feat: make things faster for orders (#1553)

src/AlgAss/AlgAss.jl

@@ -261,12 +261,14 @@ function reduce_rows_mod_hnf!(M::ZZMatrix, N::ZZMatrix, rows::Vector{Int})
   return M
 end
 
-function addmul!(a::AlgAssAbsOrdElem, b::ZZRingElem, c::AlgAssAbsOrdElem)
-  return add!(a, a, b * c)
+function addmul!(a::AlgAssAbsOrdElem, b::ZZRingElem, c::AlgAssAbsOrdElem, d = parent(a)())
+  mul!(d, b, c)
+  return add!(a, a, d)
 end
 
-function addmul!(a::AbsNumFieldOrderElem, b::ZZRingElem, c::AbsNumFieldOrderElem)
-  return add!(a, a, b * c)
+function addmul!(a::AbsNumFieldOrderElem, b::ZZRingElem, c::AbsNumFieldOrderElem, d = parent(a)())
+  mul!(d, b, c)
+  return add!(a, a, d)
 end
 
 @doc raw"""
@@ -358,13 +360,15 @@ function StructureConstantAlgebra(O::Union{AbsNumFieldOrder, AlgAssAbsOrd}, I::U
 
   local _preimage
 
-  let BO = BO, basis_elts = basis_elts, r = r
+  temp = zero(O)
+
+  let BO = BO, basis_elts = basis_elts, r = r, temp = temp
     function _preimage(a::AssociativeAlgebraElem)
       z = zero(O)::eltype(BO)
       ca = coefficients(a, copy = false)
       for i in 1:r
         l = lift(ZZ, ca[i])
-        addmul!(z, l, BO[basis_elts[i]])
+        addmul!(z, l, BO[basis_elts[i]], temp)
       end
       return z
       #return sum(lift(coefficients(a, copy = false)[i])*BO[basis_elts[i]] for i = 1:r)
@@ -407,6 +411,7 @@ function StructureConstantAlgebra(I::Union{ AbsNumFieldOrderIdeal, AlgAssAbsOrdI
   @assert order(I) === order(J)
 
   O = order(I)
+  Oalgebra = _algebra(O)
 
   n = degree(O)
   BmatJinI = hnf(basis_matrix(J, copy = false)*basis_mat_inv(I, copy = false), :lowerleft)
@@ -489,9 +494,21 @@ function StructureConstantAlgebra(I::Union{ AbsNumFieldOrderIdeal, AlgAssAbsOrdI
 
   local _preimage
 
-  let BI = BI, basis_elts = basis_elts, r = r
+  temppp = zero(Oalgebra)
+
+  let BI = BI, basis_elts = basis_elts, r = r, Oalgebra = Oalgebra, temppp = temppp
     function _preimage(a::AssociativeAlgebraElem)
-      return O(sum(lift(ZZ, coefficients(a, copy = false)[i])*BI[basis_elts[i]] for i = 1:r))
+      acoords = map(x -> QQ(lift(ZZ, x)), coefficients(a, copy = false))
+      z = zero(Oalgebra)
+      for i in 1:r
+        if is_zero(acoords[i])
+          continue
+        end
+        temppp = mul!(temppp, acoords[i], BI[basis_elts[i]])
+        z = add!(z, z, temppp)
+      end
+      _zz = O(z)
+      return _zz
     end
   end
 

src/AlgAss/AlgMatElem.jl

@@ -121,12 +121,6 @@ function add!(c::T, a::T, b::T) where {T <: MatAlgebraElem}
   parent(c) != parent(b) && error("Parents don't match.")
   A = parent(a)
 
-  if c === a || c === b
-    d = A()
-    d = add!(d, a, b)
-    return d
-  end
-
   c.matrix = add!(c.matrix, a.matrix, b.matrix)
   c.has_coeffs = false
 
@@ -159,6 +153,15 @@ function addeq!(b::T, a::T) where {T <: MatAlgebraElem}
   return b
 end
 
