Move some stuff out of HeckeMoreStuff.jl

src/HeckeMoreStuff.jl

@@ -10,9 +10,7 @@ function prime_field(F::FqPolyRepField; cached::Bool=true)
   return Native.GF(characteristic(F), cached=cached)
 end
 
-function prime_field(F::T; cached::Bool=true) where {T<:Union{fpField,FpField}}
-  return F
-end
+prime_field(F::FpField; cached::Bool=true) = F
 
 function evaluate(f::ZZPolyRingElem, r::fqPolyRepFieldElem)
   #Horner - stolen from Claus
@@ -94,6 +92,7 @@ function roots(f::ZZModPolyRingElem, p::ZZRingElem, e::Int)
   F[p] = e
   return roots(f, F)
 end
+
 function roots(f::ZZModPolyRingElem, fac::Fac{ZZRingElem})
   res = fmpz_mod_poly_factor(base_ring(f))
   _fac = fmpz_factor()
@@ -231,27 +230,6 @@ function evaluate(f::QQPolyRingElem, r::T) where {T<:RingElem}
   return s
 end
 
-function mod!(f::ZZPolyRingElem, p::ZZRingElem)
-  for i = 0:degree(f)
-    setcoeff!(f, i, mod(coeff(f, i), p))
-  end
-end
-
-function mod(f::ZZPolyRingElem, p::ZZRingElem)
-  g = parent(f)()
-  for i = 0:degree(f)
-    setcoeff!(g, i, mod(coeff(f, i), p))
-  end
-  return g
-end
-
-#Assuming that the denominator of a is one, reduces all the coefficients modulo p
-# non-symmetric (positive) residue system
-function mod!(a::AbsSimpleNumFieldElem, b::ZZRingElem)
-  @ccall libflint.nf_elem_mod_fmpz(a::Ref{AbsSimpleNumFieldElem}, a::Ref{AbsSimpleNumFieldElem}, b::Ref{ZZRingElem}, parent(a)::Ref{AbsSimpleNumField})::Nothing
-  return a
-end
-
 @doc raw"""
     numerator(a::AbsSimpleNumFieldElem) -> AbsSimpleNumFieldElem
 
@@ -266,14 +244,6 @@ function numerator(a::AbsSimpleNumFieldElem)
   return z
 end
 
-function lift(R::ZZAbsPowerSeriesRing, f::ZZModAbsPowerSeriesRingElem)
-  r = R()
-  for i = 0:length(f)-1
-    setcoeff!(r, i, lift(coeff(f, i)))
-  end
-  return r
-end
-
 function evaluate(f::fpPolyRingElem, v::Vector{fpFieldElem})
   F = base_ring(f)
   v1 = UInt[x.data for x in v]
@@ -324,35 +294,11 @@ function inv(f::T) where {T<:Union{ZZModPolyRingElem,zzModPolyRingElem}}
   return g
 end
 
-function invmod(f::ZZModPolyRingElem, M::ZZModPolyRingElem)
-  if !is_unit(f)
-    r = parent(f)()
-    ff = ZZ()
-    i = @ccall libflint.fmpz_mod_poly_invmod_f(ff::Ref{ZZRingElem}, r::Ref{ZZModPolyRingElem}, f::Ref{ZZModPolyRingElem}, M::Ref{ZZModPolyRingElem}, f.parent.base_ring.ninv::Ref{fmpz_mod_ctx_struct})::Int
-    if iszero(i)
-      error("not yet implemented")
-    else
-      return r
-    end
-  end
-  if !is_unit(leading_coefficient(M))
-    error("not yet implemented")
-  end
-  g = parent(f)(inv(constant_coefficient(f)))
-  #lifting: to invert a, start with an inverse b mod m, then
-  # then b -> b*(2-ab) is an inverse mod m^2
-  # starting with this g, and using the fact that all coeffs are nilpotent
-  # we have an inverse modulo s.th. nilpotent. Hence it works
-  c = f * g
-  rem!(c, c, M)
-  while !isone(c)
-    mul!(g, g, 2 - c)
-    rem!(g, g, M)
-    mul!(c, f, g)
-    rem!(c, c, M)
-  end
-  return g
-end
+################################################################################
+#
+#
+#
+################################################################################
 
 function round!(z::ArbFieldElem, x::ArbFieldElem, p::Int)
   @ccall libflint.arb_set_round(z::Ref{ArbFieldElem}, x::Ref{ArbFieldElem}, p::Int)::Nothing
@@ -438,10 +384,6 @@ function size(F::FqField)
   return order(F)
 end
 
-function order(R::zzModRing)
-  return ZZRingElem(R.n)
-end
-
 #################################################
 # in triplicate.... and probably cases missing...
 function elem_to_mat_row!(M::MatElem, i::Int, a::ResElem{T}) where {T<:PolyRingElem}
@@ -640,19 +582,6 @@ function image(M::Map{D,C}, a) where {D,C}
   end
 end
 
