From df474ee9b5e64456c95acdd46e42a5f77c0cd6ca Mon Sep 17 00:00:00 2001
From: Alexander Demin <asdemin_2@edu.hse.ru>
Date: Thu, 7 Dec 2023 01:03:48 +0300
Subject: [PATCH 1/2] Add vars for rational functions of multivariate
 polynomials

---
 src/Fraction.jl               | 15 +++++++++++++++
 test/generic/Fraction-test.jl | 12 ++++++++++++
 2 files changed, 27 insertions(+)

diff --git a/src/Fraction.jl b/src/Fraction.jl
index e39f7372a8..293824cbdf 100644
--- a/src/Fraction.jl
+++ b/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
diff --git a/test/generic/Fraction-test.jl b/test/generic/Fraction-test.jl
index c6eba68bb3..813531dbd4 100644
--- a/test/generic/Fraction-test.jl
+++ b/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")

From 3dce787cddba30a5c99cd4e69eb4f49dcf9b0187 Mon Sep 17 00:00:00 2001
From: Alexander Demin <60229118+sumiya11@users.noreply.github.com>
Date: Thu, 7 Dec 2023 01:47:02 +0300
Subject: [PATCH 2/2] Update src/Fraction.jl

Co-authored-by: Max Horn <max@quendi.de>
---
 src/Fraction.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/Fraction.jl b/src/Fraction.jl
index 293824cbdf..9a3a116172 100644
--- a/src/Fraction.jl
+++ b/src/Fraction.jl
@@ -51,7 +51,7 @@ function vars(a::FracElem{S}) where {S <: MPolyRingElem{<: RingElement}}
    n_vars = vars(n)
    d_vars = vars(d)
    nd_vars = union!(n_vars, d_vars)
-   return(nd_vars)
+   return nd_vars
 end
 
 ###############################################################################