From 5b2186c0df247a49a4d9bd728e6d61ef4af27ad1 Mon Sep 17 00:00:00 2001
From: Max Horn <max@quendi.de>
Date: Thu, 19 Dec 2024 19:24:32 +0100
Subject: [PATCH] Move some more things out of HeckeMoreStuff.jl (#1983)

---
 src/HeckeMoreStuff.jl | 43 -------------------------------------------
 src/antic/nf_elem.jl  | 35 +++++++++++++++++++++++++++++------
 src/flint/fmpz.jl     |  9 +++++++++
 src/flint/fmpz_mod.jl | 24 ++++++++++++++++++++++++
 src/flint/gfp_poly.jl |  8 ++++++--
 5 files changed, 68 insertions(+), 51 deletions(-)

diff --git a/src/HeckeMoreStuff.jl b/src/HeckeMoreStuff.jl
index 0bb8a65a5..994514333 100644
--- a/src/HeckeMoreStuff.jl
+++ b/src/HeckeMoreStuff.jl
@@ -225,11 +225,6 @@ function is_squarefree(x::Generic.Poly{AbsSimpleNumFieldElem})
   return isone(gcd(x, derivative(x), true))
 end
 
-###
-
-(::QQField)(a::AbsSimpleNumFieldElem) = (is_rational(a) && return coeff(a, 0)) || error("not a rational")
-(::ZZRing)(a::AbsSimpleNumFieldElem) = (is_integer(a) && return numerator(coeff(a, 0))) || error("not an integer")
-
 ################################################################################
 #
 #  Base case for dot products
@@ -312,16 +307,6 @@ function numerator(a::AbsSimpleNumFieldElem)
   return z
 end
 
-function divexact!(z::AbsSimpleNumFieldElem, x::AbsSimpleNumFieldElem, y::ZZRingElem)
-  @ccall libflint.nf_elem_scalar_div_fmpz(z::Ref{AbsSimpleNumFieldElem}, x::Ref{AbsSimpleNumFieldElem}, y::Ref{ZZRingElem}, parent(x)::Ref{AbsSimpleNumField})::Nothing
-  return z
-end
-
-function sub!(a::AbsSimpleNumFieldElem, b::AbsSimpleNumFieldElem, c::AbsSimpleNumFieldElem)
-  @ccall libflint.nf_elem_sub(a::Ref{AbsSimpleNumFieldElem}, b::Ref{AbsSimpleNumFieldElem}, c::Ref{AbsSimpleNumFieldElem}, a.parent::Ref{AbsSimpleNumField})::Nothing
-  return a
-end
-
 function lift(R::ZZAbsPowerSeriesRing, f::ZZModAbsPowerSeriesRingElem)
   r = R()
   for i = 0:length(f)-1
@@ -702,11 +687,6 @@ function evaluate(f::QQPolyRingElem, a::AbsSimpleNumFieldElem)
   return s
 end
 
-function rem!(z::fpPolyRingElem, a::fpPolyRingElem, b::fpPolyRingElem)
-  @ccall libflint.nmod_poly_rem(z::Ref{fpPolyRingElem}, a::Ref{fpPolyRingElem}, b::Ref{fpPolyRingElem}, (pointer_from_objref(base_ring(z)) + sizeof(ZZRingElem))::Ptr{Nothing})::Nothing
-  return z
-end
-
 function preimage(M::Map{D,C}, a) where {D,C}
   if isdefined(M.header, :preimage)
     p = M.header.preimage(a)::elem_type(D)
@@ -832,24 +812,6 @@ function (R::QQPolyRing)(a::Generic.RationalFunctionFieldElem{QQFieldElem})
   return R(numerator(a))
 end
 
-function Base.divrem(a::ZZModRingElem, b::ZZModRingElem)
-  R = parent(a)
-  r = rem(a, b)
-  return divexact(a - r, b), r
-end
-
-function Base.div(a::ZZModRingElem, b::ZZModRingElem)
-  R = parent(a)
-  r = rem(a, b)
-  return divexact(a - r, b)
-end
-
-function Base.rem(a::ZZModRingElem, b::ZZModRingElem)
-  R = parent(a)
-  r = R(rem(lift(a), gcd(modulus(R), lift(b))))
-  return r
-end
-
 @doc raw"""
     zeros(f::ZZPolyRingElem) -> Vector{ZZRingElem}
 
@@ -1081,11 +1043,6 @@ function (R::FqPolyRepField)(x::FpPolyRingElem)
   return z
 end
 
