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rework ranOne_projections(::WreathProduct...) using emb functions

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Still messy
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kalmar 2017-07-17 12:28:17 +02:00
parent 6ecd63197b
commit 5d6074c368
1 changed files with 21 additions and 20 deletions
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41
src/Projections.jl
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@ -75,31 +75,32 @@ end
function rankOne_projections(BN::WreathProduct, T::Type=Rational{Int})
N = BN.P.n
# projections as elements of the group rings RSₙ
# projections as elements of the group rings RSₙ
SNprojs_nc = [rankOne_projections(PermutationGroup(i), T) for i in 1:N]
# embedding into group ring of BN
RBN = GroupRing(BN)
RFFFF_projs = [central_projection(GroupRing(BN.N), g->epsilon(i,g), T)
for i in 0:BN.P.n]
Qs = [RBN(q, g -> BN(g)) for q in RFFFF_projs]
for i in 1:BN.P.n]
function incl(k::Int, g::perm, WP::WreathProduct=BN)
@assert length(g.d) + k <= WP.P.n
arr = [1:k; g.d .+ k; (length(g.d)+k+1):WP.P.n]
return WP(WP.P(arr))
e0 = central_projection(GroupRing(BN.N), g->epsilon(0,g), T)
Q0 = RBN(e0, g -> BN(g))
Qs = [RBN(q, g -> BN(g)) for q in RFFFF_projs]
all_projs = [Q0*RBN(p, g->BN(g)) for p in SNprojs_nc[N]]
range = collect(1:N)
for i in 1:N-1
Sk_first = [RBN(p, g->BN(Nemo.emb!(BN.P(), g, range[1:i]))) for p in SNprojs_nc[i]]
Sk_last = [RBN(p, g->BN(Nemo.emb!(BN.P(), g, range[i+1:end]))) for p in SNprojs_nc[N-i]]
append!(all_projs,
[Qs[i]*p1*p2 for (p1,p2) in Base.product(Sk_first,Sk_last)])
end
append!(all_projs, [Qs[N]*RBN(p, g->BN(g)) for p in SNprojs_nc[N]])
return all_projs
end
all_projs=[Qs[1]*RBN(p, g-> incl(0,g)) for p in SNprojs_nc[N]]
for i in 1:N-1
Sk_first = [RBN(p, g->incl(0,g)) for p in SNprojs_nc[i]]
Sk_last = [RBN(p, g->incl(i,g)) for p in SNprojs_nc[N-i]]
append!(all_projs,
[Qs[i+1]*p1*p2 for (p1,p2) in Base.product(Sk_first,Sk_last)])
end
append!(all_projs, [Qs[N+1]*RBN(p, g-> incl(0,g)) for p in SNprojs_nc[N]])
return all_projs
end