FakeFmpqMat -> QQMatrix for AlgAssAbsOrd[Idl]

src/AlgAss/Conversions.jl

@@ -152,6 +152,227 @@ It is assumed that $p$ is prime.
 """
 quo(I::Union{ AbsNumFieldOrderIdeal, AlgAssAbsOrdIdl }, J::Union{ AbsNumFieldOrderIdeal, AlgAssAbsOrdIdl }, p::Union{ Integer, ZZRingElem }) = StructureConstantAlgebra(I, J, p)
 
+function StructureConstantAlgebra(I::AlgAssAbsOrdIdl, J::AlgAssAbsOrdIdl, p::IntegerUnion)
+  @assert order(I) === order(J)
+
+  O = order(I)
+  Oalgebra = _algebra(O)
+
+  n = degree(O)
+  BmatJinI = _hnf_integral(basis_matrix(J, copy = false)*basis_mat_inv(I, copy = false), :lowerleft)
+  @assert isone(denominator(BmatJinI)) "J is not a subset of I"
+  BmatJinI = numerator(BmatJinI)
+  basis_elts = Vector{Int}()
+  for i = 1:n
+    if valuation(BmatJinI[i, i], p) == 0
+      continue
+    end
+
+    push!(basis_elts, i)
+  end
+
+  r = length(basis_elts)
+  Fp = GF(p, cached = false)
+
+  if r == 0
+    A = zero_algebra(Fp)
+
+    local _image_zero
+
+    let A = A
+      function _image_zero(a::Union{ AbsNumFieldOrderElem, AlgAssAbsOrdElem })
+        return A()
+      end
+    end
+
+    local _preimage_zero
+
+    let O = O
+      function _preimage_zero(a::AssociativeAlgebraElem)
+        return O()
+      end
+    end
+
+    OtoA = AbsOrdToAlgAssMor{typeof(O), elem_type(Fp)}(O, A, _image_zero, _preimage_zero)
+    return A, OtoA
+  end
+
+  BI = basis(I, copy = false)
+  BmatI = basis_matrix(I, copy = false)
+  BmatIinv = inv(BmatI)
+
+  mult_table = Array{elem_type(Fp), 3}(undef, r, r, r)
+  for i = 1:r
+    M = representation_matrix(_elem_in_algebra(BI[basis_elts[i]], copy = false))
+    M = mul!(M, BmatI, M)
+    M = mul!(M, M, BmatIinv)
+    @assert denominator(M) == 1
+    M = numerator(M) # M is now the representation matrix in the basis of I
+                     # TODO: fix type
+    if r != degree(O)
+      M = reduce_rows_mod_hnf!(M, BmatJinI, basis_elts)
+    end
+    for j = 1:r
+      for k = 1:r
+        mult_table[i, j, k] = Fp(M[basis_elts[j], basis_elts[k]])
+      end
+    end
+  end
+
+  A = StructureConstantAlgebra(Fp, mult_table)
+  if is_commutative(O)
+    A.is_commutative = 1
+  end
+
+  t = zero_matrix(QQ, 1, n)
+
+  local _image
+
+  let BmatJinI = BmatJinI, I = I, r = r, A = A, t = t, Fp = Fp
+    function _image(a::AlgAssAbsOrdElem)
+      elem_to_mat_row!(t, 1, _elem_in_algebra(a, copy = false))
+      t = mul!(t, t, basis_mat_inv(I, copy = false))
+      @assert isone(denominator(t)) "Not an element of the domain"
+      c = reduce_vector_mod_hnf(numerator(t), BmatJinI)
+      return A([ Fp(c[i]) for i in basis_elts ])
+    end
+  end
+
+  local _preimage
+
+  temppp = zero(Oalgebra)
+
+  let BI = BI, basis_elts = basis_elts, r = r, Oalgebra = Oalgebra, temppp = temppp
+    function _preimage(a::AssociativeAlgebraElem)
+      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
+
+  OtoA = AbsOrdToAlgAssMor{typeof(O), elem_type(Fp)}(O, A, _image, _preimage)
+
+  return A, OtoA
+end
+
+function StructureConstantAlgebra(I::AbsNumFieldOrderIdeal, J::AbsNumFieldOrderIdeal, p::IntegerUnion)
+  @assert order(I) === order(J)
+
+  O = order(I)
+  Oalgebra = _algebra(O)
+
+  n = degree(O)
+  BmatJinI = _hnf_integral(basis_matrix(J, copy = false)*basis_mat_inv(I, copy = false), :lowerleft)
+  @assert isone(BmatJinI.den) "J is not a subset of I"
+  BmatJinI = BmatJinI.num
+  basis_elts = Vector{Int}()
+  for i = 1:n
+    if valuation(BmatJinI[i, i], p) == 0
+      continue
+    end
+
+    push!(basis_elts, i)
+  end
+
+  r = length(basis_elts)
+  Fp = GF(p, cached = false)
+
+  if r == 0
+    A = zero_algebra(Fp)
+
+    local _image_zero
+
+    let A = A
+      function _image_zero(a::Union{ AbsNumFieldOrderElem, AlgAssAbsOrdElem })
+        return A()
+      end
+    end
+
+    local _preimage_zero
+
+    let O = O
+      function _preimage_zero(a::AssociativeAlgebraElem)
+        return O()
+      end
+    end
+
+    OtoA = AbsOrdToAlgAssMor{typeof(O), elem_type(Fp)}(O, A, _image_zero, _preimage_zero)
+    return A, OtoA
+  end
+
+  BI = basis(I, copy = false)
+  BmatI = basis_matrix(I, copy = false)
+  BmatIinv = inv(BmatI)
+
+  mult_table = Array{elem_type(Fp), 3}(undef, r, r, r)
+  for i = 1:r
+    M = FakeFmpqMat(representation_matrix(_elem_in_algebra(BI[basis_elts[i]], copy = false)))
+    M = mul!(M, BmatI, M)
+    M = mul!(M, M, BmatIinv)
+    @assert M.den == 1
+    M = M.num # M is now the representation matrix in the basis of I
+    if r != degree(O)
+      M = reduce_rows_mod_hnf!(M, BmatJinI, basis_elts)
+    end
+    for j = 1:r
+      for k = 1:r
+        mult_table[i, j, k] = Fp(M[basis_elts[j], basis_elts[k]])
+      end
+    end
+  end
+
+  A = StructureConstantAlgebra(Fp, mult_table)
+  if is_commutative(O)
+    A.is_commutative = 1
+  end
+
+  t = FakeFmpqMat(zero_matrix(ZZ, 1, n))
+
+  local _image
+
+  let BmatJinI = BmatJinI, I = I, r = r, A = A, t = t, Fp = Fp
+    function _image(a::Union{AbsNumFieldOrderElem, AlgAssAbsOrdElem})
+      elem_to_mat_row!(t.num, 1, t.den, _elem_in_algebra(a, copy = false))
+      t = mul!(t, t, basis_mat_inv(I, copy = false))
+      @assert isone(t.den) "Not an element of the domain"
+      c = reduce_vector_mod_hnf(t.num, BmatJinI)
+      return A([ Fp(c[i]) for i in basis_elts ])
+    end
+  end
+
+  local _preimage
+
+  temppp = zero(Oalgebra)
+
+  let BI = BI, basis_elts = basis_elts, r = r, Oalgebra = Oalgebra, temppp = temppp
+    function _preimage(a::AssociativeAlgebraElem)
+      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
+
+  OtoA = AbsOrdToAlgAssMor{typeof(O), elem_type(Fp)}(O, A, _image, _preimage)
+
+  return A, OtoA
+end
+
 function StructureConstantAlgebra(I::Union{ AbsNumFieldOrderIdeal, AlgAssAbsOrdIdl }, J::Union{AbsNumFieldOrderIdeal, AlgAssAbsOrdIdl}, p::IntegerUnion)
   @assert order(I) === order(J)
 

