Optimize map_coefficients, change_base_ring for some inputs (#1994)

Namely if the input polynomial is a `QQMPolyRingElem` and the
transformation "function" is `ZZ` resp. a `fpField`.

src/HeckeMoreStuff.jl

@@ -182,21 +182,6 @@ function Base.hash(f::zzModMPolyRingElem, h::UInt)
   return UInt(1) # TODO: enhance or throw error
 end
 
-function AbstractAlgebra.map_coefficients(F::fpField, f::QQMPolyRingElem; parent=polynomial_ring(F, nvars(parent(f)), cached=false)[1])
-  dF = denominator(f)
-  d = F(dF)
-  if iszero(d)
-    error("Denominator divisible by p!")
-  end
-  m = inv(d)
-  ctx = MPolyBuildCtx(parent)
-  for x in zip(coefficients(f), exponent_vectors(f))
-    el = numerator(x[1] * dF)
-    push_term!(ctx, F(el) * m, x[2])
-  end
-  return finish(ctx)
-end
-
 function tdivpow2!(B::ZZMatrix, t::Int)
   @ccall libflint.fmpz_mat_scalar_tdiv_q_2exp(B::Ref{ZZMatrix}, B::Ref{ZZMatrix}, t::Cint)::Nothing
 end

src/flint/FlintTypes.jl

@@ -1008,8 +1008,8 @@ const flint_orderings = [:lex, :deglex, :degrevlex]
 
 @attributes mutable struct ZZMPolyRing <: MPolyRing{ZZRingElem}
   nvars::Int
-  nfields::Cint
-  ord::Int
+  nfields::Int
+  ord::Cint
   deg::Cint
   rev::Cint
   lut::NTuple{Base.GMP.BITS_PER_LIMB, Int}
@@ -1136,8 +1136,8 @@ end
 
 @attributes mutable struct QQMPolyRing <: MPolyRing{QQFieldElem}
   nvars::Int
-  nfields::Cint
-  ord::Int
+  nfields::Int
+  ord::Cint
   deg::Cint
   rev::Cint
   lut::NTuple{Base.GMP.BITS_PER_LIMB, Int}

src/flint/fmpq_mpoly.jl

@@ -645,6 +645,11 @@ end
 #
 ###############################################################################
 
+_content_ptr(c::QQMPolyRingElem) = Ptr{QQFieldElem}(pointer_from_objref(c))
+_content_ptr(c::Ptr{QQMPolyRingElem}) = Ptr{QQFieldElem}(c)
+_content_ptr(c::Ref{QQMPolyRingElem}) = _content_ptr(c[])
+_zpoly_ptr(c::QQMPolyRingElemOrPtr) = Ptr{ZZMPolyRingElem}(_content_ptr(c) + sizeof(QQFieldElem))
+
 function zero!(a::QQMPolyRingElem)
   @ccall libflint.fmpq_mpoly_zero(a::Ref{QQMPolyRingElem}, a.parent::Ref{QQMPolyRing})::Nothing
   return a
@@ -748,6 +753,20 @@ sub!(a::QQMPolyRingElem, b::RationalUnion, c::QQMPolyRingElem) = neg!(sub!(a, c,
 mul!(a::QQMPolyRingElem, b::QQMPolyRingElem, c::RationalUnion) = mul!(a, b, flintify(c))
 mul!(a::QQMPolyRingElem, b::RationalUnion, c::QQMPolyRingElem) = mul!(a, c, b)
 
+# special: multiply a QQMPolyRingElem by an integer and store the result as a ZZMPolyRingElem.
+# obviously this only works if the integers is a multiple of the denominator of the polynomial
+function mul!(a::ZZMPolyRingElem, b::QQMPolyRingElem, c::IntegerUnion)
+  x = QQFieldElem()
+  GC.@preserve b x begin
+    x = mul!(x, _content_ptr(b), c)
+    bp = _zpoly_ptr(b)
+    xp = _num_ptr(x)
+    @ccall libflint.fmpz_mpoly_scalar_mul_fmpz(a::Ref{ZZMPolyRingElem}, bp::Ref{ZZMPolyRingElem}, xp::Ref{ZZRingElem}, parent(a)::Ref{ZZMPolyRing})::Nothing
+  end
+  return a
+end
+
+
 divexact!(a::QQMPolyRingElem, b::QQMPolyRingElem, c::RationalUnion) = divexact!(a, b, flintify(c))
 
