1
\documentclass[a4paper]{article}
\usepackage{amsmath}
\begin{document}

Instead of $f(x) = x^2 + 17 \mod 43$, I prefer $f(x) = x^2 + 17\hspace{-1mm}\mod 43$.  

\end{document}

Why was the modulo operator defined with this apparent extra space? Is there a rationale behind it?

I'm on the brink of redefining it.

3

First and foremost: it is not an “operator”, but a traditional way to write a particular equivalence relation. Also the correct syntax is \mod{43}.

Plain TeX only has \pmod, defined as

% plain.tex, line 1089
\def\pmod#1{\allowbreak\mkern18mu({\rm mod}\,\,#1)}

so the space is 1em (in the math symbol font), because 18mu is 1em.

In the LaTeX kernel the definition is essentially the same, namely

% latex.ltx, line 4437:
\def\pmod#1{%
  \allowbreak\mkern18mu({\operator@font mod}\,\,#1)}

On the other hand, amsmath also defines \mod and \pod. The former omits parentheses and the latter has parentheses but no “mod”.

\newcommand{\pod}[1]{\allowbreak
  \if@display\mkern18mu\else\mkern8mu\fi(#1)}
\renewcommand{\pmod}[1]{\pod{{\operator@font mod}\mkern6mu#1}}
\newcommand{\mod}[1]{\allowbreak\if@display\mkern18mu
  \else\mkern12mu\fi{\operator@font mod}\,\,#1}

The definition of \pmod is in terms of \pod; you can see that a\equiv b\pod{n} will have, after b, 1em of space in display style or 8/18em in other styles, followed by (n). With \pmod the spacing before the parenthesis is the same, but after the parentheses “mod” and a space of 6/18em will precede n.

With \mod the spacing is essentially the same, but 12/18em would be used instead of 8/18em in text style or below. Note that \,\, is the same as \mkern 6mu.

So it's just you. ;-)

Of course you're free to change the spacing by redefining \pod and \mod.

  • It's great that you prove your comments by showing the original definitions. – Joep Awinita Feb 13 at 18:07
1

The even spaced version is \bmod as in Sebastiano's now deleted answer which has the spacing you seem to want but is the wrong thing here as it would mean x^2 + (17 mod 43) which is the wrong interpretation. You want the bigger space before mod to separate it from the 17 and make it clear that it's a side condition applying to the equality which is to be interpreted as a congruence mod 43.

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.