src/AlgAssAbsOrd/Elem.jl

@@ -31,10 +31,10 @@ end
 end
 
 (O::AlgAssAbsOrd{S, T})(arr::Vector{ZZRingElem}) where {S, T} = begin
-  M = basis_matrix(FakeFmpqMat, O, copy = false)
+  M = basis_matrix(O, copy = false)
   N = matrix(ZZ, 1, degree(O), arr)
   NM = N*M
-  x = elem_from_mat_row(algebra(O), NM.num, 1, NM.den)
+  x = elem_from_mat_row(algebra(O), NM, 1)
   return AlgAssAbsOrdElem{S, T}(O, x, deepcopy(arr))
 end
 
@@ -366,31 +366,31 @@ The multiplication is from the left if `action == :left` and from the right if
 function representation_matrix(x::AlgAssAbsOrdElem, action::Symbol = :left)
 
   O = parent(x)
-  M = basis_matrix(FakeFmpqMat, O, copy = false)
-  M1 = basis_mat_inv(FakeFmpqMat, O, copy = false)
+  M = basis_matrix(O, copy = false)
+  M1 = basis_matrix_inverse(O, copy = false)
 
-  B = FakeFmpqMat(representation_matrix(elem_in_algebra(x, copy = false), action))
+  B = representation_matrix(elem_in_algebra(x, copy = false), action)
   B = mul!(B, M, B)
   B = mul!(B, B, M1)
 
-  @assert B.den == 1
-  return B.num
+  @assert is_one(denominator(B))
+  return numerator(B)
 end
 
 function representation_matrix_mod(x::AlgAssAbsOrdElem, d::ZZRingElem, action::Symbol = :left)
   O = parent(x)
-  M = basis_matrix(FakeFmpqMat, O, copy = false)
-  M1 = basis_mat_inv(FakeFmpqMat, O, copy = false)
+  M = basis_matrix(O, copy = false)
+  M1 = basis_matrix_inverse(O, copy = false)
 
-  A = FakeFmpqMat(representation_matrix(elem_in_algebra(x, copy = false), action))
-  d2 = M.den * M1.den*A.den
+  A = representation_matrix(elem_in_algebra(x, copy = false), action)
+  d2 = denominator(M) * denominator(M1) * denominator(A)
   d2c, d2nc = ppio(d2, d)
   d1 = d * d2c
-  A1 = A.num
-  mod!(A.num, d1)
-  S1 = mod(M.num, d1)
+  A1 = numerator(A)
+  mod!(A1, d1)
+  S1 = mod(numerator(M), d1)
   mul!(A1, S1, A1)
-  S2 = mod(M1.num, d1)
+  S2 = mod(numerator(M1), d1)
   mul!(A1, A1, S2)
   mod!(A1, d1)
   divexact!(A1, A1, d2c)

src/AlgAssAbsOrd/ICM.jl

@@ -210,7 +210,7 @@ function ideals_containing(S::T, a::T2, R::T) where { T <: Union{ AbsNumFieldOrd
       end
     end
     if typeof(R) <: AlgAssAbsOrd
-      M = basis_matrix(potential_basis, FakeFmpqMat)
+      M = basis_matrix(potential_basis)
       return ideal(algebra(R), R, M)
     else
       M = basis_matrix(potential_basis, FakeFmpqMat)*basis_mat_inv(FakeFmpqMat, R, copy = false)