The Sign Command

The Sign command lets you manipulate and move minus signs in expressions. Minus signs are manipulated by other commands, for example, the Equivalence command, but the sign command gives more flexibility in controlling where the signs end up making it useful for moving signs around in more complicated expressions. The keystroke for the Sign command is the i key.

It wouldn't be practical to list every possible way to move a minus sign in a long expression. So we introduce a special object, the MinusOne object, that can be moved around and simplified to get the signs where you want them. Unlike the normal minus sign, the MinusOne object doesn't automatically get combined with other objects making it easier to put the signs were you want them.

The normal usage of the sign command involves initially using this command to convert signs to MinusOne objects, moving those objects around (and possibly simplifying) and finally using the sign command again to convert the MinusOne objects back into normal subtractions and minus signs.

A few examples will make this idea clear. Suppose you are starting with the expression

and want to change this to

One way to do this would be to use the Sign command, highlight each MinusOne object an use the Factor command, simplify the whole expression, then use the Sign command again to put the expression in its final form

Once you have changed the expression to contain MinusOne objects, you can move these objects around using other commands (like Expand, Factor, Simplify and so on) just like you would for any other term in an expression.

Note that the MinusOne object simplifies in the same way that an ordinary (-1) would. MinusOne times itself is 1 and powers of MinusOne simplify to either MinusOne or 1 depending on whether the power is an odd or even integer.