Is it possible to shorten the use of \left and \right?

So I'm writing a latex document that has the following code in it

\begin{align*}
n! - k &= n! - \sum_{i=1}^{\left\lfloor\frac{n}{r}\right\rfloor}(-1)^{i+1}\binom{n}{r,\dots,n-ir} ((r-1)!)^i(n-ir)!\frac{1}{i!}\\[1em]
&= n! - \sum_{i=1}^{\left\lfloor\frac{n}{r}\right\rfloor}(-1)^{i+1} \frac{n!}{(r!)^i(n-ir)!}((r-1)!)^i(n-ir)!\frac{1}{i!}\\[1em]
&= n! - \sum_{i=1}^{\left\lfloor\frac{n}{r}\right\rfloor}(-1)^{i+1} \frac{n!}{r^i(n-ir)!}(n-ir)!\frac{1}{i!}\\[1em]
&= n! - \sum_{i=1}^{\left\lfloor\frac{n}{r}\right\rfloor}(-1)^{i+1}\frac{n!}{r^i*i!}\\[1em]
&= n!\left(1-\sum_{i=1}^{\left\lfloor\frac{n}{r}\right\rfloor}(-1)^{i+1}\frac{1}{r^i*i!}\right)\\[1em]
&= n!\left((-1)^0\frac{1}{r^0*0!}-\sum_{i=1}^{\left\lfloor\frac{n}{r}\right\rfloor}(-1)^{i+1}\frac{1}{r^i*i!}\right)\\[1em]
&= n!\sum_{i=0}^{\left\lfloor\frac{n}{r}\right\rfloor}(-1)^{i}\frac{1}{r^i*i!}
\end{align*}


I think you would agree with me that it looks disgusting. Generally because it seems to be filled with so many \left\lfloor <...> \right\rfloor strings.

Is it possible to define a command that writes \left and \right for me in the general case? I've read this post here Is it possible to write \left( \right) in one command? but it only covers the case when I want to use round brackets. What if I want to use square brackets, vertical bars or ceiling braces?

You could load the mathtools package and use its \DeclarePairedDelimiter macro to create a macro called, say, \floor as follows:

\DeclarePairedDelimiter\floor\lfloor\rfloor


and replace all instances of \left\lfloor\frac{n}{r}\right\rfloor with \floor{\frac{n}{r}}. (For more information on the uses of \DeclarePairedDelimiter, please see section 3.6., "Paired delimiters", in the user guide of the mathtools package.)

And, since there are quite a few instances of \floor{\frac{n}{r}}, it's useful to create a shorthand macro for them, say,

\newcommand\flnr{\floor{\frac{n}{r}}}


In addition, I would replace all instances of the multiplicative * with \,, i.e., thinspace. Also, use \biggl( and \biggr) for the large parentheses in rows 5 and 6, as the parentheses produced by \left( and \right) are too large from a purely typographic/aesthetic perspective.

\documentclass{article}
\usepackage{mathtools} % for '\DeclarePairedDelimiter' macro
\DeclarePairedDelimiter\floor\lfloor\rfloor
\newcommand\flnr{\floor{\frac{n}{r}}} % handy shortcut macro

\begin{document}
\begin{align*}
n!-k
&= n! - \sum_{i=1}^{\flnr} (-1)^{i+1} \binom{n}{r,\dots,n-ir} ((r-1)!)^i(n-ir)!\,\frac{1}{i!}\\[1ex]
&= n! - \sum_{i=1}^{\flnr} (-1)^{i+1} \frac{n!}{(r!)^i(n-ir)!}((r-1)!)^i(n-ir)!\,\frac{1}{i!}\\[1ex]
&= n! - \sum_{i=1}^{\flnr} (-1)^{i+1} \frac{n!}{r^i(n-ir)!}(n-ir)!\,\frac{1}{i!}\\[1ex]
&= n! - \sum_{i=1}^{\flnr} (-1)^{i+1}\frac{n!}{r^i\,i!}\\[1ex]
&= n!\biggl(1-\sum_{i=1}^{\flnr} (-1)^{i+1}\frac{1}{r^i\,i!}\biggr)\\[1ex]
&= n!\biggl((-1)^0\frac{1}{r^0\,0!}-\sum_{i=1}^{\flnr} (-1)^{i+1}\frac{1}{r^i\,i!}\biggr)\\[1ex]
&= n!\sum_{i=0}^{\flnr} (-1)^{i}\frac{1}{r^i\,i!}
\end{align*}
\end{document}

