Add ZZ[i] and QQ[i]

src/Fields.jl

@@ -26,3 +26,5 @@ include("calcium/qqbar.jl")
 
 include("calcium/ca.jl")
 
+include("gaussiannumbers/QQi.jl")
+

src/Nemo.jl

@@ -397,6 +397,8 @@ include("arb/ArbTypes.jl")
 
 include("calcium/CalciumTypes.jl")
 
+include("gaussiannumbers/GaussianNumberTypes.jl")
+
 #include("ambiguities.jl") # remove ambiguity warnings
 
 include("flint/adhoc.jl")

src/Rings.jl

@@ -102,6 +102,8 @@ include("arb/arb_mat.jl")
 
 include("arb/acb_mat.jl")
 
+include("gaussiannumbers/ZZi.jl")
+
 include("Factor.jl")
 
 include("polysubst.jl")

src/flint/fmpq.jl

@@ -850,23 +850,6 @@ end
 
 add!(c::fmpq, a::Int, b::fmpq) = add!(c, b, a)
 
-###############################################################################
-#
-#   Conversions to/from flint Julia rationals
-#
-###############################################################################
-
-function Rational(z::fmpq)
-   r = Rational{BigInt}(0)
-   ccall((:fmpq_get_mpz_frac, libflint), Nothing,
-         (Ref{BigInt}, Ref{BigInt}, Ref{fmpq}), r.num, r.den, z)
-   return r
-end
-
-function Rational(z::fmpz)
-   return Rational{BigInt}(BigInt(z))
-end
-
 ###############################################################################
 #
 #   Parent object call overloads
@@ -939,8 +922,27 @@ promote_rule(::Type{fmpq}, ::Type{fmpz}) = fmpq
 
 Base.promote_rule(::Type{fmpq}, ::Type{Rational{T}}) where {T <: Integer} = fmpq
 
+function Base.convert(::Type{Rational{T}}, a::fmpq) where T <: Integer
+   return Rational{T}(convert(T, numerator(a)), convert(T, denominator(a)))
+end
+
+function Base.convert(::Type{fmpq}, a::Rational{T}) where T <: Integer
+   return convert(fmpz, numerator(a))//convert(fmpz, denominator(a))
+end
+
 convert(::Type{Rational{BigInt}}, a::fmpq) = Rational(a)
 
+function Rational(z::fmpq)
+   r = Rational{BigInt}(0)
+   ccall((:fmpq_get_mpz_frac, libflint), Nothing,
+         (Ref{BigInt}, Ref{BigInt}, Ref{fmpq}), r.num, r.den, z)
+   return r
+end
+
+function Rational(z::fmpz)
+   return Rational{BigInt}(BigInt(z))
+end
+
 ###############################################################################
 #
 #   FractionField constructor

src/flint/fmpz.jl

@@ -1994,6 +1994,98 @@ end
 #
 ###############################################################################
 
+function zero!(z::fmpz)
+   ccall((:fmpz_zero, libflint), Nothing,
+         (Ref{fmpz},), z)
+   return z
+end
+
+function one!(z::fmpz)
+   ccall((:fmpz_set_ui, libflint), Nothing,
+         (Ref{fmpz}, UInt),
+         z, 1)
+   return z
+end
+
+function set!(z::fmpz, a::fmpz)
+   ccall((:fmpz_set, libflint), Nothing,
+         (Ref{fmpz}, Ref{fmpz}),
+         z, a)
+   return z
+end
+
+function swap!(a::fmpz, b::fmpz)
+   ccall((:fmpz_swap, libflint), Nothing,
+         (Ref{fmpz}, Ref{fmpz}),
+         a, b)
+end
+
+function addeq!(z::fmpz, x::fmpz)
+   ccall((:fmpz_add, libflint), Nothing,
+         (Ref{fmpz}, Ref{fmpz}, Ref{fmpz}), z, z, x)
+   return z
+end
+
+function add!(z::fmpz, x::fmpz, y::fmpz)
+   ccall((:fmpz_add, libflint), Nothing,
+         (Ref{fmpz}, Ref{fmpz}, Ref{fmpz}), z, x, y)
+   return z
+end
+
+function add!(z::fmpz, x::fmpz, y::Int)
+   ccall((:fmpz_add_si, libflint), Nothing,
+         (Ref{fmpz}, Ref{fmpz}, Int), z, x, y)
+   return z
+end
+
+function add!(z::fmpz, a::fmpz, b::UInt)
+   ccall((:fmpz_add_ui, libflint), Nothing,
+         (Ref{fmpz}, Ref{fmpz}, UInt),
+         z, a, b)
+   return z
+end
+
+add!(z::fmpz, a::fmpz, b::Integer) = add!(z, a, fmpz(b))
+add!(z::fmpz, x::Int, y::fmpz) = add!(z, y, x)
+
+function neg!(z::fmpz, a::fmpz)
+   ccall((:fmpz_neg, libflint), Nothing,
+         (Ref{fmpz}, Ref{fmpz}),
+         z, a)
+   return z
+end
+
+function sub!(z::fmpz, a::fmpz, b::fmpz)
+   ccall((:fmpz_sub, libflint), Nothing,
+         (Ref{fmpz}, Ref{fmpz}, Ref{fmpz}),
+         z, a, b)
+   return z
+end
+
+function sub!(z::fmpz, a::fmpz, b::Int)
+   ccall((:fmpz_sub_si, libflint), Nothing,
+         (Ref{fmpz}, Ref{fmpz}, Int),
+         z, a, b)
+   return z
+end
+
+function sub!(z::fmpz, a::fmpz, b::UInt)
+   ccall((:fmpz_sub_ui, libflint), Nothing,
+         (Ref{fmpz}, Ref{fmpz}, UInt),
+         z, a, b)
+   return z
+end
+
+function sub!(z::fmpz, a::fmpz, b::Integer)
+   return sub!(z, a, fmpz(b))
+end
+
+function sub!(z::fmpz, b::Integer, a::fmpz)
+   sub!(z, a, b)
+   return neg!(z, z)
+end
+
+
 function mul!(z::fmpz, x::fmpz, y::fmpz)
    ccall((:fmpz_mul, libflint), Nothing,
          (Ref{fmpz}, Ref{fmpz}, Ref{fmpz}), z, x, y)
@@ -2006,6 +2098,15 @@ function mul!(z::fmpz, x::fmpz, y::Int)
    return z
 end
 
