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Add auto-distribution #52

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4 changes: 4 additions & 0 deletions src/Symbolics/Expression.fs
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Original file line number Diff line number Diff line change
Expand Up @@ -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
Expand All @@ -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
Expand Down
2 changes: 1 addition & 1 deletion src/SymbolicsUnitTests/Operators/Exponential.fs
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Expand Up @@ -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"
Expand Down
13 changes: 7 additions & 6 deletions src/SymbolicsUnitTests/Tests.fs
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Expand Up @@ -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"
Expand Down Expand Up @@ -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)"]
Expand Down Expand Up @@ -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" {
Expand Down Expand Up @@ -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"
Expand Down