Prevent creation of fields with one element (#2233)

Author: fingolfin

src/Fraction.jl

@@ -821,6 +821,7 @@ that it will always be returned by a call to the constructor when the same
 base ring $R$ is supplied.
 """
 function fraction_field(R::Ring; cached::Bool=true)
+   @req !is_trivial(R) "Base ring must not be the zero ring."
    return Generic.fraction_field(R; cached=cached)
 end
 

src/ResidueField.jl

@@ -466,7 +466,9 @@ residue ring parent object is cached and returned for any subsequent calls
 to the constructor with the same base ring $R$ and element $a$.
 """
 function residue_field(R::Ring, a::RingElement; cached::Bool = true)
+   @req !is_trivial(R) "Base ring must not be the zero ring."
    iszero(a) && throw(DivideError())
+   @req !is_unit(a) "Cannot create a field with one element"
    T = elem_type(R)
    S = EuclideanRingResidueField{T}(R(a), cached)
    return S, Generic.EuclideanRingResidueMap(R, S)

test/generic/Fraction-test.jl

@@ -51,6 +51,11 @@
    @test !(a in [b])
    @test a in keys(Dict(a => 1))
    @test !(b in keys(Dict(a => 1)))
+
+   # trivial rings can not be fields
+   R = residue_ring(ZZ, 1)[1]
+   @test is_trivial(R)
+   @test_throws ArgumentError fraction_field(R)
 end
 
 @testset "Generic.FracFieldElem.printing" begin

test/generic/ResidueField-test.jl

@@ -67,6 +67,12 @@
 
    @test x in keys(Dict(x => 1))
    @test !(y in keys(Dict(x => 1)))
+
+   # trivial rings can not be fields
+   @test_throws ArgumentError residue_field(ZZ, 1)
+   R = residue_ring(ZZ, 1)[1]
+   @test is_trivial(R)
+   @test_throws ArgumentError residue_field(R, R(2))
 end
 
 @testset "EuclideanRingResidueFieldElem.printing" begin