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I have an expression which can be simplified to a simpler one under the condition that two of its components are equal, and I'd like to put this fact into a single line equation.

Is there a generally-accepted notation for denoting that an equality is subject to a condition?

Some ways I can think of, but am not sure if they are universally understood (or possibly universally understood to mean something different...):

$a = \left. \frac{(c - d)e}{c^2 - d^2}= \frac{d}{c + d}\right|_{d=e} $

$a = \frac{(c - d)e}{c^2 - d^2}= \left(\frac{d}{c + d}\right)_{d=e} $

(Yes, I know that the middle term can already be simplified if d and e are not equal, but I don't care about that case — if I did, I could just use a curly brace conditional and list both options. I'm trying to keep it very short here.)

I think the method that would cause least confusion would be to put the "d=e" text below the equal sign, but I don't seem to be able to find a way to do that in LaTeX.

Zak
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    An acceptable and frequent use of that bar notation is $$\left. \frac{(c - d)e}{c^2 - d^2}\right|_{d=e}= \frac{d}{c + d},.$$ What you are trying to do I find confusing. Is paper that expensive that you have to find the shortest possible way to express a condition you may as well mention with a few words? – Kurt G. Sep 01 '23 at 15:24
  • Unknown to me if there is a universally accepted syntax. Your first one, re $~\cdots ~|_{\text{condition}}~$ is what I am accustomed to, with the alternative syntax of $~\cdots ~: ~\text{condition}.$ That is, you substitute the colon, $~:~$ for the vertical bar, $~|$ – user2661923 Sep 01 '23 at 15:25
  • Regarding how to put "$d=e$" below the equal sign: see \overset and \underset. But I agree with Kurt G that writing things out in words is much much better than using compact but potentially ambiguous notation. – angryavian Sep 01 '23 at 15:46
  • Paper is mostly electronic these days, but some conference abstracts have strict limits on length. Also, if I can say something, definitely in one line, why wouldn't I? Prose can be easier to misunderstand, or sometimes my phrasing has a tendency to be easy to misread, or devolves into chain sentences, and then I have to iterate, or add explanations, and ... plain maths makes that easier -- if the notation allows it. – Zak Sep 01 '23 at 17:50
  • @Zak There is some discussion on the topic of prose vs. symbols here. Regarding papers: abstracts usually do not contain math notation. If you meant limits on the conference paper length, I will just add that clarity helps greatly in getting your paper through the review process. I agree that in some cases math notation is less ambiguous and more concise than plain words, but in my opinion the example in your question above is not such a case. – angryavian Sep 08 '23 at 05:38

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