# How to punctuate multiline equations?

This might be off topic, yet I wouldn't know where else to ask. I want to keep up with the good habit of punctuating displayed equations. For example I know the comma (,) is compulsory in

Here, we can reduce $$f$$ to a more simple form
$f(t) = \exp{-t_c/t},$
where $$t_c$$ is called the damping constant.


Yet how should I treat multiline equations? Take a look at this

The function $$g$$ is simply the derivative of $$f$$, so
\begin{align*}
g(t) &= \deriv{f(t)}{t}\\
&= \frac{t_c}{t^2}\exp{-t_c/t},
\end{align*}
so $$g(t)$$ will be smaller than $$f(t)$$ for large $$t$$.


is this correctly punctuated?

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I think that punctuation in equations is only confusing. Avoid it! –  N.N. Jan 2 '12 at 17:46
Imho, your multi-line equation is correctly punctuated because the second line follows directly from the first. A piece-wise defined function (for example), would warrant commas at the end of each line. –  cmhughes Jan 2 '12 at 17:52
@N.N. Wait til Knuth puts on his boxing gloves. –  Marc van Dongen Jan 2 '12 at 20:09

Mathematics are just symbolic sentences. Punctuate them as you would verbal ones. You can find some resources here. Read your maths aloud. If they sound ungrammatical you need to rewrite them. Your first example would read better as:

If we call t_c the damping constant, we can reduce f to the simple form f(t) = \exp{-t_c/t}.

And the punctuation would automatically make sense.

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Although this may be negligible you might wish to consider removing the horizontal spacing added through proper punctuation within a display equation (by using \rlap). For example, you could use

The function $$g$$ is simply the derivative of $$f$$, so
\begin{align*}
g(t) &= \deriv{f(t)}{t}\\
&= \frac{t_c}{t^2}\exp{-t_c/t}\rlap{,}
\end{align*}
so $$g(t)$$ will be smaller than $$f(t)$$ for large $$t$$.


to make sure that the widest stretch of align* is centered within the text block.

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wow, TeX for the really sensitive. I do use slap etc a lot to fix other stuff, but this haha. Correct is correct I guess ;) –  romeovs Jan 2 '12 at 20:07
Rather than writing \rlap{,} I'd write \,,. I cannot remember where I saw this advice before, but I've been using it ever since and it looks very good. –  Marc van Dongen Jan 2 '12 at 20:11
@romeovs: It is what it is. The align environment makes no distinction between the "math" and "text" components of its contents. –  Werner Jan 2 '12 at 20:18
@MarcvanDongen: Sure, and you could even use \rlap{\,,}, since amsmath redefines \, to be "math and text sensitive", allowing its use in math or text mode; \rlap forces the latter. –  Werner Jan 2 '12 at 20:23
@Werner Thanks for that. –  Marc van Dongen Jan 2 '12 at 20:32