 # Set the n-th coefficient of a to c. If zero coefficients are inserted, they
@@ -1047,3 +1066,54 @@ function (R::QQMPolyRing)(a::Vector{Any}, b::Vector{Vector{T}}) where T
 
   return R(newaa, newbb)
 end
+
+###############################################################################
+#
+#   Changing base ring, mapping coefficients
+#
+###############################################################################
+
+function map_coefficients(R::ZZRing, f::QQMPolyRingElem;
+                          cached::Bool = true,
+                          parent::ZZMPolyRing = AbstractAlgebra._change_mpoly_ring(R, parent(f), cached))
+  @req isinteger(_content_ptr(f)) "input polynomial must have integral coefficients"
+  @req ngens(parent) == ngens(Nemo.parent(f)) "parents must have matching numbers of generators"
+  if internal_ordering(parent) == internal_ordering(Nemo.parent(f))
+    return mul!(zero(parent), f, 1)
+  end
+
+  ctx = MPolyBuildCtx(parent)
+  for (c, ev) in zip(coefficients(f), exponent_vectors(f))
+    push_term!(ctx, ZZ(c), ev)
+  end
+  return finish(ctx)
+end
+
+function map_coefficients(F::fpField, f::QQMPolyRingElem;
+                          cached::Bool = true,
+                          parent::MPolyRing = AbstractAlgebra._change_mpoly_ring(F, parent(f), cached))
+  dF = denominator(f)
+  d = F(dF)
+  @req !iszero(d) "Denominator divisible by p!"
+  m = inv(d)
+  ctx = MPolyBuildCtx(parent)
+  # TODO: rewrite this code using `_zpoly_ptr(f)`: convert that into the desired
+  # element, then multiply the result once by m at the end
+  for (c, ev) in zip(coefficients(f), exponent_vectors(f))
+    el = numerator(c * dF)
+    push_term!(ctx, F(el) * m, ev)
+  end
+  return finish(ctx)
+end
+
+function change_base_ring(R::ZZRing, f::QQMPolyRingElem;
+                          cached::Bool = true,
+                          parent::ZZMPolyRing = AbstractAlgebra._change_mpoly_ring(R, parent(f), cached))
+  return map_coefficients(R, f; cached, parent)
+end
+
+function change_base_ring(F::fpField, f::QQMPolyRingElem;
+                          cached::Bool = true,
+                          parent::fpMPolyRing = AbstractAlgebra._change_mpoly_ring(F, parent(f), cached))
+  return map_coefficients(F, f; cached, parent)
+end

test/flint/fmpq_mpoly-test.jl

@@ -813,3 +813,50 @@ end
   @test abc - a - b == c
   @test abc - ab == c
 end
+
+@testset "QQMPolyRingElem.convert_to_ZZMPolyRingElem" begin
+  Qxy, (x,y) = QQ[:x,:y]
+  f = 11*(x^2/2 + ZZ(3)^50*x*y^5/7 + y^6/12)
+
+  R = ZZ
+  Rxy, (u,v) = polynomial_ring(R, [:u,:v])
+  g = 462*u^2 + 94762534375324541717672868*u*v^5 + 77*v^6
+
+  @test g == @inferred mul!(zero(Rxy), f, 84)
+  @test g == change_base_ring(R, f*84; parent = Rxy)
+  @test g == map_coefficients(R, f*84; parent = Rxy)
+
+  # test error handling
+  @test_throws ArgumentError change_base_ring(R, f/5; parent = Rxy)
+  @test_throws ArgumentError map_coefficients(R, f/5; parent = Rxy)
+
+  # test ordering mismatch
+  Rxy, (u,v) = polynomial_ring(R, [:u,:v]; internal_ordering = :deglex)
+  g = 462*u^2 + 94762534375324541717672868*u*v^5 + 77*v^6
+
+  @test g == change_base_ring(R, f*84; parent = Rxy)
+  @test g == map_coefficients(R, f*84; parent = Rxy)
+end
+
+@testset "QQMPolyRingElem.convert_to_fpMPolyRing" begin
+  Qxy, (x,y) = QQ[:x,:y]
+  f = 11*(x^2/2 + ZZ(3)^50*x*y^5/7 + y^6/12)
+
+  R = Native.GF(5)
+  Rxy, (u,v) = polynomial_ring(R, [:u,:v])
+  g = 462*u^2 + 94762534375324541717672868*u*v^5 + 77*v^6
+
+  @test g == change_base_ring(R, f*84; parent = Rxy)
+  @test g == map_coefficients(R, f*84; parent = Rxy)
+
+  # test error handling
+  @test_throws ArgumentError change_base_ring(R, f/5; parent = Rxy)
+  @test_throws ArgumentError map_coefficients(R, f/5; parent = Rxy)
+
+  # test ordering mismatch
+  Rxy, (u,v) = polynomial_ring(R, [:u,:v]; internal_ordering = :deglex)
+  g = 462*u^2 + 94762534375324541717672868*u*v^5 + 77*v^6
+
+  @test g == change_base_ring(R, f*84; parent = Rxy)
+  @test g == map_coefficients(R, f*84; parent = Rxy)
+end