Invisible Operators

MathML uses an "invisible multiplication" character to explicitly denote when two variables or expressions are being multiplied. There is also an "invisible apply function" character that differentiates between multiplication and functions. For example, ab might mean "a times b", or the two-letter variable "ab". Similarly a(b+c) might mean "a times b + c" or it might mean, "apply a function a to the argument b+c". By inserting the proper invisible character, either multiplication or apply function, the semantics become clear.

The option "Recognize Common Functions" on the General Editing Preferences dialog dictates how invisible multiplication and apply function are handled by default. Selecting this option changes whether the MathFlow Editor favors using invisible multiplication or apply function characters.

If the "Recognize Common Functions" option is not selected, the MathFlow Editor favors using multiplication characters and its automatic tokenizing behavior helps remind you to code equations properly. If you just type "a" followed by "b", it will group them both into one token and switch the typeface to upright. This is a visual cue that what you entered was the two-letter variable "ab". To enter "a times b", you need to put an invisible times between them.

When you hit the spacebar following an identifier, the MathFlow Editor will insert an InvisibleTimes character. By doing so, the "a" and the "b" will each go into identifier tokens of their own, with the InvisibleTimes operator token in between. The "a" and the "b" will remain in the customary italic typeface, giving you a visual cue that you have encoded a multiplication.

If you hit the space bar after anything other than an identifier, the MathFlow Editor will insert a space character as usual. You can customize the behavior of the spacebar from the General Editing Preferences dialog if you don't like the default. You can also access the invisible characters palette on the "Standard" toolbar, and explicitly insert InvisibleTimes characters without using the space bar.

If the "Recognize Common Functions" option is selected, the editor favors using apply function characters over multiplication. Because this option causes the editor to look for common functions, the editor will automatically insert an apply function character when it finds a function it recognizes.