• Quick q: why do you use \biggl and \biggr instead of left and right? Also, I noticed that the floor braces don't span to the bottom of the fraction. This can be a problem because if the fraction was bigger, then the floor braces would not fit. I think this is on me because I provided a poor example of code. – Kookie Jun 1 at 9:21
• I have essentially the same code, but with \floor{n/r}, which is much less intrusive. I'd also recommend !\, when the factorial is followed by something that doesn't add space by itself. – egreg Jun 1 at 9:23
• @Kookie - Because the parentheses produced if \left( and \right) are too big relative to what's optimal from a typographic point of view. For more on this topic see, e.g., this answer to the query Is it ever bad to use \left and \right?. [Shameless self-citation alert!] – Mico Jun 1 at 9:24
• Oh, that's interesting, [also, I really don't mind self-citation. A source is a source lul.] – Kookie Jun 1 at 9:26

My proposal is almost the same as Mico's, but with some significant differences:

1. use n/r instead of \frac{n}{r};
2. add \, when a factorial is followed by another object to be multiplied with (if that object doesn't produce space by itself, like in the last line);
3. two instances of nested parentheses are dealt with using \bigl and \bigr;
4. no additional vertical space is necessary (due to the n/r in the upper bound of summations).

I endorse the proposal of avoiding * for multiplication and substituting it with \, in those denominators; it's not generally necessary, these cases seem to want it, mostly because of the same letter in the exponent and in the following symbol.

\documentclass{article}
\usepackage{amsmath,mathtools}

\DeclarePairedDelimiter{\floor}{\lfloor}{\rfloor}

\begin{document}

\begin{align*}
n! - k
&= n! - \sum_{i=1}^{\floor{n/r}}(-1)^{i+1}\binom{n}{r,\dots,n-ir}
\bigl((r-1)!\bigr)^i(n-ir)!\,\frac{1}{i!}
\\
&= n! - \sum_{i=1}^{\floor{n/r}}(-1)^{i+1}
\frac{n!}{(r!)^i(n-ir)!}\bigl((r-1)!\bigr)^i(n-ir)!\,\frac{1}{i!}
\\
&= n! - \sum_{i=1}^{\floor{n/r}}(-1)^{i+1} \frac{n!}{r^i(n-ir)!}(n-ir)!\,\frac{1}{i!}
\\
&= n! - \sum_{i=1}^{\floor{n/r}}(-1)^{i+1}\frac{n!}{r^i\,i!}
\\
&= n!\,\biggl(1-\sum_{i=1}^{\floor{n/r}}(-1)^{i+1}\frac{1}{r^i\,i!}\biggr)
\\
&= n!\,\biggl((-1)^0\frac{1}{r^0\,0!}-
\sum_{i=1}^{\floor{n/r}}(-1)^{i+1}\frac{1}{r^i\,i!}\biggr)
\\
&= n!\sum_{i=0}^{\floor{n/r}}(-1)^{i}\frac{1}{r^i\,i!}
\end{align*}

\end{document}


• Wow! Looks great, thanks for the advice! Maybe this is just a style thing, but I'm not a big fan of inline maths. – Kookie Jun 1 at 9:41
• @Kookie Two-story fractions are really big; they're necessary for clarity in the main parts, but when superscripted they're generally better treated with the slashed form, provided numerator and denominator are simple. – egreg Jun 1 at 9:57
• Ok, I will consider using inline math a little more. – Kookie Jun 1 at 10:59

You can use \qty from physics and \binom from amsmath, here's how they work:

\documentclass{article}
\usepackage{physics, amsmath}

\begin{document}

\begin{align*}
S &= \qty(\sum_{k=0}^n \binom{n}{k} x^k y^{n-k})\\
S &= \qty{\sum_{k=0}^n \binom{n}{k} x^k y^{n-k}}\\
S &= \qty[\sum_{k=0}^n \binom{n}{k} x^k y^{n-k}]
\end{align*}

\end{document}


The physics package also helps with writing down matrices a little bit more easily with \mqty. You just need to write \mqty, then use the delimiters you want (), [], or {}, then, write whatever you like. Separate each column with & and each row with \\ just like in a usual array.

• Do you know where I can find documentation for this? – Kookie Jun 2 at 1:55
• Yes, here's the documentation for the physics package: link with \qty at page 2 and \mqty at page 7 Here's amsmath's user guide: link with \binom being at page 16 The physics package is one of my favorite, it simplifies so many things and adds really useful commands for physics majors/physicists – Cat Admirer Jun 5 at 15:03
• Wau! The physics package is awesome! Although I am not studying physics, it contains commands to bold symbols and shortens things like derivatives. My mind is blown really. Thanks for showing me both guides! – Kookie Jun 5 at 17:07