Improve coercion from QQBarFieldElem to RealField/ComplexField

Now the precision can be specified as an argument

src/calcium/qqbar.jl

@@ -1423,13 +1423,12 @@ function (R::AcbField)(a::QQBarFieldElem)
 end
 
 @doc raw"""
-    (R::RealField)(a::QQBarFieldElem)
+    (R::RealField)(a::QQBarFieldElem, prec::Int = precision(Balls))
 
-Convert `a` to a real ball with the precision of the parent field `R`.
+Convert `a` to a real ball with the given precision.
 Throws if `a` is not a real number.
 """
-function (R::RealField)(a::QQBarFieldElem)
-  prec = precision(Balls)
+function (R::RealField)(a::QQBarFieldElem, prec::Int = precision(Balls))
   z = R()
   ccall((:qqbar_get_arb, libflint),
         Nothing, (Ref{RealFieldElem}, Ref{QQBarFieldElem}, Int), z, a, prec)
@@ -1438,12 +1437,11 @@ function (R::RealField)(a::QQBarFieldElem)
 end
 
 @doc raw"""
-    (R::ComplexField)(a::QQBarFieldElem)
+    (R::ComplexField)(a::QQBarFieldElem, prec::Int = precision(Balls))
 
-Convert `a` to a complex ball with the precision of the parent field `R`.
+Convert `a` to a complex ball with the given precision.
 """
-function (R::ComplexField)(a::QQBarFieldElem)
-  prec = precision(Balls)
+function (R::ComplexField)(a::QQBarFieldElem, prec::Int = precision(Balls))
   z = R()
   ccall((:qqbar_get_acb, libflint),
         Nothing, (Ref{ComplexFieldElem}, Ref{QQBarFieldElem}, Int), z, a, prec)
@@ -1485,18 +1483,18 @@ function ZZRingElem(a::QQBarFieldElem)
 end
 
 function (::Type{ComplexF64})(x::QQBarFieldElem)
-  z = AcbField(57, cached = false)(x)
-  x = real(z)
+  z = ComplexField()(x)
+  x = real(z; prec=57)
   xx = Float64(x)
-  y = imag(z)
+  y = imag(z; prec=57)
   yy = Float64(y)
   return ComplexF64(xx, yy)
 end
 
 function (::Type{Float64})(x::QQBarFieldElem)
   isreal(x) || throw(InexactError(:Float64, Float64, x))
-  z = AcbField(57, cached = false)(x)
-  x = real(z)
+  z = ComplexField()(x)
+  x = real(z; prec=57)
   return Float64(x)
 end