-function setcoeff!(x::fqPolyRepFieldElem, n::Int, u::UInt)
-  @ccall libflint.nmod_poly_set_coeff_ui(x::Ref{fqPolyRepFieldElem}, n::Int, u::UInt)::Nothing
-end
-
-function basis(k::fpField)
-  return [k(1)]
-end
-
-function basis(k::fpField, l::fpField)
-  @assert k == l
-  return [k(1)]
-end
-
 function basis(K::fqPolyRepField, k::fpField)
   @assert characteristic(K) == characteristic(k)
   return basis(K)
@@ -673,15 +602,6 @@ function base_field(K::fqPolyRepField)
   return Native.GF(Int(characteristic(K)))
 end
 
-function gen(k::fpField)
-  return k(1)
-end
-
-function defining_polynomial(k::fpField)
-  kx, x = polynomial_ring(k, cached=false)
-  return x - k(1)
-end
-
 @doc raw"""
     mod!(A::Generic.Mat{AbsSimpleNumFieldElem}, m::ZZRingElem)
 
@@ -928,16 +848,6 @@ function (R::FqPolyRepField)(x::FpPolyRingElem)
   return z
 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
-end
-
-function rem!(a::FpPolyRingElem, b::FpPolyRingElem, c::FpPolyRingElem)
-  @ccall libflint.fmpz_mod_poly_rem(a::Ref{FpPolyRingElem}, b::Ref{FpPolyRingElem}, c::Ref{FpPolyRingElem}, a.parent.base_ring.ninv::Ref{fmpz_mod_ctx_struct})::Nothing
-  return a
-end
-
 ########################################
 #
 # misc infinity changes that need to stay in Nemo (after moving the rest to AA) # TODO: move somewhere sensible

src/antic/nf_elem.jl

@@ -1312,6 +1312,13 @@ base_field(::AbsSimpleNumField) = QQ
 #
 ###############################################################################
 
+#Assuming that the denominator of a is one, reduces all the coefficients modulo p
+# non-symmetric (positive) residue system
+function mod!(a::AbsSimpleNumFieldElem, b::ZZRingElem)
+  @ccall libflint.nf_elem_mod_fmpz(a::Ref{AbsSimpleNumFieldElem}, a::Ref{AbsSimpleNumFieldElem}, b::Ref{ZZRingElem}, parent(a)::Ref{AbsSimpleNumField})::Nothing
+  return a
+end
+
 function mod_sym!(a::AbsSimpleNumFieldElem, b::ZZRingElem)
   @ccall libflint.nf_elem_smod_fmpz(a::Ref{AbsSimpleNumFieldElem}, a::Ref{AbsSimpleNumFieldElem}, b::Ref{ZZRingElem}, parent(a)::Ref{AbsSimpleNumField})::Nothing
   return a

src/flint/fmpz_mod_abs_series.jl

@@ -615,6 +615,20 @@ for (etype, rtype, ctype, mtype, brtype) in (
   end # eval
 end # for
 
+################################################################################
+#
+#  Lifting
+#
+################################################################################
+
+function lift(R::ZZAbsPowerSeriesRing, f::ZZModAbsPowerSeriesRingElem)
+  r = R()
+  for i = 0:length(f)-1
+    setcoeff!(r, i, lift(coeff(f, i)))
+  end
+  return r
+end
+
 ###############################################################################
 #
 #   Square root

src/flint/fmpz_mod_poly.jl

@@ -420,6 +420,16 @@ end
 
 mod(x::T, y::T) where {T <: Zmodn_fmpz_poly} = rem(x, y)
 
+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
+end
+
+function rem!(a::FpPolyRingElem, b::FpPolyRingElem, c::FpPolyRingElem)
+  @ccall libflint.fmpz_mod_poly_rem(a::Ref{FpPolyRingElem}, b::Ref{FpPolyRingElem}, c::Ref{FpPolyRingElem}, a.parent.base_ring.ninv::Ref{fmpz_mod_ctx_struct})::Nothing
+  return a
+end
+
 ################################################################################
 #
 #  Removal and valuation
@@ -506,6 +516,36 @@ function invmod(x::T, y::T) where {T <: Zmodn_fmpz_poly}
   r == 0 ? error("Impossible inverse in invmod") : return z
 end
 
