DragginMath: Drag Sideways/Away for Magenta Mode

Magenta Mode is about rearranging terms.

Many people are surprised to learn that the Commutative Property and Rearranging Terms are not the same thing. For example, a+b+c = a+c+b, but you need more than the Commutative Property to prove it. Look at a DragginMath operator tree to see why: you must first use the Associative Property to bring b and c under the same + operator before you can commute them, then use the Associative Property again to make the parentheses go away. Yes, you really need all of that for a full algebraic proof. If there are any subtractions in an expression, even more algebraic tools are necessary to rearrange the terms.

But people expect to rearrange terms easily, so DragginMath makes that possible in Magenta Mode. The underlying mechanism is the Permutative Process, which is rarely taught but implicitly learned and used by everyone with more than a little experience with algebra. Most people think this is what the Commutative Property means. Does this distinction matter? Of course it does. In DragginMath, you can experience the difference by turning Magenta Mode off in Configuration.

To convert a+b−c into b−c+a, first drag a sideways away from b until a changes color to magenta. Drop a onto − to get b−c+a.

To convert a+b−c into a−c+b, first drag b sideways away from a until b changes color to magenta. Drop b onto − to get a−c+b.

These last two examples used Magenta Mode to drag up/right. You can also use Magenta Mode to drag down/left.

To convert a+b−c into -c+a+b, first drag c sideways away from + until c changes color to magenta. Drop c onto a to get -c+a+b.

To convert a+b−c into a−c+b, first drag c sideways away from + until c changes color to magenta. Drop c onto + to get a−c+b.

These are just small examples: the expressions you rearrange can be much more complicated. The Permutative Process works for additive expressions (those containing + and −) and multiplicative expressions (those containing ∗ and ÷). You can also rearrange chains of exponents and chains of root indexes. If you drag across categories, for example additive and multiplicative operators, the rearrangement will not work and everything goes back as it was.

DragginMath’s current implementation of the Permutative Process does not allow dragging across parentheses. If you need to do this, use the Associative Property to remove the parentheses from your expression, then rearrange its terms. For example, reassociate a−(b+c)−d into a−b−c−d before rearranging b or c with a or d.

The rule is different for exponent chains, where you must drag across parentheses if you use the standard right-associative configuration for exponents.