Matrix groups: cleanup some use of frobenius

src/Groups/matrices/matrix_manipulation.jl

@@ -37,12 +37,21 @@ end
     conjugate_transpose(x::MatElem{T}) where T <: FinFieldElem
 
 If the base ring of `x` is `GF(q^2)`, return the matrix `transpose( map ( y -> y^q, x) )`.
- An exception is thrown if the base ring does not have even degree.
+An exception is thrown if the base ring does not have even degree.
 """
 function conjugate_transpose(x::MatElem{T}) where T <: FinFieldElem
-   @req iseven(degree(base_ring(x))) "The base ring must have even degree"
-   e = div(degree(base_ring(x)),2)
-   return transpose(map(y -> frobenius(y,e),x))
+  e = degree(base_ring(x))
+  @req iseven(e) "The base ring must have even degree"
+  e = div(e, 2)
+
+  y = similar(x, ncols(x), nrows(x))
+  for i in 1:nrows(x), j in 1:ncols(x)
+    # This code could be *much* faster, by precomputing the Frobenius map
+    # once; see also FrobeniusCtx in Hecke (but that does not yet support all
+    # finite field types at the time this comment was written).
+    # If you need this function to be faster, talk to Claus or Max.
+    y[i,j] = frobenius([x[j,i]],e)
+  end
 end
 
 
@@ -124,14 +133,12 @@ Return `false` if `B` is not a square matrix, or the field has not even degree.
 """
 function is_hermitian(B::MatElem{T}) where T <: FinFieldElem
    n = nrows(B)
-   n==ncols(B) || return false
+   n == ncols(B) || return false
    e = degree(base_ring(B))
    iseven(e) ? e = div(e,2) : return false
 
-   for i in 1:n
-      for j in i:n
-         B[i,j]==frobenius(B[j,i],e) || return false
-      end
+   for i in 1:n, j in i:n
+      B[i,j] == frobenius(B[j,i],e) || return false
    end
 
    return true

src/Groups/matrices/transform_form.jl

@@ -49,7 +49,11 @@ function _find_radical(B::MatElem{T}, F::Field, nr::Int, nc::Int; e::Int=0, _is_
 #   A = matrix(vcat(type_vector[embU(v) for v in gens(U)], type_vector[embK(v) for v in gens(K)] ))
 
    if _is_symmetric
-      return A*B*transpose(map(y -> frobenius(y,e),A)), A, d
+      if e == 0
+         return A*B*transpose(A), A, d
+      else
+         return A*B*conjugate_transpose(A), A, d
+      end
    else
       A = transpose(A)
       return B*A, A, d
@@ -64,7 +68,7 @@ end
 # returns D, A such that A*B*transpose(frobenius(A)) = D and 
 # D is diagonal matrix (or with blocks [0 1 s 0])
 # f = dimension of the zero block in B in the isotropic case
-function _block_anisotropic_elim(B::MatElem{T}, _type::Symbol; isotr=false, f=0)  where T <: FinFieldElem
+function _block_anisotropic_elim(B::MatElem{T}, ::Val{_type}; isotr=false, f=0)  where {T <: FinFieldElem, _type}
 
    d = nrows(B)
    F = base_ring(B)
@@ -75,17 +79,17 @@ function _block_anisotropic_elim(B::MatElem{T}, _type::Symbol; isotr=false, f=0)
    if _type==:symmetric
       degF=0
       s=1
+      star(X) = transpose(X)
    elseif _type==:alternating
       degF=0
       s=-1
+      star(X) = transpose(X)
    elseif _type==:hermitian
       degF=div(degree(F),2)
       s=1
+      star(X) = conjugate_transpose(X)
    end
 
-   # conjugate transpose in hermitian case
-   # transpose in the other cases
-   star(X) = transpose(map(y -> frobenius(y,degF),X))
 
    if isotr
       q = characteristic(F)^degF
@@ -181,9 +185,9 @@ function _block_herm_elim(B::MatElem{T}, _type) where T <: FinFieldElem
    c = Int(ceil(d/2))
    B2 = B[1:c, 1:c]
    if B2==0
-      D,A = _block_anisotropic_elim(B,_type; isotr=true, f=c)
+      D,A = _block_anisotropic_elim(B, Val(_type); isotr=true, f=c)
    else
-      D,A = _block_anisotropic_elim(B,_type)
+      D,A = _block_anisotropic_elim(B, Val(_type))
    end
 
    return D,A