-@inline function rem!(a::ZZRingElem, b::ZZRingElem, c::ZZRingElem)
-  @ccall libflint.fmpz_mod(a::Ref{ZZRingElem}, b::Ref{ZZRingElem}, c::Ref{ZZRingElem})::Nothing
-  return a
-end
-
 function rem!(a::ZZModPolyRingElem, b::ZZModPolyRingElem, c::ZZModPolyRingElem)
   @ccall libflint.fmpz_mod_poly_rem(a::Ref{ZZModPolyRingElem}, b::Ref{ZZModPolyRingElem}, c::Ref{ZZModPolyRingElem}, a.parent.base_ring.ninv::Ref{fmpz_mod_ctx_struct})::Nothing
   return a
diff --git a/src/antic/nf_elem.jl b/src/antic/nf_elem.jl
index da613c6ab..312f88eff 100644
--- a/src/antic/nf_elem.jl
+++ b/src/antic/nf_elem.jl
@@ -262,24 +262,21 @@ function +(a::AbsSimpleNumFieldElem, b::AbsSimpleNumFieldElem)
   parent(a) == parent(b) || return force_op(+, a, b)::AbsSimpleNumFieldElem
   check_parent(a, b)
   r = a.parent()
-  @ccall libflint.nf_elem_add(r::Ref{AbsSimpleNumFieldElem}, a::Ref{AbsSimpleNumFieldElem}, b::Ref{AbsSimpleNumFieldElem}, a.parent::Ref{AbsSimpleNumField})::Nothing
-  return r
+  return add!(r, a, b)
 end
 
 function -(a::AbsSimpleNumFieldElem, b::AbsSimpleNumFieldElem)
   parent(a) == parent(b) || return force_op(-, a, b)::AbsSimpleNumFieldElem
   check_parent(a, b)
   r = a.parent()
-  @ccall libflint.nf_elem_sub(r::Ref{AbsSimpleNumFieldElem}, a::Ref{AbsSimpleNumFieldElem}, b::Ref{AbsSimpleNumFieldElem}, a.parent::Ref{AbsSimpleNumField})::Nothing
-  return r
+  return sub!(r, a, b)
 end
 
 function *(a::AbsSimpleNumFieldElem, b::AbsSimpleNumFieldElem)
   parent(a) == parent(b) || return force_op(*, a, b)::AbsSimpleNumFieldElem
   check_parent(a, b)
   r = a.parent()
-  @ccall libflint.nf_elem_mul(r::Ref{AbsSimpleNumFieldElem}, a::Ref{AbsSimpleNumFieldElem}, b::Ref{AbsSimpleNumFieldElem}, a.parent::Ref{AbsSimpleNumField})::Nothing
-  return r
+  return mul!(r, a, b)
 end
 
 ###############################################################################
@@ -724,6 +721,11 @@ end
 
 add!(c::AbsSimpleNumFieldElem, a::AbsSimpleNumFieldElem, b::Integer) = add!(c, a, flintify(b))
 
+function sub!(a::AbsSimpleNumFieldElem, b::AbsSimpleNumFieldElem, c::AbsSimpleNumFieldElem)
+  @ccall libflint.nf_elem_sub(a::Ref{AbsSimpleNumFieldElem}, b::Ref{AbsSimpleNumFieldElem}, c::Ref{AbsSimpleNumFieldElem}, a.parent::Ref{AbsSimpleNumField})::Nothing
+  return a
+end
+
 function sub!(c::AbsSimpleNumFieldElem, a::AbsSimpleNumFieldElem, b::QQFieldElem)
   @ccall libflint.nf_elem_sub_fmpq(c::Ref{AbsSimpleNumFieldElem}, a::Ref{AbsSimpleNumFieldElem}, b::Ref{QQFieldElem}, a.parent::Ref{AbsSimpleNumField})::Nothing
   return c
@@ -775,6 +777,23 @@ end
 
 mul!(c::AbsSimpleNumFieldElem, a::AbsSimpleNumFieldElem, b::Integer) = mul!(c, a, flintify(b))
 
+function divexact!(z::AbsSimpleNumFieldElem, x::AbsSimpleNumFieldElem, y::Int)
+  @ccall libflint.nf_elem_scalar_div_si(r::Ref{AbsSimpleNumFieldElem}, a::Ref{AbsSimpleNumFieldElem}, b::Int, parent(x)::Ref{AbsSimpleNumField})::Nothing
+  return z
+end
+
+function divexact!(z::AbsSimpleNumFieldElem, x::AbsSimpleNumFieldElem, y::ZZRingElem)
+  @ccall libflint.nf_elem_scalar_div_fmpz(z::Ref{AbsSimpleNumFieldElem}, x::Ref{AbsSimpleNumFieldElem}, y::Ref{ZZRingElem}, parent(x)::Ref{AbsSimpleNumField})::Nothing
+  return z
+end
+
+function divexact!(z::AbsSimpleNumFieldElem, x::AbsSimpleNumFieldElem, y::QQFieldElem)
+  @ccall libflint.nf_elem_scalar_div_fmpq(z::Ref{AbsSimpleNumFieldElem}, x::Ref{AbsSimpleNumFieldElem}, y::Ref{QQFieldElem}, parent(x)::Ref{AbsSimpleNumField})::Nothing
+  return z
+end
+
+divexact!(z::AbsSimpleNumFieldElem, x::AbsSimpleNumFieldElem, y::RationalUnion) = divexact!(z, x, flintify(y))
+
 ###############################################################################
 #
 #   Speedups for polynomials over number fields
@@ -1016,6 +1035,10 @@ function (a::QQPolyRing)(b::AbsSimpleNumFieldElem)
   return r
 end
 
