i) for i in p]...)
return AutSymbol(gen, 1, :(σ($p)), σ(p), σ(array(inv(perm))))
return AutSymbol(gen, 1, :(σ($p, 1)), σ(p, 1))
end
end