Auto-distribute -1 into parentheses, -(a + b) = -a - b

Author: diluculo

src/Symbolics/Expression.fs

@@ -298,6 +298,7 @@ module Operators =
             | x -> Product (List.rev x)
 
         /// Multiply a number with an expression (potentially a denormalized product)
+        /// Intentionally distribte -1, e.g. -(a + b) = -a - b
         let rec valueMul (v:Value) x =
             if Value.isZero v then zero else
             match x with
@@ -306,6 +307,9 @@ module Operators =
             | Product [a] -> if Value.isOne v then a else Product [Values.unpack v; a]
             | Product ((Values.Value a)::ax) -> valueMul (Value.product (a,v)) (Product ax)
             | Product ax -> if Value.isOne v then x else Product (Values.unpack v::ax)
+            | Sum ax as x'-> if Value.isOne v then x'
+                             else if Value.isMinusOne v then ax |> List.map (function xi -> valueMul v xi) |> Sum
+                             else Product [Values.unpack v; x']
             | x -> if Value.isOne v then x else Product [Values.unpack v; x]
 
         match x, y with

src/SymbolicsUnitTests/Operators/Exponential.fs

@@ -18,7 +18,7 @@ let tests =
             }
 
             test "Special Values" {
-                exp(x + y - (x + y)) ==> "exp(x + y - (x + y))" // "1"
+                exp(x + y - (x + y)) ==> "1"
 
                 exp(-1Q) ==> "1/e"
                 exp(1Q/2Q*pi*Constant I) ==> "j"

src/SymbolicsUnitTests/Tests.fs

@@ -237,12 +237,13 @@ let tests =
 
         test "Algebraic Expansion" {
 
-            // Auto-simplification does not expand expressions:
-            (a+b)-(a+b) ==> "a + b - (a + b)"
+            // Auto-simplification does not expand expressions, but -1 distributes inside parentheses:
+            (a+b)-(a+b) ==> "0"
             (a+b)-(a+b) |> Algebraic.expand ==> "0"
-            2*(a+b)-(a+b) ==> "a + b"
+            2*(a+b)-(a+b) ==> "-a - b + 2*(a + b)"
             (a+b)-2*(a+b) |> Algebraic.expand ===> "(-1)*a + (-1)*b"
             (a+b)-2*(a+b) |> Algebraic.expand ==> "-a - b"
+            -(a + b) + 2*(a + b) ==> "-a - b + 2*(a + b)"
 
             (a*b)/(b*a) ==> "1"
             (a*b)**2/(b*a) ==> "a*b"
@@ -285,7 +286,7 @@ let tests =
 
         test "Algebaric Operators" {
 
-            negate (x + y**2) ==> "-(x + y^2)"
+            negate (x + y**2) ==> "-x - y^2"
 
             Algebraic.factors (b*cos(x)*ln(d)*x) ==+> ["b"; "x"; "ln(d)"; "cos(x)"]
             Algebraic.factors (b*cos(x)*log10(d)*x) ==+> ["b"; "x"; "log(d)"; "cos(x)"]
@@ -402,7 +403,7 @@ let tests =
 
             // TODO: expected: 0
             Trigonometric.simplify (sin(x) + sin(y) - 2*sin(x/2+y/2)*cos(x/2-y/2))
-                ==> "sin(y) - sin(x - y)/2 - sin(x/2 - y/2 - (x/2 - y/2))/2 - sin(-x/2 + y/2 - (x/2 - y/2))/2 - sin(x/2 + y/2 - (x/2 - y/2))"
+                ==> "-sin(-x + y)/2 - sin(x - y)/2" // "0"
         }
 
         test "Differentiation and Taylor Series" {
@@ -482,7 +483,7 @@ let tests =
             solve x (2+3*x) ==> "-2/3"
 
             // sin(a)+x*cos(b)+c = 0 --> x =
-            solve x (sin(a)+x*cos(b)+c) ==> "-(c + sin(a))/cos(b)"
+            solve x (sin(a)+x*cos(b)+c) ==> "(-c - sin(a))/cos(b)"
 
             // (x^2-1)/(x+1) = 0 --> x =
             solve x ((x**2-1)/(x+1)) ==> "1"