+(::QQField)(a::AbsSimpleNumFieldElem) = (is_rational(a) && return coeff(a, 0)) || error("not a rational")
+
+(::ZZRing)(a::AbsSimpleNumFieldElem) = (is_integer(a) && return numerator(coeff(a, 0))) || error("not an integer")
+
 ###############################################################################
 #
 #   Random generation
diff --git a/src/flint/fmpz.jl b/src/flint/fmpz.jl
index 7c811794f..84dc6fddc 100644
--- a/src/flint/fmpz.jl
+++ b/src/flint/fmpz.jl
@@ -482,6 +482,7 @@ function rem(x::ZZRingElemOrPtr, ::Type{UInt64})
 end
 
 function rem(x::ZZRingElem, c::ZZRingElem)
+  # FIXME: it seems `rem` and `rem!` for `ZZRingElem` do different things?
   q, r = Base.divrem(x, c)
   return r
 end
@@ -2609,6 +2610,14 @@ divexact!(z::ZZRingElemOrPtr, a::ZZRingElemOrPtr, b::Integer) = divexact!(z, a,
 
 #
 
+function rem!(a::ZZRingElem, b::ZZRingElem, c::ZZRingElem)
+  # FIXME: it seems `rem` and `rem!` for `ZZRingElem` do different things?
+  @ccall libflint.fmpz_mod(a::Ref{ZZRingElem}, b::Ref{ZZRingElem}, c::Ref{ZZRingElem})::Nothing
+  return a
+end
+
+#
+
 function pow!(z::ZZRingElemOrPtr, a::ZZRingElemOrPtr, b::Integer)
   @ccall libflint.fmpz_pow_ui(z::Ref{ZZRingElem}, a::Ref{ZZRingElem}, UInt(b)::UInt)::Nothing
   return z
diff --git a/src/flint/fmpz_mod.jl b/src/flint/fmpz_mod.jl
index 596037b96..2c36f81c5 100644
--- a/src/flint/fmpz_mod.jl
+++ b/src/flint/fmpz_mod.jl
@@ -294,6 +294,30 @@ function divides(a::ZZModRingElem, b::ZZModRingElem)
   return true, rr
 end
 
+###############################################################################
+#
+#   Division with remainder
+#
+###############################################################################
+
+function Base.divrem(a::ZZModRingElem, b::ZZModRingElem)
+  R = parent(a)
+  r = rem(a, b)
+  return divexact(a - r, b), r
+end
+
+function Base.div(a::ZZModRingElem, b::ZZModRingElem)
+  R = parent(a)
+  r = rem(a, b)
+  return divexact(a - r, b)
+end
+
+function Base.rem(a::ZZModRingElem, b::ZZModRingElem)
+  R = parent(a)
+  r = R(rem(lift(a), gcd(modulus(R), lift(b))))
+  return r
+end
+
 ###############################################################################
 #
 #   GCD
diff --git a/src/flint/gfp_poly.jl b/src/flint/gfp_poly.jl
index cb1aaddc9..36d68ce52 100644
--- a/src/flint/gfp_poly.jl
+++ b/src/flint/gfp_poly.jl
@@ -193,12 +193,16 @@ end
 #
 ################################################################################
 
+function rem!(z::fpPolyRingElem, x::fpPolyRingElem, y::fpPolyRingElem)
+  @ccall libflint.nmod_poly_rem(z::Ref{fpPolyRingElem}, x::Ref{fpPolyRingElem}, y::Ref{fpPolyRingElem})::Nothing
+  return z
+end
+
 function rem(x::fpPolyRingElem, y::fpPolyRingElem)
   check_parent(x,y)
   iszero(y) && throw(DivideError())
   z = parent(x)()
-  @ccall libflint.nmod_poly_rem(z::Ref{fpPolyRingElem}, x::Ref{fpPolyRingElem}, y::Ref{fpPolyRingElem})::Nothing
-  return z
+  return rem!(z, x, y)
 end
 
 ################################################################################