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How best to present long equations in two-column papers?

I've tried splitting them in two or more lines along operators, but that still looks a bit weird to me, especially when parentheses have to be carried along across the lines. Also, I've considered stretching them across both columns, but that seems only an acceptable solution if the equation is of outstanding importance, e.g. the final result and not some middle section of a proof.

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    This might fit better in Tex.SE. See e.g., tex.stackexchange.com/questions/117051/… – Ran G. Nov 13 '14 at 19:57
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    This might also depend on where you publish. For instance, wide equations (that cross over the two columns, with separating rulers) are very common in Physical Review journals. – Ran G. Nov 13 '14 at 19:59
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    What does the style guide for your target publication say? What did the editor there say? What have other papers in your target journal done? – 410 gone Nov 13 '14 at 20:25
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    To expand on what @RanG. said: revtex (Physical Review's latex class) provides explicit support for this and generates pretty good looking output. – dmckee --- ex-moderator kitten Nov 13 '14 at 20:26
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    It is, however, only reasonable for TeX - LaTeX if the OP is using or contemplating using a TeX based stack to prepare the paper. Of course, I'd recommend doing so. – dmckee --- ex-moderator kitten Nov 13 '14 at 20:27
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When I have had occasion to deal with obnoxiously large equations, I find that there are four strategies that do well for me. In order of readability, they are:

  1. Shrink the font: if you are allowed (any many venues do allow this), you can usually shrink the font on an equation a few points without affecting readability.
  2. Map separable terms of the equation to new variables, which can be given their own independent definition lines. This can really help readability in a complex equation as well.

--- The line of desperation ---

  1. Break the equation across two lines: this works up to about 1.6 lines worth of smaller-font equation. When combined with adjusting font size, you can often adjust where the break occurs to make it look reasonable.
  2. Move the equations to a full-width figure, where you can play all of the same games.
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    For extremely long equations (e.g. I have one in my thesis that occupied a whole page) one might also consider to place the equation in a rotated (horizontal) page. – Miguel Dec 22 '14 at 14:13
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    When I see Option 1 being used, I'm en train de getting my knife and finding your address /sarcasm Now seriously: That is the worst thing ever, the equations get completely unreadable in small print and the result never looks good. – yo' Dec 23 '14 at 11:36
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    @yo's assessment is a bit harsh, but I do agree... shrinking font size is often a pretty poor choice. Multi-line is much preferred. – eykanal Dec 23 '14 at 14:21
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I suggest you check chapter 3.3.4 in the book Mathematics into Type published by the American Mathematical Society (AMS).

The book sets up specific rules for breaking the equations and also how to align these after breaking. The rules are too complex to be reproduced or duplicated well here so anyone interested should download the book using the link above for reference.

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What a programmer would do is break the formula into sub-functions along boundaries that reflect the way the formula itself breaks up into individual concepts, define those, and then define the top-level formula in terms of those. I can't see any reason that wouldn't work here, at least to some degree...

(This is like @jakebeal's suggestion to define new variables, but taking it one step farther to point out that when several of those variables are of the same form, you can define a parameterized function rather than having to spell out every one.)

In my experience, what a pure mathematician would do is the same thing, but they'd call their functions operators and assign them symbols rather than names. :-)

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    "Operators" are only a very specific kind of mathematical function. When working routinely with things like "functions that take functions and return other functions", one feels the need to call them in different ways, to be more expressive and keep their sanity. :) – Federico Poloni Nov 14 '14 at 10:12

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