Skip to content

Commutative Swap

The Commutative Property of numbers says that we can re-order two addition or multiplication terms so that one occurs before the other in the expression, without changing the value of the expression.

The formulation of this property is the same for addition and multiplication:

  • Addition a + b = b + a
  • Multiplication a * b = b * a

The commutative property is used for re-arranging the order of parts of an expression, and is as such very important for working with mathematical expressions.

Transformations

Given a common parent node, this rule switches the order of the children of that node. It can only be applied to addition or multiplication nodes.

Addition

a + b = b + a

        +                  +
       / \                / \
      /   \     ->       /   \
     /     \            /     \
    a       b          b       a

Multiplication

a * b = b * a

        *                  *
       / \                / \
      /   \     ->       /   \
     /     \            /     \
    a       b          b       a

Examples

Info

All the examples shown below are drawn from the mathy test suite that verifies the expected input/output combinations for rule transformations.

Input Output Valid
2x + 1y^3 + 7j + -2q + 93m + 6x 2x + 1y^3 + 7j + -2q + 6x + 93m
2x + 1y^3 + 7j + -2q + 6x + 93m 2x + 1y^3 + 7j + 6x + -2q + 93m
2x + 1y^3 + 7j + 6x + -2q + 93m 2x + 1y^3 + 6x + 7j + -2q + 93m
2x + 1y^3 + 6x + 7j + -2q + 93m 2x + 6x + 1y^3 + 7j + -2q + 93m
12x * 10y (x * 12) * 10y
2530z + 1m + 3.5x + 2z + 8.9c 2530z + 3.5x + 1m + 2z + 8.9c
(5 + 12) * a a * (5 + 12)
2b^4 * 3x (b^4 * 2) * 3x
4 + 17 17 + 4
4x x * 4
(7 + x) + 2 x + 7 + 2
12x + 10y 10y + 12x
8y^4 --- ---
4x --- ---
4 / 3 --- ---
7 / x --- ---

Last update: December 29, 2019