<p>I’ve worked in a few areas of applied mathematics, and each field has its own conventions. You just need to be internally consistent. Just some comments.</p>

<ul>
<li>As noted in another answer, using ‘ to denote derivatives is  awkward. (I’ve not seen it done since high school physics.)</li>
<li>If you are indexing things, subscripts are pretty much a necessity. Superscripts are generally assumed to be powers (<span class="math-container">$x^2$</span>). If you using superscripts for things like states, you have to be using things that will not be confused with numbers (like uppercase letters denoting states), or the entity being superscripted cannot be taken to a power.</li>
<li>Using functional notation is probably easier if you have a lot of variables used as indices.</li>
<li>You can mark variables by sticking markers like “hats” on top of the variable (<span class="math-container">$\hat{c}$</span>).</li>
<li>I’m guessing here, but if I had a function <span class="math-container">$f$</span> with a parameter <span class="math-container">$\alpha$</span>, and I wanted to fix <span class="math-container">$\alpha=1$</span>, the following might be okay <span class="math-container">$\left. f\right|_{\alpha=1}$</span>. (My preference would be to mark this as a new function, defining it explicitly.)</li>
</ul>

CC BY-SA 4.0
2020-03-07T02:57:11.900Z
2020-03-07T02:57:11.900Z
Brian Romanchuk
<p>This is only partial answer since your question is quite broad but in my work I had similar problems. </p>

<p>When ti comes to optimal values and derivatives I choose to use Leibniz's notation as it does the job quite nicely:</p>

<p>instead of writing this <span class="math-container">$\pi^{'*}$</span>, I would write this <span class="math-container">$\frac{\partial \pi^*}{\partial x}$</span> or if you like it more  <span class="math-container">$\frac{\partial }{\partial x}(\pi^*)$</span>, sure it takes some time to type out but in my humble opinion it looks quite good. I try to use Leibniz's notation any time there are some other superscripts or subscripts (as with multivariate function even derivatives with subscripts can be problematic).</p>

<p>For conditions consider maybe notation borrowed from statistics so instead of <span class="math-container">$p^{*,\alpha =1} $</span> I would use <span class="math-container">$[p^*|\alpha=1]$</span></p>

<p>Regarding those numbered solutions, I was once told by older scientist, during my internship at one research institute, that when  you have one letter subscripts you can just put them without comma but if one of the subscripts has multiple letters always put comma so for example <span class="math-container">$x_{itj}$</span> is fine but when I need to put <span class="math-container">$t-1$</span> I would put it as <span class="math-container">$x_{ij,t-1}$</span> (to be honest I have no idea to this day if there could be some issue with this but so far nobody complained - not even at  conferences/workshops where I was presenting my work, nor any referee - although I dont have that many published work yet as I am very young researcher, so maybe take that as a caveat regarding my suggestions). </p>

CC BY-SA 4.0
2020-03-09T09:26:01.080Z
Thanks a lot for the answer! Just a small clarification question: would you write $[p^* |\alpha=1]$ or $p^* |\alpha=1$. In other words, are the square brackets set intentionally or just in the context of the writing above? I assume that they are intentional as we would have two $=$ signs otherwise.
Karl A
CC BY-SA 4.0
2020-03-09T10:44:25.667Z
@KarlA no they are intentional to make clear the condition applies to p although I must say I like Brian’s answer to this (in his last point) more than my original answer
1muflon1
CC BY-SA 4.0
2020-03-06T20:35:23.853Z
2020-03-06T20:53:25.563Z
2020-03-06T20:53:25.563Z
1muflon1
<p>I want to establish a consistent notation in my work, however, I struggle with the correct notation when more than one condition is present.</p>

<p>First, I am wondering what to put in the superscripts and what in subscripts. </p>

<p>I figured that the following is often in superscripts:</p>

<ul>
<li>denoting that something is optimal, e.g., <span class="math-container">$p^*$</span></li>
<li>describing that something is a special condition, e.g., <span class="math-container">$p^{\alpha=1}$</span></li>
<li>denoting critical values, e.g., <span class="math-container">$b^{crit}$</span></li>
</ul>

<p>I figured that the following is often in subscripts:</p>

<ul>
<li>denoting an individuum, firm, combination, <span class="math-container">$p_i$</span>, <span class="math-container">$\pi_j$</span>, <span class="math-container">$p_{ij}$</span></li>
<li>numbers of different solutions <span class="math-container">$c_1$</span>, <span class="math-container">$c_2$</span></li>
</ul>

<p>Some cases were not very consistent</p>

<ul>
<li>"states" or strategic alternatives are sometimes sub/subscripted, <span class="math-container">$\pi_M$</span> and <span class="math-container">$\pi^M$</span></li>
</ul>

<p>So my first question is: Is there a rule, guideline or best practice for what to put where? </p>

<p>Second, I am wondering how to correctly write combinations of different subscripts or superscripts. </p>

<ul>
<li>As an example, one could take the first derivative of the optimal price. Would that be <span class="math-container">${\pi^*}^{'}$</span>  (<code>{\pi^*}^{'}</code>) or is it better to write <span class="math-container">$\pi^{'*}$</span> (<code>\pi^{'*}</code>) or <span class="math-container">$\pi^{*'}$</span> (<code>\pi^{*'}</code>)?</li>
<li>Similarly, how do we combine for example special conditions and optimal values <span class="math-container">$p^{\alpha=1,*}$</span> or <span class="math-container">$p^{*,\alpha=1}$</span>, <span class="math-container">${p^{\alpha=1}}^{*}$</span> or <span class="math-container">${p^{*}}^{\alpha=1}$</span>?</li>
<li>Where do we place numbered solutions for specific conditions when both are used in subscripts (e.g., <span class="math-container">$c_1$</span> in <span class="math-container">$\pi_M$</span>)? is it  <span class="math-container">$c_{1M}$</span>, <span class="math-container">$c_{M1}$</span>,  <span class="math-container">$c_{M,1}$</span>,  <span class="math-container">$c_{1,M}$</span>?</li>
</ul>

