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rework group actions
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@ -186,25 +186,19 @@ function (g::GroupRingElem)(y::GroupRingElem)
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return res
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end
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###############################################################################
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#
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# perm actions
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#
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###############################################################################
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function (g::Generic.Perm)(y::GroupRingElem)
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function (g::GroupElem)(y::GroupRingElem)
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RG = parent(y)
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result = zero(RG, eltype(y.coeffs))
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for (idx, c) in enumerate(y.coeffs)
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if c!= zero(eltype(y.coeffs))
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if !iszero(c)
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result[g(RG.basis[idx])] = c
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end
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end
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return result
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end
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function (g::Generic.Perm)(y::GroupRingElem{T, <:SparseVector}) where T
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function (g::GroupElem)(y::GroupRingElem{T, <:SparseVector}) where T
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RG = parent(y)
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index = [RG.basis_dict[g(RG.basis[idx])] for idx in y.coeffs.nzind]
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@ -213,6 +207,12 @@ function (g::Generic.Perm)(y::GroupRingElem{T, <:SparseVector}) where T
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return result
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end
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###############################################################################
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#
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# perm && WreathProductElems actions: MatAlgElem
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#
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###############################################################################
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function (p::Generic.Perm)(A::MatAlgElem)
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length(p.d) == size(A, 1) == size(A,2) || throw("Can't act via $p on matrix of size $(size(A))")
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result = similar(A)
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@ -224,24 +224,6 @@ function (p::Generic.Perm)(A::MatAlgElem)
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return result
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end
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###############################################################################
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#
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# WreathProductElems action on MatAlgElem
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#
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###############################################################################
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function (g::WreathProductElem)(y::GroupRingElem)
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RG = parent(y)
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result = zero(RG, eltype(y.coeffs))
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for (idx, c) in enumerate(y.coeffs)
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if c!= zero(eltype(y.coeffs))
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result[g(RG.basis[idx])] = c
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end
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end
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return result
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end
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function (g::WreathProductElem{N})(A::MatAlgElem) where N
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# @assert N == size(A,1) == size(A,2)
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flips = ntuple(i->(g.n[i].d[1]==1 && g.n[i].d[2]==2 ? 1 : -1), N)
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@ -257,8 +239,6 @@ function (g::WreathProductElem{N})(A::MatAlgElem) where N
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else
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result[g.p[i], g.p[j]] = -x
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end
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# result[i, j] = AbstractAlgebra.mul!(x, x, flips[i]*flips[j])
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# this mul! needs to be separately defined, but is 2x faster
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end
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end
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return result
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@ -266,33 +246,33 @@ end
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###############################################################################
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#
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# Action of WreathProductElems on AutGroupElem
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# perm && WreathProductElems actions: Automorphism
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#
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###############################################################################
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function AutFG_emb(A::AutGroup, g::WreathProductElem)
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function (g::GroupElem)(a::Automorphism)
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Ag = parent(a)(g)
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Ag_inv = inv(Ag)
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res = append!(Ag, a, Ag_inv)
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return Groups.freereduce!(res)
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end
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(A::AutGroup)(p::Generic.Perm) = A(Groups.AutSymbol(p))
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function (A::AutGroup)(g::WreathProductElem)
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isa(A.objectGroup, FreeGroup) || throw("Not an Aut(Fₙ)")
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parent(g).P.n == length(A.objectGroup.gens) || throw("No natural embedding of $(parent(g)) into $A")
