How can I redefine the minus sign to be of the same width as plus?

Question

The situation

In the standard Computer Modern (and also in Latin Modern) the math-mode minus and plus symbols are, in some font sizes, not of the same width. This causes slight misalignments in formulas. I would like to redefine the math-mode - to have the same width as +, in any font size.

The example

\documentclass[12pt]{standalone}%
%
\begin{document}%
\newlength{\test}%
\begin{tabular}{rll}%
textstyle & \fbox{$-$} & \settowidth{\test}{$-$}\the\test\\
textstyle & \fbox{$+$} & \settowidth{\test}{$+$}\the\test\\
scriptstyle & \fbox{$\scriptstyle-$} & \settowidth{\test}{$\scriptstyle-$}\the\test\\
scriptstyle & \fbox{$\scriptstyle+$} & \settowidth{\test}{$\scriptstyle+$}\the\test\\
scriptscriptstyle & \fbox{$\scriptscriptstyle-$} & \settowidth{\test}{$\scriptscriptstyle-$}\the\test\\
scriptscriptstyle & \fbox{$\scriptscriptstyle+$} & \settowidth{\test}{$\scriptscriptstyle+$}\the\test\\
\end{tabular}%
\end{document}%

This shows that the minus is wider than the plus in both 12pt and 6pt math fonts, but has the same width in 8pt.

The solution?

I'll post one below, but I am not happy with it.

Answer 1

Note: I take a very different view of the original question in the following discussions and solutions. And, no, I do not like the idea of making + and/or - active in math mode just for alignment purposes.

This problem exists not only for Computer Modern/Latin Modern, and not only for the + and - pair

With the default Computer Modern family (or the Latin Modern family), the width difference problem is barely visible. However, with other math fonts such as newtxmath, newpxmath and mtpro2, this problem is much more visible and it goes beyond the + and - pair. The following MWE illustrates this point:

\documentclass{article}
\usepackage{mathtools}
% Latin Modern
%\usepackage{lmodern}
% newtxmath
\usepackage{newtxtext}
\usepackage{newtxmath}
% mtpro2
%\usepackage{newtxtext}
%\usepackage[lite]{mtpro2}
\begin{document}
Cases: $f(x) = \begin{cases}
                +1 & x>0 \\
                -1 & x=0 \\
                -1 & x\le0
               \end{cases}$

Stacked subscripts: $\displaystyle \sum_{\substack{i=0 \\ i>0}}$
\end{document}

We may now conclude that the width differences are by design. More importantly, the behavior is unpredictable across different math fonts and across different design/optical sizes. Clearly, any solutions that involve active +, -, = and so on would be ineffective and dangerous.

How can we get mono-width symbols?

Instead of making characters active (and possibly breaking other things), I propose two specially designed commands:

\tabularrel{<arg>}

and

\tabularbin{<arg>}

The names are inspired by “proportional versus tabular figures”. Each of the two commands essentially makes a box of fixed width according to some “standard symbol”, then it puts the actual symbol horizontally centered. Note that \mathpalette is needed to get the correct math style. Of course, this method of aligning tabular-like math can be applied to any math fonts.

Here is a MWE:

\documentclass{article}
\usepackage{mathtools}
% Latin Modern
%\usepackage{lmodern}
% newtxmath
\usepackage{newtxtext}
\usepackage{newtxmath}
% mtpro2
%\usepackage{newtxtext}
%\usepackage[lite]{mtpro2}

% Standard relation and binary symbols
\newcommand*\standardrel{<}% Change this to `=' for mtpro2
\newcommand*\standardbin{+}
% Tabular relation and binary symbols
\makeatletter
\newcommand*\tabularrel[1]{%
  \mathrel{\mathpalette{\@tabularsym\standardrel}{#1}}%
}
\newcommand*\tabularbin[1]{%
  \mathbin{\mathpalette{\@tabularsym\standardbin}{#1}}%
}
\newcommand*\@tabularsym[3]{%
  % #1: standard symbol
  % #2: math style
  % #3: user symbol
  \setbox\z@\hbox{$#2#1\m@th$}%
  \hbox to\wd\z@{\hss$#2#3\m@th$\hss}%
}
\makeatother

\begin{document}
Cases: $f(x) = \begin{cases}
                \tabularbin+1 & x\tabularrel>0 \\
                \tabularbin-1 & x\tabularrel=0 \\
                \tabularbin-1 & x\tabularrel\le0
               \end{cases}$

Stacked subscripts: $\displaystyle \sum_{\substack{i\tabularrel=0 \\ i\tabularrel>0}}$
\end{document}

Voilà!!!

For most “one-liner” equations, there are no need for mono-width symbols. However, when typing inside tabular-like environments, e.g., tables, arrays, cases, matrices, etc., horizontal alignment may be crucial.

Answer 2

My attempt at a solution

\newlength{\widthplus}%
\newcommand{\minuspalette}[2]{\settowidth{\widthplus}{$#1+$}\mathbin{\makebox[\widthplus]{$#1#2$}}}%
\newcommand{\goodminus}{\mathpalette{\minuspalette}{\mathchar"2200}}% use \mathchar"2200 instead of - to avoid infinite recursion
{\catcode`-13\gdef-{\goodminus}}% make - active temporarily, so that it can be redefined
\mathcode`-"8000% make - active in math mode

I simply define a box that has the same width as a plus sign, but will be filled with a minus glyph. I do not shrink the symbol, only make its bounding box smaller. Via \mathpalette the definition is automatically correct for all math sizes. Then I make - active (but only temporarily), such that it can be redefined. And finally I make - permanently active in math-mode only (not to mess with text-mode hyphens), such that the new definition is used there.

What I don't like about it

Precisely because minus is now active in math-mode I can no longer use it as a single superscript or subscript, such as in $e^-$. It can now only be used if extra braces are put around the -. This is inconvenient and breaks many things in my existing project. Can anyone think of a solution which achieves the same effect as mine, but without this downside?