monomial/lex_lt: sort by abs degree, positive first

Author: Alexey Stukalov

src/ordering.jl

@@ -124,15 +124,20 @@ end
 function monomial_lt(degs1, degs2)
     d1 = sum(last, degs1, init=0)
     d2 = sum(last, degs2, init=0)
-    d1 != d2 ? d1 < d2 : lexlt(degs1, degs2)
+    d1 != d2 ?
+        # lower absolute degree first, or if equal, positive degree first
+        (abs(d1) < abs(d2) || abs(d1) == abs(d2) && d1 > d2) :
+        lexlt(degs1, degs2)
 end
 
 function lexlt(degs1, degs2)
-    for (a, b) in zip(degs1, degs2)
-        if a[1] == b[1] && a[2] != b[2]
-            return a[2] > b[2] # higher degree first
-        elseif a[1] != b[1]
-            return a[1] < b[1] # lexicographic order for the base
+    for ((a_base, a_deg), (b_base, b_deg)) in zip(degs1, degs2)
+        if a_base == b_base && a_deg != b_deg
+            # same base, higher absolute degree first, positive degree first
+            return abs(a_deg) > abs(b_deg) || abs(a_deg) == abs(b_deg) && a_deg > b_deg
+        elseif a_base != b_base
+            # lexicographic order for the base
+            return a_base < b_base
         end
     end
     return false # they are equal

test/basics.jl

@@ -222,7 +222,11 @@ end
     @test repr(a + b3 + b1 + d2 + c) == "a + b[1] + b[3] + c + d[2]"
     @test repr(expand((c + b3 - d1)^3)) == "b[3]^3 + 3(b[3]^2)*c - 3(b[3]^2)*d[1] + 3b[3]*(c^2) - 6b[3]*c*d[1] + 3b[3]*(d[1]^2) + c^3 - 3(c^2)*d[1] + 3c*(d[1]^2) - (d[1]^3)"
     # test negative powers sorting
-    @test repr((b3^2)^(-2) + a^(-3) + (c*d1)^(-2)) == "1 / (b[3]^4) + 1 / ((c^2)*(d[1]^2)) + 1 / (a^3)"
+    @test repr((b3^2)^(-2) + a^(-3) + (c*d1)^(-2)) == "1 / (a^3) + 1 / (b[3]^4) + 1 / ((c^2)*(d[1]^2))"
+
+    # test that the "x^2 + y^-1 + sin(a)^3.5 + 2t + 1//1" expression from Symbolics.jl/build_targets.jl is properly sorted
+    @syms x1 y1 a1 t1
+    @test repr(x1^2 + y1^-1 + sin(a1)^3.5 + 2t1 + 1//1) == "(1//1) + 2t1 + 1 / y1 + x1^2 + sin(a1)^3.5"
 end
 
 @testset "inspect" begin