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Groups.jl
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new functions defining AutSymbols actions

This commit is contained in:
kalmar 2017-05-12 20:05:32 +02:00
parent b130417a38
commit 51baeb1326
1 changed files with 17 additions and 25 deletions
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42
src/automorphism_groups.jl
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@ -20,9 +20,6 @@ end
function id()
return v -> v
end
function ϱ(i,j, pow=1)
# @assert i ≠ j
@ -34,15 +31,8 @@ function λ(i,j, pow=1)
return v -> [(k==i ? v[j]^pow*v[i] : v[k]) for k in eachindex(v)]
end
function σ(perm, pow=1)
# @assert sort(perm) == collect(1:length(perm))
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
function σ(p::perm, pow=1)
return v -> [v[(p^pow)[k]] for k in eachindex(v)]
end
ɛ(i, pow=1) = v -> [(k==i ? v[k]^(-1*(2+pow%2)%2) : v[k]) for k in eachindex(v)]
@ -54,30 +44,32 @@ function subscriptify(n::Int)
join([Char(subscript_0 + i) for i in dig])
end
function rmul_AutSymbol(i,j; pow::Int=1)
function id_autsymbol()
return AutSymbol("(id)", 0, :(id()), identity)
end
function rmul_autsymbol(i, j; pow::Int=1)
gen = "ϱ"*subscriptify(i)*subscriptify(j)
return AutSymbol(gen, pow, :(ϱ($i,$j, $pow)), ϱ(i,j, pow))
return AutSymbol(gen, pow, :(ϱ($i, $j, $pow)), ϱ(i, j, pow))
end
function lmul_AutSymbol(i,j; pow::Int=1)
function lmul_autsymbol(i, j; pow::Int=1)
gen = "λ"*subscriptify(i)*subscriptify(j)
return AutSymbol(gen, pow, :(λ($i,$j, $pow)), λ(i,j, pow))
return AutSymbol(gen, pow, :(λ($i, $j, $pow)), λ(i, j, pow))
end
function flip_AutSymbol(j; pow::Int=1)
gen = "ɛ"*subscriptify(j)
return AutSymbol(gen, (2+pow%2)%2, :(ɛ($j, $pow)), ɛ(j,pow))
function flip_autsymbol(i; pow::Int=1)
gen = "ɛ"*subscriptify(i)
pow = (2+pow%2)%2
return AutSymbol(gen, pow, :(ɛ($i, $pow)), ɛ(i, pow))
end
function symmetric_AutSymbol(perm::Vector{Int}; pow::Int=1)
perm = Permutations.Permutation(perm)
perm = perm^pow
p = array(perm)
if p == collect(1:length(p))
function perm_autsymbol(p::perm; pow::Int=1)
if p == parent(p)()
return one(AutSymbol)
else
gen = "σ"*join([subscriptify(i) for i in p])
return AutSymbol(gen, 1, :(σ($p, 1)), σ(p, 1))
return AutSymbol(gen, 1, :(σ($(p.d), 1)), σ(p, 1))
end
end