+function invmod(f::ZZModPolyRingElem, M::ZZModPolyRingElem)
+  if !is_unit(f)
+    r = parent(f)()
+    ff = ZZ()
+    i = @ccall libflint.fmpz_mod_poly_invmod_f(ff::Ref{ZZRingElem}, r::Ref{ZZModPolyRingElem}, f::Ref{ZZModPolyRingElem}, M::Ref{ZZModPolyRingElem}, f.parent.base_ring.ninv::Ref{fmpz_mod_ctx_struct})::Int
+    if iszero(i)
+      error("not yet implemented")
+    else
+      return r
+    end
+  end
+  if !is_unit(leading_coefficient(M))
+    error("not yet implemented")
+  end
+  g = parent(f)(inv(constant_coefficient(f)))
+  #lifting: to invert a, start with an inverse b mod m, then
+  # then b -> b*(2-ab) is an inverse mod m^2
+  # starting with this g, and using the fact that all coeffs are nilpotent
+  # we have an inverse modulo s.th. nilpotent. Hence it works
+  c = f * g
+  rem!(c, c, M)
+  while !isone(c)
+    mul!(g, g, 2 - c)
+    rem!(g, g, M)
+    mul!(c, f, g)
+    rem!(c, c, M)
+  end
+  return g
+end
+
 function mulmod(x::T, y::T, z::T) where {T <: Zmodn_fmpz_poly}
   check_parent(x, y)
   check_parent(y, z)

src/flint/fmpz_poly.jl

@@ -330,6 +330,20 @@ end
 
 divexact(x::ZZPolyRingElem, y::Integer; check::Bool=true) = divexact(x, flintify(y); check=check)
 
+function mod!(f::ZZPolyRingElem, p::ZZRingElem)
+  for i = 0:degree(f)
+    setcoeff!(f, i, mod(coeff(f, i), p))
+  end
+end
+
+function mod(f::ZZPolyRingElem, p::ZZRingElem)
+  g = parent(f)()
+  for i = 0:degree(f)
+    setcoeff!(g, i, mod(coeff(f, i), p))
+  end
+  return g
+end
+
 ###############################################################################
 #
 #   Pseudodivision

src/flint/fq_nmod.jl

@@ -55,28 +55,33 @@ function coeffs_raw(x::fqPolyRepFieldElem)
   return Vcopy
 end
 
+function setcoeff!(x::fqPolyRepFieldElem, n::Int, u::UInt)
+  @ccall libflint.nmod_poly_set_coeff_ui(x::Ref{fqPolyRepFieldElem}, n::Int, u::UInt)::Nothing
+  return x
+end
+
 # set the i-th coeff of x to c, internal use only
 function setindex_raw!(x::fqPolyRepFieldElem, c::UInt, i::Int)
   len = degree(parent(x))
   i > len - 1 && error("Index out of range")
-  @ccall libflint.nmod_poly_set_coeff_ui(x::Ref{fqPolyRepFieldElem}, i::Int, c::UInt)::Nothing
+  setcoeff!(x, i, c)
   return x
 end
 
 zero(a::fqPolyRepField) = zero!(a())
 
 one(a::fqPolyRepField) = one!(a())
 
+iszero(a::fqPolyRepFieldElem) = @ccall libflint.fq_nmod_is_zero(a::Ref{fqPolyRepFieldElem}, a.parent::Ref{fqPolyRepField})::Bool
+
+isone(a::fqPolyRepFieldElem) = @ccall libflint.fq_nmod_is_one(a::Ref{fqPolyRepFieldElem}, a.parent::Ref{fqPolyRepField})::Bool
+
 function gen(a::fqPolyRepField)
   d = a()
   @ccall libflint.fq_nmod_gen(d::Ref{fqPolyRepFieldElem}, a::Ref{fqPolyRepField})::Nothing
   return d
 end
 
-iszero(a::fqPolyRepFieldElem) = @ccall libflint.fq_nmod_is_zero(a::Ref{fqPolyRepFieldElem}, a.parent::Ref{fqPolyRepField})::Bool
-
-isone(a::fqPolyRepFieldElem) = @ccall libflint.fq_nmod_is_one(a::Ref{fqPolyRepFieldElem}, a.parent::Ref{fqPolyRepField})::Bool
-
 is_gen(a::fqPolyRepFieldElem) = a == gen(parent(a)) # there is no is_gen in flint
 
 function characteristic(a::fqPolyRepField)

src/flint/gfp_elem.jl

@@ -68,6 +68,32 @@ characteristic(R::fpField) = ZZRingElem(R.n)
 
 degree(::fpField) = 1
 
+function gen(k::fpField)
+  return k(1)
+end
+
+prime_field(F::fpField; cached::Bool=true) = F
+
+function defining_polynomial(k::fpField)
+  kx, x = polynomial_ring(k, cached=false)
+  return x - k(1)
+end
+
+################################################################################
+#
+#  Basis
+#
+################################################################################
+
+function basis(k::fpField)
+  return [k(1)]
+end
+
+function basis(k::fpField, l::fpField)
+  @assert k == l
+  return [k(1)]
+end
+
 ###############################################################################
 #
 #   AbstractString I/O

src/flint/nmod.jl

@@ -54,6 +54,8 @@ isone(a::zzModRingElem) = (a.parent.n == 1) || (a.data == 1)
 
 modulus(R::zzModRing) = R.n
 
+order(R::zzModRing) = ZZRingElem(R.n)
+
 function krull_dim(R::zzModRing)
   is_trivial(R) && return -inf
   return 0