<p>So my second question is: Is there a rule, guideline or best practice of how to combine different subscripts vs. superscripts</p>

CC BY-SA 4.0
2020-03-06T15:08:19.023Z
This question has a good foundation, but as phrased currently it seems very broad, and it is also unlikely to get a definitive answer. Could you please rephrase it in a way that makes it a better fit for the SE format?
Giskard
CC BY-SA 4.0
2020-03-06T15:32:51.710Z
Thanks, I tried my best to be more specific. Any additional hints on how to improve?
Karl A
<microeconomics>
Notation conventions for superscripts and subscripts
Karl A
# Notation conventions for superscripts and subscripts

(Asked by: username_0 on 2020-03-06)

I want to establish a consistent notation in my work, however, I struggle with the correct notation when more than one condition is present.

First, I am wondering what to put in the superscripts and what in subscripts.

I figured that the following is often in superscripts:

* denoting that something is optimal, e.g., $p^\*$
* describing that something is a special condition, e.g., $p^{\alpha=1}$
* denoting critical values, e.g., $b^{crit}$

I figured that the following is often in subscripts:

* denoting an individuum, firm, combination, $p\_i$, $\pi\_j$, $p\_{ij}$
* numbers of different solutions $c\_1$, $c\_2$

Some cases were not very consistent

* "states" or strategic alternatives are sometimes sub/subscripted, $\pi\_M$ and $\pi^M$

So my first question is: Is there a rule, guideline or best practice for what to put where?

Second, I am wondering how to correctly write combinations of different subscripts or superscripts.

* As an example, one could take the first derivative of the optimal price. Would that be ${\pi^\*}^{'}$ (`{\pi^*}^{'}`) or is it better to write $\pi^{'\*}$ (`\pi^{'*}`) or $\pi^{\*'}$ (`\pi^{*'}`)?
* Similarly, how do we combine for example special conditions and optimal values $p^{\alpha=1,\*}$ or $p^{\*,\alpha=1}$, ${p^{\alpha=1}}^{\*}$ or ${p^{\*}}^{\alpha=1}$?
* Where do we place numbered solutions for specific conditions when both are used in subscripts (e.g., $c\_1$ in $\pi\_M$)? is it $c\_{1M}$, $c\_{M1}$, $c\_{M,1}$, $c\_{1,M}$?

So my second question is: Is there a rule, guideline or best practice of how to combine different subscripts vs. superscripts

**Tags:** microeconomics
> **Comments:**
> **username_1**: This question has a good foundation, but as phrased currently it seems very broad, and it is also unlikely to get a definitive answer. Could you please rephrase it in a way that makes it a better fit for the SE format?  
> **username_0**: Thanks, I tried my best to be more specific. Any additional hints on how to improve?  

---

## 2 answers

### Answer by username_3 on 2020-03-06. Score: 4 | Accepted answer

This is only partial answer since your question is quite broad but in my work I had similar problems.

When ti comes to optimal values and derivatives I choose to use Leibniz's notation as it does the job quite nicely:

instead of writing this $\pi^{'\*}$, I would write this $\frac{\partial \pi^\*}{\partial x}$ or if you like it more $\frac{\partial }{\partial x}(\pi^\*)$, sure it takes some time to type out but in my humble opinion it looks quite good. I try to use Leibniz's notation any time there are some other superscripts or subscripts (as with multivariate function even derivatives with subscripts can be problematic).

For conditions consider maybe notation borrowed from statistics so instead of $p^{\*,\alpha =1} $ I would use $[p^\*|\alpha=1]$

Regarding those numbered solutions, I was once told by older scientist, during my internship at one research institute, that when you have one letter subscripts you can just put them without comma but if one of the subscripts has multiple letters always put comma so for example $x\_{itj}$ is fine but when I need to put $t-1$ I would put it as $x\_{ij,t-1}$ (to be honest I have no idea to this day if there could be some issue with this but so far nobody complained - not even at conferences/workshops where I was presenting my work, nor any referee - although I dont have that many published work yet as I am very young researcher, so maybe take that as a caveat regarding my suggestions).

> **Comments:**
> **username_0**: Thanks a lot for the answer! Just a small clarification question: would you write $[p^* |\alpha=1]$ or $p^* |\alpha=1$. In other words, are the square brackets set intentionally or just in the context of the writing above? I assume that they are intentional as we would have two $=$ signs otherwise.  
> **username_3**: @KarlA no they are intentional to make clear the condition applies to p although I must say I like Brian’s answer to this (in his last point) more than my original answer  

---

### Answer by username_2 on 2020-03-07. Score: 3

I’ve worked in a few areas of applied mathematics, and each field has its own conventions. You just need to be internally consistent. Just some comments.

* As noted in another answer, using ‘ to denote derivatives is awkward. (I’ve not seen it done since high school physics.)
* If you are indexing things, subscripts are pretty much a necessity. Superscripts are generally assumed to be powers ($x^2$). If you using superscripts for things like states, you have to be using things that will not be confused with numbers (like uppercase letters denoting states), or the entity being superscripted cannot be taken to a power.
* Using functional notation is probably easier if you have a lot of variables used as indices.
* You can mark variables by sticking markers like “hats” on top of the variable ($\hat{c}$).
* I’m guessing here, but if I had a function $f$ with a parameter $\alpha$, and I wanted to fix $\alpha=1$, the following might be okay $\left. f\right|\_{\alpha=1}$. (My preference would be to mark this as a new function, defining it explicitly.)


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