Math Accents

Accents are quite common in mathematical text. For example, in physics one uses one- to four-dot accents to designate the first through fourth time derivatives, respectively. Primes are often used on integration variables. Transforms can be designated by tildes and averages by overlines. While accents are usually applied to a single base character, they can in principle be applied to any mathematical expression. This differs considerably from natural language accents, which generally apply to a single character. Accordingly no attempt to handle math accents using fully composed characters was made in Unicode even though most accented characters for natural language have managed to sneak into Unicode as fully composed characters. Instead for math accents, one needs a special accent object that sizes the accent to fit the base.

To enter math accents in Microsoft Office applications, you can use the approach described in the Unicode linear format paper. Since Unicode combining marks follow the associated base characters, the linear format accent operators do so too. For example for ä, one would type a\ddot followed by an operator or, if no operator is needed, by two spaces. You can also enter one of the math accent structures on the math ribbon and then fill in the base and accent. The linear format approach is significantly faster, but not as easily discovered.

One thing the linear format paper doesn’t discuss (at least in the current version) is what happens to the dots on i and j. With Unicode, the dots vanish when a combining mark follows. Similarly in the linear format, the dots vanish when an accent operator follows an i or a j. This is kind of handy and is simpler than the method in TeX, which requires use of \imath and \jmath for dotless i and j, respectively.

The question then arises as to whether the dots should vanish when the base is part of a mathematical expression. Should one have

Generally it should be the latter. In PowerPoint 2010 and OneNote 2010, the dot is only removed if the base consists of i or j alone. In Word 2010, the dots are removed even when the base has more than one character. We need to fix this, but fortunately you can force either choice. In fact, the tilde expressions above were both created in Word 2010 (although their images appear blurred here).

To force a dot to appear, enter i\dot or j\dot. So the second tilde expression above can be entered as (\i\dot+\j\dot)\tilde. This works in all three applications. If you want the first tilde expression, you can also get it in all three applications by using \imath and \jmath to get dotless i and dotless j, respectively as in TeX.

Math accents are also discussed in Unicode Technical Report #25, Unicode Support for Mathematics.