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PropertyT.jl
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allow arbitrary actions in orbit_decomposition (defaults to ^)

This commit is contained in:
kalmarek 2020-10-10 12:55:02 +02:00
parent c467a52f83
commit 6ab18d0283
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GPG Key ID: 8BF1A3855328FC15
2 changed files with 37 additions and 26 deletions
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57
src/orbitdata.jl
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@ -58,9 +58,14 @@ function orthSVD(M::AbstractMatrix{T}) where {T<:AbstractFloat}
return fact.U[:,1:M_rank]
end
orbit_decomposition(G::Group, E::AbstractVector, rdict=GroupRings.reverse_dict(E)) = orbit_decomposition(collect(G), E, rdict)
orbit_decomposition(
G::Group,
E::AbstractVector,
rdict = GroupRings.reverse_dict(E);
op = ^,
) = orbit_decomposition(collect(G), E, rdict; op=op)
function orbit_decomposition(elts::AbstractVector{<:GroupElem}, E::AbstractVector, rdict=GroupRings.reverse_dict(E))
function orbit_decomposition(elts::AbstractVector{<:GroupElem}, E::AbstractVector, rdict=GroupRings.reverse_dict(E); op=^)
tovisit = trues(size(E));
orbits = Vector{Vector{Int}}()
@ -71,7 +76,7 @@ function orbit_decomposition(elts::AbstractVector{<:GroupElem}, E::AbstractVecto
if tovisit[i]
g = E[i]
Threads.@threads for j in eachindex(elts)
orbit[j] = rdict[elts[j](g)]
orbit[j] = rdict[op(g, elts[j])]
end
tovisit[orbit] .= false
push!(orbits, unique(orbit))
@ -139,7 +144,7 @@ end
function perm_repr(g::GroupElem, E::Vector, E_dict)
p = Vector{Int}(undef, length(E))
for (i,elt) in enumerate(E)
p[i] = E_dict[g(elt)]
p[i] = E_dict[elt^g]
end
return p
end
@ -178,29 +183,33 @@ end
#
###############################################################################
function (g::GroupRingElem)(y::GroupRingElem)
function Base.:^(y::GroupRingElem, g::GroupRingElem, op = ^)
res = parent(y)()
for elt in GroupRings.supp(g)
res += g[elt]*elt(y)
res += g[elt] * ^(y, elt, op)
end
return res
end
function (g::GroupElem)(y::GroupRingElem)
function Base.:^(y::GroupRingElem, g::GroupElem, op = ^)
RG = parent(y)
result = zero(RG, eltype(y.coeffs))
for (idx, c) in enumerate(y.coeffs)
if !iszero(c)
result[g(RG.basis[idx])] = c
result[op(RG.basis[idx], g)] = c
end
end
return result
end
function (g::GroupElem)(y::GroupRingElem{T, <:SparseVector}) where T
function Base.:^(
y::GroupRingElem{T,<:SparseVector},
g::GroupElem,
op = ^,
) where {T}
RG = parent(y)
index = [RG.basis_dict[g(RG.basis[idx])] for idx in y.coeffs.nzind]
index = [RG.basis_dict[op(RG.basis[idx], g)] for idx in y.coeffs.nzind]
result = GroupRingElem(sparsevec(index, y.coeffs.nzval, y.coeffs.n), RG)
@ -213,28 +222,29 @@ end
#
###############################################################################
function (p::Generic.Perm)(A::MatAlgElem)
length(p.d) == size(A, 1) == size(A,2) || throw("Can't act via $p on matrix of size $(size(A))")
function Base.:^(A::MatAlgElem, p::Generic.Perm)
length(p.d) == size(A, 1) == size(A, 2) ||
throw("Can't act via $p on matrix of size $(size(A))")
result = similar(A)
@inbounds for i in 1:size(A, 1)
for j in 1:size(A, 2)
result[p[i], p[j]] = A[i,j] # action by permuting rows and colums/conjugation
@inbounds for i = 1:size(A, 1)
for j = 1:size(A, 2)
result[p[i], p[j]] = A[i, j] # action by permuting rows and colums/conjugation
end
end
return result
end
function (g::WreathProductElem{N})(A::MatAlgElem) where N
function Base.:^(A::MatAlgElem, g::WreathProductElem{N}) where {N}
# @assert N == size(A,1) == size(A,2)
flips = ntuple(i->(g.n[i].d[1]==1 && g.n[i].d[2]==2 ? 1 : -1), N)
flips = ntuple(i -> (g.n[i].d[1] == 1 && g.n[i].d[2] == 2 ? 1 : -1), N)
result = similar(A)
R = base_ring(parent(A))
tmp = R(1)
@inbounds for i = 1:size(A,1)
for j = 1:size(A,2)
@inbounds for i = 1:size(A, 1)
for j = 1:size(A, 2)
x = A[i, j]
if flips[i]*flips[j] == 1
if flips[i] * flips[j] == 1
result[g.p[i], g.p[j]] = x
else
result[g.p[i], g.p[j]] = -x
@ -250,7 +260,7 @@ end
#
###############################################################################
function (g::GroupElem)(a::Automorphism)
function Base.:^(a::Automorphism, g::GroupElem)
Ag = parent(a)(g)
Ag_inv = inv(Ag)
res = append!(Ag, a, Ag_inv)
@ -261,10 +271,11 @@ end
function (A::AutGroup)(g::WreathProductElem)
isa(A.objectGroup, FreeGroup) || throw("Not an Aut(Fₙ)")
parent(g).P.n == length(A.objectGroup.gens) || throw("No natural embedding of $(parent(g)) into $A")
parent(g).P.n == length(A.objectGroup.gens) ||
throw("No natural embedding of $(parent(g)) into $A")
elt = one(A)
Id = one(parent(g.n.elts[1]))
for i in 1:length(g.p.d)
for i = 1:length(g.p.d)
if g.n.elts[i] != Id
push!(elt, Groups.flip(i))
end

6
src/sqadjop.jl
View File

@ -19,7 +19,7 @@ function Sq(RG::GroupRing, N::Integer)
sq = RG()
for σ in Alt_N
GroupRings.addeq!(sq, *(σ(Δ₂), σ(Δ₂), false))
GroupRings.addeq!(sq, *(Δ₂^σ, Δ₂^σ, false))
end
return sq÷factorial(N-2)
end
@ -30,7 +30,7 @@ function Adj(RG::GroupRing, N::Integer)
Δ₂ = length(S₂)*one(RG, ℤ) - RG(S₂, ℤ);
Alt_N = [g for g in SymmetricGroup(N) if parity(g) == 0]
Δ₂s = Dict(σ=>σ(Δ₂) for σ in Alt_N)
Δ₂s = Dict(σ=>Δ₂^σ for σ in Alt_N)
adj = RG()
for σ in Alt_N
@ -52,7 +52,7 @@ function Op(RG::GroupRing, N::Integer)
Δ₂ = length(S₂)*one(RG, ℤ) - RG(S₂, ℤ);
Alt_N = [g for g in SymmetricGroup(N) if parity(g) == 0]
Δ₂s = Dict(σ=>σ(Δ₂) for σ in Alt_N)
Δ₂s = Dict(σ=>Δ₂^σ for σ in Alt_N)
op = RG()
for σ in Alt_N