more efficient actions of autS

groups/autfreegroup.jl

@@ -39,10 +39,10 @@ end
 function AutFG_emb(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")
-    Id = parent(g.n[1])()
-    powers = ((el == Id ? 0: 1) for el in g.n.elts)
     elt = A()
-    Groups.r_multiply!(elt, [Groups.flip_autsymbol(i, pow=p) for (i,p) in enumerate(powers)], reduced=false)
+    Id = parent(g.n.elts[1])()
+    flips = Groups.AutSymbol[Groups.flip_autsymbol(i) for i in 1:length(g.p.d) if g.n.elts[i] != Id]
+    Groups.r_multiply!(elt, flips, reduced=false)
     Groups.r_multiply!(elt, [Groups.perm_autsymbol(g.p)])
     return elt
 end
@@ -54,13 +54,16 @@ function AutFG_emb(A::AutGroup, p::perm)
 end
 
 function (g::WreathProductElem)(a::Groups.Automorphism)
-    g = AutFG_emb(parent(a),g)
-    return g*a*g^-1
+    A = parent(a)
+    g = AutFG_emb(A,g)
+    res = A()
+    Groups.r_multiply!(res, g.symbols, reduced=false)
+    Groups.r_multiply!(res, a.symbols, reduced=false)
+    Groups.r_multiply!(res, [inv(s) for s in reverse!(g.symbols)])
+    return res
 end
 
 function (p::perm)(a::Groups.Automorphism)
     g = AutFG_emb(parent(a),p)
-    return g*a*g^-1
-end
-
+    return g*a*inv(g)
 end

groups/speciallinear.jl

@@ -71,21 +71,23 @@ end
 #
 ###############################################################################
 
-function matrix_emb(MM::MatSpace, g::WreathProductElem)
-    parent(g).P.n == MM.cols == MM.rows || throw("No natural embedding of $(parent(g)) in ")
-    powers = [(elt == parent(elt)() ? 0: 1) for elt in g.n.elts]
-    elt = diagm([(-1)^(elt == parent(elt)() ? 0: 1) for elt in g.n.elts])
-    return MM(elt)*MM(Nemo.matrix_repr(g.p)')
+function matrix_emb(n::DirectProductGroupElem, p::perm)
+    Id = parent(n.elts[1])()
+    elt = diagm([(-1)^(el == Id ? 0 : 1) for el in n.elts])
+    return elt[:, p.d]
 end
 
 function (g::WreathProductElem)(A::MatElem)
-    G = matrix_emb(parent(A), g)
-    inv_G = matrix_emb(parent(A), inv(g))
-    return G*A*inv_G
+    g_inv = inv(g)
+    G = matrix_emb(g.n, g_inv.p)
+    G_inv = matrix_emb(g_inv.n, g.p)
+    M = parent(A)
+    res = M(G_inv)
+    Nemo.mul!(res, A, res)
+    return Nemo.mul!(res, M(G), res)
 end
 
 function (p::perm)(A::MatElem)
     length(p.d) == A.r == A.c || throw("Can't act via $p on matrix of size ($(A.r), $(A.c))")
-    R = parent(A)
     return p*A*inv(p)
 end