proper expressify for n_transExt (#394)

src/number/NumberTypes.jl

@@ -309,6 +309,7 @@ mutable struct N_FField <: Field
    ptr::libSingular.coeffs_ptr
    base_ring::Field
    refcount::Int
+   S::Array{Symbol, 1}
 
    function N_FField(F::Field, S::Array{Symbol, 1}, cached::Bool = true)
       if cached && haskey(N_FFieldID, (F, S))
@@ -317,7 +318,7 @@ mutable struct N_FField <: Field
          v = [pointer(Base.Vector{UInt8}(string(str)*"\0")) for str in S]
          cf = libSingular.nCopyCoeff(F.ptr)
          ptr = libSingular.transExt_helper(cf, v)
-         d = new(ptr, F, 1)
+         d = new(ptr, F, 1, S)
          finalizer(_Ring_finalizer, d)
          if cached
             N_FFieldID[F, S] = d

src/number/n_transExt.jl

@@ -43,6 +43,10 @@ function characteristic(R::N_FField)
    return ZZ(libSingular.n_GetChar(R.ptr))
 end
 
+function symbols(R::N_FField)
+   return R.S
+end
+
 function deepcopy_internal(a::n_transExt, dict::IdDict)
    return parent(a)(libSingular.n_Copy(a.ptr, parent(a).ptr))
 end
@@ -101,9 +105,9 @@ Return `true` if $n$ is a unit in the field, i.e. nonzero.
 """
 isunit(n::n_transExt) = !iszero(n)
 
-function _tExt_to_poly(R, cached)
+function _tExt_to_poly(R::N_FField, cached)
    n = transcendence_degree(R)
-   P, = PolynomialRing(base_ring(R), ["a$i" for i in 1:n], cached = cached)
+   P, = PolynomialRing(base_ring(R), map(string, symbols(R)), cached = cached)
    return P
 end
 
@@ -151,21 +155,15 @@ function show(io::IO, F::N_FField)
    print(io, "Function Field over ", base_ring(F), " with transcendence basis ", transcendence_basis(F))
 end
 
-function AbstractAlgebra.expressify(n::n_transExt; context = nothing)::Any
-   # TODO this easy method might not be the best
-   libSingular.StringSetS("")
-   libSingular.n_Write(n.ptr, parent(n).ptr, false)
-   s = libSingular.StringEndS()
-   e = Meta.parse(s)
-   if !isa(e, Expr)
-      return e
-   elseif e.head == :incomplete
-      return s
-   elseif e.head == :call && length(e.args) == 3 && e.args[1] == :/
-      e.args[1] = ://
-      return e
+function AbstractAlgebra.expressify(a::n_transExt; context = nothing)::Any
+   n = numerator(a)
+   n = AbstractAlgebra.expressify(n_transExt_to_spoly(n), context = context)
+   d = denominator(a)
+   if isone(d)
+      return n
    else
-      return e
+      d = AbstractAlgebra.expressify(n_transExt_to_spoly(d), context = context)
+      return Expr(:call, ://, n, d)
    end
 end
 

test/number/n_transExt-test.jl

@@ -35,6 +35,12 @@ end
 
    @test sprint(show, "text/plain", q) == "(a*c + b)//c*x^2"
    @test string(q) == "(a*c + b)//c*x^2"
+
+   @test sprint(show, "text/plain", R(3)) == "3"
+   @test string(R(3)) == "3"
+
+   @test sprint(show, "text/plain", R(big(3)^80)) == string(big(3)^80)
+   @test string(R(big(3)^80)) == string(big(3)^80)
 end
 
 @testset "n_transExt.manipulation" begin