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much faster WreathProductElem actions
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@ -225,39 +225,31 @@ end
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function matrix_emb(n::DirectPowerGroupElem, p::perm)
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Id = parent(n.elts[1])()
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elt = Diagonal([(-1)^(el == Id ? 0 : 1) for el in n.elts])
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elt = Diagonal([(el == Id ? 1 : -1) for el in n.elts])
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return elt[:, p.d]
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end
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function (g::WreathProductElem)(A::MatElem)
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g_inv = inv(g)
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G = matrix_emb(g.n, g_inv.p)
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G_inv = matrix_emb(g_inv.n, g.p)
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M = parent(A)
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return M(G)*A*M(G_inv)
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end
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import Base.*
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@doc doc"""
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*(x::AbstractAlgebra.MatElem, P::Generic.perm)
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> Apply the pemutation $P$ to the rows of the matrix $x$ and return the result.
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"""
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function *(x::AbstractAlgebra.MatElem, P::Generic.perm)
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z = similar(x)
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m = nrows(x)
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n = ncols(x)
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for i = 1:m
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for j = 1:n
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z[i, j] = x[i,P[j]]
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end
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end
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return z
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function (g::WreathProductElem{N})(A::MatElem) 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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result = similar(A)
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@inbounds for i = 1:size(A,1)
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for j = 1:size(A,2)
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result[i, j] = A[g.p[i], g.p[j]]*(flips[i]*flips[j])
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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 (p::perm)(A::MatElem)
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length(p.d) == A.r == A.c || throw("Can't act via $p on matrix of size ($(A.r), $(A.c))")
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return p*A*inv(p)
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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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@inbounds for i in 1:size(A, 1)
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for j in 1:size(A, 2)
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result[p[i],p[j]] = A[i,j] # action by permuting rows and colums/conjugation
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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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###############################################################################
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