Add vars for rational functions of multivariate polynomials (#1520)

src/Fraction.jl

@@ -39,6 +39,21 @@ function check_parent(a::FracElem, b::FracElem, throw::Bool = true)
    return !fl
 end
 
+@doc raw"""
+    vars(a::FracElem{S}) where {S <: MPolyRingElem{<: RingElement}}
+
+Return the variables actually occurring in $a$. Returned variables are elements
+of `base_ring(a)`. The variables from the numerator go first.
+"""
+function vars(a::FracElem{S}) where {S <: MPolyRingElem{<: RingElement}}
+   n = numerator(a, false)
+   d = denominator(a, false)
+   n_vars = vars(n)
+   d_vars = vars(d)
+   nd_vars = union!(n_vars, d_vars)
+   return nd_vars
+end
+
 ###############################################################################
 #
 #   Constructors

test/generic/Fraction-test.jl

@@ -61,6 +61,18 @@ end
    @test !occursin("\n", sprint(show, fraction_field(S)))
 end
 
+@testset "Generic.FracFieldElem.vars" begin
+   S, (x,y,z) = polynomial_ring(QQ, ["x", "y", "z"])
+   K = fraction_field(S)
+
+   a = K(zero(S), one(S))
+   res = vars(a)
+   @test isempty(res) && eltype(res) == elem_type(S)
+
+   @test parent(first(vars(1 // z))) == base_ring(a)
+   @test vars((2y) // 3one(S)) == [y]
+   @test vars((y + z) // (x + y)) == [y, z, x]
+end
 
 @testset "Generic.FracFieldElem.rand" begin
    S, x = polynomial_ring(ZZ, "x")