faster permutation actions on GroupElements

src/orbitdata.jl

@@ -178,18 +178,45 @@ end
 #
 ###############################################################################
 
-function (p::perm)(A::GroupRingElem)
-    RG = parent(A)
-    result = zero(RG, eltype(A.coeffs))
+function (g::perm)(y::GroupRingElem)
+    RG = parent(y)
+    result = zero(RG, eltype(y.coeffs))
 
-    for (idx, c) in enumerate(A.coeffs)
-        if c!= zero(eltype(A.coeffs))
-            result[p(RG.basis[idx])] = c
+    for (idx, c) in enumerate(y.coeffs)
+        if c!= zero(eltype(y.coeffs))
+            result[g(RG.basis[idx])] = c
         end
     end
     return result
 end
 
+function (g::perm)(y::GroupRingElem{T, <:SparseVector}) where T
+    RG = parent(y)
+    index = [RG.basis_dict[g(RG.basis[idx])] for idx in y.coeffs.nzind]
+
+    result = GroupRingElem(sparsevec(index, y.coeffs.nzval, y.coeffs.n), RG)
+
+    return result
+end
+
+function (g::GroupRingElem)(y::GroupRingElem)
+    res = parent(y)()
+    for elt in GroupRings.supp(g)
+        res += g[elt]*elt(y)
+    end
+    return res
+end
+
+function (p::perm)(A::MatElem)
+    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[i, j] = A[p[i], p[j]] # action by permuting rows and colums/conjugation
+        end
+    return result
+end
+
 ###############################################################################
 #
 #  Action of WreathProductElems on Nemo.MatElem