Fix comparison of terms with non-comparable coefficients

Author: blegat

src/operators.jl

@@ -3,13 +3,24 @@
 Base.@pure Base.isless(v1::AbstractVariable, v2::AbstractVariable) = name(v1) > name(v2)
 Base.isless(m1::AbstractTermLike, m2::AbstractTermLike) = isless(promote(m1, m2)...)
 
+# Implement this to make coefficients be compared with terms.
+function isless_coefficient(a::Real, b::Real)
+    return a < b
+end
+function isless_coefficient(a::Number, b::Number)
+    return abs(a) < abs(b)
+end
+# By default, coefficients are not comparable so `a` is not strictly
+# less than `b`, they are considered sort of equal.
+isless_coefficient(a, b) = false
+
 function Base.isless(t1::AbstractTerm, t2::AbstractTerm)
     if monomial(t1) < monomial(t2)
-        true
+        return true
     elseif monomial(t1) == monomial(t2)
-        abs(coefficient(t1)) < abs(coefficient(t2))
+        return isless_coefficient(coefficient(t1), coefficient(t2))
     else
-        false
+        return false
     end
 end
 

test/term.jl

@@ -1,3 +1,7 @@
+struct CoefNotComparable
+end
+Base.iszero(::CoefNotComparable) = false
+
 @testset "Term" begin
     Mod.@polyvar x
     @test convert(Any, 1x) == 1x
@@ -49,7 +53,6 @@
     @test_throws InexactError push!([1], 2x)
     @test_throws ErrorException push!([x^2], 2x)
 
-
     @testset "Effective variables" begin
         T = variable_union_type(x)
         @test x isa T
@@ -61,4 +64,35 @@
         @test T[y] == @inferred effective_variables(x^0 * y)
         @test T[y] == @inferred effective_variables(y * x^0)
     end
+
+    @testset "Compare terms" begin
+        t1 = 1 * x
+        t2 = 2 * x
+        @test t1 < t2
+        @test t1 <= t2
+        @test !(t1 > t2)
+        @test !(t1 >= t2)
+
+        t1 = (1 + 1im) * x
+        t2 = (2 + 2im) * x
+        @test t1 < t2
+        @test t1 <= t2
+        @test !(t1 > t2)
+        @test !(t1 >= t2)
+
+        a = CoefNotComparable()
+        b = CoefNotComparable()
+        t1 = a * x
+        t2 = b * y
+        @test t1 > t2
+        @test t1 >= t2
+        @test !(t1 < t2)
+        @test !(t1 <= t2)
+        t1 = a * x
+        t2 = b * x
+        @test !(t1 > t2)
+        @test t1 >= t2
+        @test !(t1 < t2)
+        @test t1 <= t2
+    end
 end