proper singular_ring(::AnticNumberField) (#563)

* proper singular_ring(::AnticNumberField)

* bump singular version

Project.toml

@@ -27,5 +27,5 @@ Nemo = "0.25.0"
 Polymake = "0.5.6"
 RandomExtensions = "0.4.3"
 Requires = "1.0"
-Singular = "0.5.5"
+Singular = "0.5.7"
 julia = "1.3"

experimental/ModStd/ModStdNF.jl

@@ -11,10 +11,6 @@ function __init__()
 end
 
 
-function Oscar.singular_ring(F::AnticNumberField)
-  return Singular.CoefficientRing(F)
-end
-
 function stdhilb(I::Singular.sideal, h::Array{Int32, 1}; complete_reduction::Bool=false)
   R = base_ring(I)
 #  @show "stdhilb", I

src/Rings/mpoly.jl

@@ -598,6 +598,22 @@ singular_ring(F::Nemo.GaloisField) = Singular.Fp(Int(characteristic(F)))
 singular_ring(F::Nemo.NmodRing) = Singular.Fp(Int(characteristic(F)))
 singular_ring(R::Singular.PolyRing; keep_ordering::Bool = true) = R
 
+# Note: Several Singular functions crash if they get the catch-all
+# Singular.CoefficientRing(F) instead of the native Singular equivalent as
+# conversions to/from factory are not implemented.
+function singular_ring(K::AnticNumberField)
+  minpoly = defining_polynomial(K)
+  Qa = parent(minpoly)
+  a = gen(Qa)
+  SQa, (Sa,) = Singular.FunctionField(Singular.QQ, map(String, symbols(Qa)))
+  Sminpoly = SQa(coeff(minpoly, 0))
+  for i in 1:degree(minpoly)
+    Sminpoly += SQa(coeff(minpoly, i))*Sa^i
+  end
+  SK, _ = Singular.AlgebraicExtensionField(SQa, Sminpoly)
+  return SK
+end
+
 function singular_ring(Rx::MPolyRing{T}; keep_ordering::Bool = true) where {T <: RingElem}
   if keep_ordering
     return Singular.PolynomialRing(singular_ring(base_ring(Rx)),