+function mul!(z::fmpz, a::fmpz, b::UInt)
+   ccall((:fmpz_mul_ui, libflint), Nothing,
+         (Ref{fmpz}, Ref{fmpz}, UInt),
+         z, a, b)
+   return z
+end
+
+mul!(z::fmpz, a::fmpz, b::Integer) = mul!(z, a, fmpz(b))
+
 mul!(z::fmpz, x::Int, y::fmpz) = mul!(z, y, x)
 
 function addmul!(z::fmpz, x::fmpz, y::fmpz)
@@ -2024,29 +2125,24 @@ end
 
 addmul!(z::fmpz, x::fmpz, y::Int, ::fmpz) = addmul!(z, x, y)
 
-function addeq!(z::fmpz, x::fmpz)
-   ccall((:fmpz_add, libflint), Nothing,
-         (Ref{fmpz}, Ref{fmpz}, Ref{fmpz}), z, z, x)
-   return z
-end
-
-function add!(z::fmpz, x::fmpz, y::fmpz)
-   ccall((:fmpz_add, libflint), Nothing,
-         (Ref{fmpz}, Ref{fmpz}, Ref{fmpz}), z, x, y)
+function submul!(z::fmpz, a::fmpz, b::fmpz)
+   ccall((:fmpz_submul, libflint), Nothing,
+         (Ref{fmpz}, Ref{fmpz}, Ref{fmpz}),
+         z, a, b)
    return z
 end
 
-function add!(z::fmpz, x::fmpz, y::Int)
-   ccall((:fmpz_add_si, libflint), Nothing,
-         (Ref{fmpz}, Ref{fmpz}, Int), z, x, y)
+function divexact!(z::fmpz, a::fmpz, b::fmpz)
+   ccall((:fmpz_divexact, libflint), Nothing,
+         (Ref{fmpz}, Ref{fmpz}, Ref{fmpz}),
+         z, a, b)
    return z
 end
 
-add!(z::fmpz, x::Int, y::fmpz) = add!(z, y, x)
-
-function zero!(z::fmpz)
-   ccall((:fmpz_zero, libflint), Nothing,
-         (Ref{fmpz},), z)
+function pow!(z::fmpz, a::fmpz, b::Union{Int, UInt})
+   ccall((:fmpz_pow_ui, libflint), Nothing,
+         (Ref{fmpz}, Ref{fmpz}, UInt),
+         z, a, UInt(b))
    return z
 end
 

src/gaussiannumbers/GaussianNumberTypes.jl

@@ -0,0 +1,22 @@
+#### QQ(i) and ZZ(i) ####
+
+mutable struct FlintZZiRing <: Nemo.Ring
+end
+
+const ZZi = FlintZZiRing()
+
+struct fmpzi <: RingElem
+  x::fmpz
+  y::fmpz
+end
+
+mutable struct FlintQQiField <: Nemo.Field
+end
+
+const QQi = FlintQQiField()
+
+struct fmpqi <: FieldElem
+  num::fmpzi
+  den::fmpz
+end
+