diff --git a/src/MultivariatePolynomials.jl b/src/MultivariatePolynomials.jl
index 9de4709e..740e3f3d 100644
--- a/src/MultivariatePolynomials.jl
+++ b/src/MultivariatePolynomials.jl
@@ -58,6 +58,7 @@ Abstract type for a polynomial of coefficient type `T`, i.e. a sum of `AbstractT
 abstract type AbstractPolynomial{T} <: AbstractPolynomialLike{T} end
 
 const _APL{T} = AbstractPolynomialLike{T}
+const _Constant = Union{Number,MA.AbstractMutable,AbstractArray}
 
 include("zip.jl")
 include("lazy_iterators.jl")
diff --git a/src/comparison.jl b/src/comparison.jl
index 504d6da7..6ba25e2f 100644
--- a/src/comparison.jl
+++ b/src/comparison.jl
@@ -10,14 +10,8 @@ function Base.isone(p::AbstractPolynomial)
     return isone(nterms(p)) && isone(first(terms(p)))
 end
 
-# See https://github.com/blegat/MultivariatePolynomials.jl/issues/22
-# avoids the call to be transfered to left_constant_eq
-Base.:(==)(α::Nothing, x::_APL) = false
-Base.:(==)(x::_APL, α::Nothing) = false
 Base.:(==)(α::Dict, x::_APL) = false
 Base.:(==)(x::_APL, α::Dict) = false
-Base.:(==)(α::Nothing, x::RationalPoly) = false
-Base.:(==)(x::RationalPoly, α::Nothing) = false
 Base.:(==)(α::Dict, x::RationalPoly) = false
 Base.:(==)(x::RationalPoly, α::Dict) = false
 
@@ -133,16 +127,16 @@ Base.:(==)(p::RationalPoly, q::RationalPoly) = p.num * q.den == q.num * p.den
 # Solve ambiguity with (::PolyType, ::Any)
 Base.:(==)(p::_APL, q::RationalPoly) = p * q.den == q.num
 Base.:(==)(q::RationalPoly, p::_APL) = p == q
-Base.:(==)(α, q::RationalPoly) = α * q.den == q.num
-Base.:(==)(q::RationalPoly, α) = α == q
+Base.:(==)(α::_Constant, q::RationalPoly) = α * q.den == q.num
+Base.:(==)(q::RationalPoly, α::_Constant) = α == q
 function Base.isequal(p::RationalPoly, q::RationalPoly)
     return isequal(p.num * q.den, q.num * p.den)
 end
 # Solve ambiguity with (::PolyType, ::Any)
 Base.isequal(p::_APL, q::RationalPoly) = isequal(p * q.den, q.num)
 Base.isequal(q::RationalPoly, p::_APL) = isequal(p, q)
-Base.isequal(α, q::RationalPoly) = isequal(α * q.den, q.num)
-Base.isequal(q::RationalPoly, α) = isequal(α, q)
+Base.isequal(α::_Constant, q::RationalPoly) = isequal(α * q.den, q.num)
+Base.isequal(q::RationalPoly, α::_Constant) = isequal(α, q)
 
 # α could be a JuMP affine expression
 isapproxzero(α; ztol::Real = 0.0) = false
diff --git a/src/operators.jl b/src/operators.jl
index fa8f55cc..fcbf909d 100644
--- a/src/operators.jl
+++ b/src/operators.jl
@@ -30,18 +30,20 @@ for (op, fun) in [
     (:+, :right_constant_plus),
     (:-, :right_constant_minus),
     (:*, :right_constant_mult),
-    (:(==), :right_constant_eq),
 ]
     @eval Base.$op(p::_APL, α) = $fun(p, α)
 end
+Base.:(==)(p::_APL, α::_Constant) = right_constant_eq(p, α)
+
 for (op, fun) in [
     (:+, :left_constant_plus),
     (:-, :left_constant_minus),
     (:*, :left_constant_mult),
-    (:(==), :left_constant_eq),
 ]
     @eval Base.$op(α, p::_APL) = $fun(α, p)
 end
+Base.:(==)(α::_Constant, p::_APL) = left_constant_eq(α, p)
+
 ## Fix ambiguity between above methods and methods in MA
 Base.:+(::MA.Zero, p::_APL) = MA.copy_if_mutable(p)
 Base.:+(p::_APL, ::MA.Zero) = MA.copy_if_mutable(p)
diff --git a/test/commutative/comparison.jl b/test/commutative/comparison.jl
index 7d6d9aa3..27d1443b 100644
--- a/test/commutative/comparison.jl
+++ b/test/commutative/comparison.jl
@@ -109,16 +109,27 @@
         @testset "RationalPoly equality" begin
             Mod.@polyvar x y
             @test (x^2 - x - 6) / (x + 2) != x + 3
+            @test !isequal((x^2 - x - 6) / (x + 2), x + 3)
             @test x - 3 == (x^2 - x - 6) / (x + 2)
+            @test isequal(x - 3, (x^2 - x - 6) / (x + 2))
             @test (x^2 - x - 6) / (x - 3) == x + 2
+            @test isequal((x^2 - x - 6) / (x - 3), x + 2)
             @test 3 != 4x / 2x
+            @test !isequal(3, 4x / 2x)
             @test 4x / 2x == 2
+            @test isequal(4x / 2x, 2)
             @test 3 != 4x / 2x
+            @test !isequal(3, 4x / 2x)
             @test 1 - 1 / x == (x - 1) / x
+            @test isequal(1 - 1 / x, (x - 1) / x)
             @test 1 - 1 / x != (1 - x) / x
+            @test !isequal(1 - 1 / x, (1 - x) / x)
             @test x + x / x == 1 + x^2 / x
+            @test isequal(x + x / x, 1 + x^2 / x)
             @test x - x / x == -(1 - x^2 / x)
+            @test isequal(x - x / x, -(1 - x^2 / x))
             @test (1 + x) / x - 1 == 1 / x
+            @test isequal((1 + x) / x - 1, 1 / x)
             @test isapprox((1 + 1e-8)x, (x * y) / y, rtol = 1e-7)
             @test isapproxzero(((1 + 1e-8)x - x) / y, ztol = 1e-7)
             @test !isapproxzero(((1 + 1e-8)x - y) / y, ztol = 1e-9)