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elt = one(A)
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Id = one(parent(g.n.elts[1]))
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flips = Groups.AutSymbol[Groups.flip_autsymbol(i) for i in 1:length(g.p.d) if g.n.elts[i] != Id]
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Groups.r_multiply!(elt, flips, reduced=false)
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Groups.r_multiply!(elt, [Groups.perm_autsymbol(g.p)])
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for i in 1:length(g.p.d)
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if g.n.elts[i] != Id
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push!(elt, Groups.flip(i))
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end
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end
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push!(elt, Groups.AutSymbol(g.p))
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return elt
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end
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function (g::WreathProductElem)(a::Groups.Automorphism)
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A = parent(a)
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g_emb = AutFG_emb(A,g)
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res = deepcopy(g_emb)
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res = Groups.r_multiply!(res, a.symbols, reduced=false)
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res = Groups.r_multiply!(res, [inv(s) for s in reverse!(g_emb.symbols)])
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return res
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end
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function (p::Generic.Perm)(a::Groups.Automorphism)
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res = parent(a)(Groups.perm_autsymbol(p))
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res = Groups.r_multiply!(res, a.symbols, reduced=false)
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res = Groups.r_multiply!(res, [Groups.perm_autsymbol(inv(p))])
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return res
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end
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# fallback:
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Base.one(p::Generic.Perm) = Perm(length(p.d))
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@ -3,12 +3,9 @@
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ssgs(M::MatAlgebra, i, j) = (S = [Eij(M, i, j), Eij(M, j, i)];
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S = unique([S; inv.(S)]); S)
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rmul = Groups.rmul_autsymbol
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lmul = Groups.lmul_autsymbol
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function ssgs(A::AutGroup, i, j)
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rmuls = [rmul(i,j), rmul(j,i)]
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lmuls = [lmul(i,j), lmul(j,i)]
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rmuls = [Groups.transvection_R(i,j), Groups.transvection_R(j,i)]
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lmuls = [Groups.transvection_L(i,j), Groups.transvection_L(j,i)]
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gen_set = A.([rmuls; lmuls])
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return unique([gen_set; inv.(gen_set)])
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end
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@ -33,7 +30,7 @@
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elt2 = E_R[rand(sizes[1]:sizes[2])]
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y = 2RG(elt2) - RG(elt)
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for G in [PermGroup(N), WreathProduct(PermGroup(2), PermGroup(N))]
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for G in [SymmetricGroup(N), WreathProduct(SymmetricGroup(2), SymmetricGroup(N))]
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@test all(g(one(M)) == one(M) for g in G)
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@test all(rdict[g(m)] <= sizes[1] for g in G for m in S)
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@test all(g(m)*g(n) == g(m*n) for g in G for m in S for n in S)
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@ -50,9 +47,9 @@
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Sij = ssgs(M, i,j)
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Δij= PropertyT.spLaplacian(RG, Sij)
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@test all(p(Δij) == PropertyT.spLaplacian(RG, ssgs(M, p[i], p[j])) for p in PermGroup(N))
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@test all(p(Δij) == PropertyT.spLaplacian(RG, ssgs(M, p[i], p[j])) for p in SymmetricGroup(N))
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@test all(g(Δij) == PropertyT.spLaplacian(RG, ssgs(M, g.p[i], g.p[j])) for g in WreathProduct(PermGroup(2), PermGroup(N)))
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@test all(g(Δij) == PropertyT.spLaplacian(RG, ssgs(M, g.p[i], g.p[j])) for g in WreathProduct(SymmetricGroup(2), SymmetricGroup(N)))
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end
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end
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end
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@ -79,7 +76,7 @@ end
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elt2 = E_R[rand(sizes[1]:sizes[2])]
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y = 2RG(elt2) - RG(elt)
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for G in [PermGroup(N), WreathProduct(PermGroup(2), PermGroup(N))]
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for G in [SymmetricGroup(N), WreathProduct(SymmetricGroup(2), SymmetricGroup(N))]
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@test all(g(one(M)) == one(M) for g in G)
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@test all(rdict[g(m)] <= sizes[1] for g in G for m in S)
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@test all(g(m)*g(n) == g(m*n) for g in G for m in S for n in S)
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@ -95,9 +92,9 @@ end
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Sij = ssgs(M, i,j)
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Δij= PropertyT.spLaplacian(RG, Sij)
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@test all(p(Δij) == PropertyT.spLaplacian(RG, ssgs(M, p[i], p[j])) for p in PermGroup(N))
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@test all(p(Δij) == PropertyT.spLaplacian(RG, ssgs(M, p[i], p[j])) for p in SymmetricGroup(N))
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@test all(g(Δij) == PropertyT.spLaplacian(RG, ssgs(M, g.p[i], g.p[j])) for g in WreathProduct(PermGroup(2), PermGroup(N)))
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@test all(g(Δij) == PropertyT.spLaplacian(RG, ssgs(M, g.p[i], g.p[j])) for g in WreathProduct(SymmetricGroup(2), SymmetricGroup(N)))
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end
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end
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