+function mul!(c::MatAlgebraElem{T}, a::MatAlgebraElem{T}, b::T) where {T}
+  parent(c) !== parent(a) && error("Parents don't match.")
+  A = parent(a)
+
+  c.matrix = mul!(c.matrix, a.matrix, b)
+  c.has_coeffs = false
+  return c
+end
+
 ################################################################################
 #
 #  Ad hoc operations

src/AlgAss/Elem.jl

@@ -871,19 +871,34 @@ _set_to_copy!(M::QQMatrix, i, j, c) = M[i, j] = c
 
 _set_to_copy!(M, i, j, c) = M[i, j] = deepcopy(c)
 
-function _addmul!(M::MatrixElem, i, j, b, c)
+function _addmul!(M::MatrixElem, i, j, b, c, temp = nothing)
   return M[i, j] = addmul!(M[i, j], b, c)
 end
 
-function _addmul!(M::QQMatrix, i, j, a::QQFieldElem, b::QQFieldElem)
-  c = mat_entry_ptr(M, i, j)
-  ccall((:fmpq_addmul, libflint), Nothing, (Ptr{QQFieldElem}, Ref{QQFieldElem}, Ref{QQFieldElem}), c, a, b)
+function _addmul!(M::QQMatrix, i, j, a::QQFieldElem, b::QQFieldElem, temp = nothing)
+  GC.@preserve M begin
+    c = mat_entry_ptr(M, i, j)
+    ccall((:fmpq_addmul, libflint), Nothing, (Ptr{QQFieldElem}, Ref{QQFieldElem}, Ref{QQFieldElem}), c, a, b)
+  end
+end
+
+function _addmul!(M::FqMatrix, i, j, a::FqFieldElem, b::FqFieldElem, temp = base_ring(M)())
+  GC.@preserve M begin
+    c = Nemo.fq_default_mat_entry_ptr(M, i, j)
+    mul!(temp, a, b)
+    ccall((:fq_default_add, libflint), Nothing, (Ptr{FqFieldElem}, Ptr{FqFieldElem}, Ref{FqFieldElem}, Ref{FqField}), c, c, temp, base_ring(M))
+  end
 end
 
 function representation_matrix!(a::Union{AssociativeAlgebraElem, MatAlgebraElem}, M::MatElem, action::Symbol = :left)
   A = parent(a)
   acoeff = coefficients(a, copy = false)
   mt = multiplication_table(A, copy = false)
+  if base_ring(A) isa QQField
+    temp = nothing
+  else
+    temp = base_ring(A)()
+  end
   GC.@preserve M begin
     if action == :left
       for i = 1:dim(A)
@@ -892,7 +907,7 @@ function representation_matrix!(a::Union{AssociativeAlgebraElem, MatAlgebraElem}
         end
         for j = 1:dim(A)
           for k = 1:dim(A)
-            _addmul!(M, j, k, acoeff[i], mt[i, j, k])
+            _addmul!(M, j, k, acoeff[i], mt[i, j, k], temp)
             #M[j, k] += acoeff[i] * mt[i, j, k]
           end
         end

src/AlgAssAbsOrd/Elem.jl

@@ -190,13 +190,14 @@ function -(x::T, y::T) where { T <: Union{ AlgAssAbsOrdElem, AlgAssRelOrdElem }
 end
 
 function *(n::IntegerUnion, x::AlgAssAbsOrdElem)
-  O=x.parent
-  y=Vector{ZZRingElem}(undef, O.dim)
-  z=coordinates(x, copy = false)
-  for i=1:O.dim
-    y[i] = z[i] * n
+  #O=x.parent
+  O = parent(x)
+  y = O(n * elem_in_algebra(x, copy = false))
+  if x.has_coord
+    y.coordinates = n .* coordinates(x, copy = false)
+    y.has_coord = true
   end
-  return O(y)
+  return y
 end
 
 *(x::AlgAssAbsOrdElem, n::IntegerUnion) = n*x

src/AlgAssAbsOrd/Ideal.jl

@@ -1141,7 +1141,7 @@ function _islocally_free_left(O::AlgAssAbsOrd, I::AlgAssAbsOrdIdl, p::Union{Int,
     end
 
     for i = 1:length(basiseIJoverZ)
-      a += mod(toOpO\(toOJ\(AtoOJ(BtoA(BtoC\C[i]))))*basiseIJoverZ[i], pI)
+      add!(a, a, mod(toOpO\(toOJ\(AtoOJ(BtoA(BtoC\C[i]))))*basiseIJoverZ[i], pI))
     end
   end