Writing an equation with cases when case description is long

Question

This question seeks advice on what is common or at least acceptable in typing a certain inequality in a research paper.

I have an equality that looks like this: \begin{equation*} f_{a,b,c}(x)\leq \begin{cases} f_{1}(x),& \text{if "condition 1 on the parameters $a,ドル $b,ドル $c$";}\\ f_{2}(x),& \text{if "condition 2 on the parameters $a,ドル $b,ドル $c$";}\\ f_{3}(x),& \text{if "condition 3 on the parameters $a,ドル $b,ドル $c$".} \end{cases} \end{equation*}

The problem is the conditions 1, 2, and 3 are all too wide and cause a "bad box" message in latex. Trying to make these conditions shorter by introducing more parameters is not possible. Think of something irreducible such as $a<b<c<2a$. The expressions $f_{1}$, $f_{2}$, and $f_{3}$ are too wide, and don't have any sort of a common factor that can be used to shorten them.

So, I introduced three cases:

(C1) "condition 1 on the parameters $a$, $b$, $c$";

(C2) "condition 2 on the parameters $a$, $b$, $c$";

(C3) "condition 3 on the parameters $a$, $b$, $c$",

and then wrote \begin{equation*} f_{a,b,c}(x)\leq \begin{cases} f_1(x),& \textbf{(C1)};\\ f_2(x),& \textbf{(C2)};\\ f_3(x),& \textbf{(C3)}. \end{cases} \end{equation*}

Would that be acceptable in writing a paper ? Precisely, can one write the name of a condition rather than the condition itself inside a cases environment ?

• darij grinberg: Probably better to call the conditions something like $C\left(a,b,c\right),\ D\left(a,b,c\right),\ E\left(a,b,c\right),ドル if you ever think of using them with different values of $a,b,c$. But yes, giving names to conditions (or any kinds of statements) is legitimate and common practice.
• Carl-Fredrik Nyberg Brodda: The goal of any writing is communication. If your notation communicates what you want it to (which I think is certainly true here), it is acceptable!
• Ben McKay: This seems like a question for tex.stackexchange.

Answer 1

It is very acceptable. Perhaps instead of "(C1)", write "if (C1) holds". Then it will be even more acceptable. Good luck!

• LSpice: I think that, if (C1) etc. recurs frequently, then this is a good answer; but, if it is an ad hoc device introduced just to write three inequalities at once, then it is not such a good idea.
• GH from MO: @LSpice I agree. I think the rule of thumb is that the writing should be clear and concise (efficient). If something fits in 3 lines instead of 3+3 lines, then 3 lines is the way to go.
• Medo: @LSpice the cases $(C1)$ - $(C3)$ are in fact referred to on other occasions. Would you agree with GH from MO that the last format of the inequality is acceptable ?
• GH from MO: @Medo You worry about this thing too much. As I said, it is very acceptable.

Answer 2

You can also use multi-line conditions via tabular or parbox. Here's an example, but I had to use array instead of tabular, because for some reason MO doesn't know tabular: $$ f_{a,b,c}(x) \le \begin{cases} f_1(x), &\begin{array}[t]{@{}l@{}} \text{if the parameters $a,b,c$ satisfy $a<b<c$}\\ \text{and also $a\ne0$ and $c\ne7,ドル} \\ \end{array}\\ f_2(x) &\begin{array}[t]{@{}l@{}} \text{if the parameters $a,b,c$ satisfy $a>b>c$}\\ \text{and also $a\ne2$ and $b\ne9$.} \\ \end{array}\\ f_3(x) &\begin{array}[t]{@{}l@{}} \text{if the parameters $a,b,c$ satisfy $a>b$ and $c>0$}\\ \text{and also $ab\ne17$ and $b<1728$.} \\ \end{array}\\ \end{cases} $$

Answer 3

Another option is to shorten the expressions $f_1(x)$, etc. instead of the conditions.

\begin{equation*} f_{a,b,c}(x)\leq \begin{cases} f_{1}(x),& \text{if "condition 1 on the parameters $a,ドル $b,ドル $c$";}\\ f_{2}(x),& \text{if "condition 2 on the parameters $a,ドル $b,ドル $c$";}\\ f_{3}(x),& \text{if "condition 3 on the parameters $a,ドル $b,ドル $c$".} \end{cases} \end{equation*} \begin{align*} f_1(x) &=\text{put complete expression here}\\ f_2(x) &=\text{put complete expression here}\\ f_3(x) &=\text{put complete expression here} \end{align*}

Answer 4

Here is my suggestion, especially if the conditions are not referred to by name later.

The following bounds are available and cover all cases:

• If $\ldots$, then $f_{a,b,c}(x)\le f_1(x)$.
• If $\ldots$, then $f_{a,b,c}(x)\le f_2(x)$.
• If $\ldots$, then $f_{a,b,c}(x)\le f_3(x)$.