Automatically number inequalities

Question

I have a long chain of inequalities and I would like to add some explanation for some of the steps under those inequalities. I have seen people do this like \stackrel{(i)}{\leq}. This is what I would like but I would like to have a counter that does this for me, so (i), (ii), and so on with an automatic increment so that I will not have to change everything if I add a line.

The biggest issue that I can think of and which I don't know how to solve is that that counter has to be reset when I use it again in a new equation (or something similar) environment. Any suggestions?

Answer 1

Here's a try:

\documentclass{article}
\usepackage{amsmath}
\newcounter{hints}
\renewcommand{\thehints}{\roman{hints}}
\newcommand{\hintedrel}[2][]{%
  \refstepcounter{hints}%
  \if\relax\detokenize{#1}\relax\else\label{#1}\fi
  \mathrel{\overset{\mathrm{(\thehints)}}{\vphantom{\le}{#2}}}%
}
\newcommand{\restarthintedrel}{\setcounter{hints}{0}}

\begin{document}
$a\hintedrel[lab1]{\le}b\hintedrel[lab2]{<}c$

(\ref{lab1}): because it's so.

(\ref{lab2}): I tell you it is.

$\restarthintedrel a\hintedrel[lab3]{\le}b\hintedrel[lab4]{<}c$

(\ref{lab3}): because it's so.

(\ref{lab4}): I tell you it is.
\end{document}

The \hintedrel command has an optional argument, a label for referring later to the inequality.

Before a new chain of hinted inequalities you can write \restarthintedrel to restart from 1.

Different implementation

\documentclass{article}
\usepackage{amsmath,etoolbox}
\AfterEndEnvironment{equation}{\restarthintedrel}
\AfterEndEnvironment{align}{\restarthintedrel}
\newcounter{hints}
\renewcommand{\thehints}{\roman{hints}}
\newcommand{\hintedrel}[2][]{%
  \stepcounter{hints}%
  \if\relax\detokenize{#1}\relax\else\csxdef{hint@#1}{\thehints}\fi
  \mathrel{\overset{\textrm{(\thehints)}}{\vphantom{\le}{#2}}}%
}
\newcommand{\restarthintedrel}{\setcounter{hints}{0}}
\newcommand{\hintref}[1]{\csuse{hint@#1}}

\begin{document}
\begin{equation}
a\hintedrel[lab1]{\le}b\hintedrel[lab2]{<}c\overset{*}{\le}d
\end{equation}

(\hintref{lab1}): because it's so.

(\hintref{lab2}): I tell you it is.

\begin{align}
a&\hintedrel[lab3]{\le}b\\
&\hintedrel[lab4]{<}c
\end{align}

(\hintref{lab3}): because it's so.

(\hintref{lab4}): I tell you it is.
\end{document}

This assumes that the hints will be referred to only after they are defined (with the standard \label-\ref mechanism amsmath would raise an error). You have to add similar \AfterEndEnvironment for each math environment you use.

Answer 2

This might be what you're after, using a counter that increments at every use and resets at the start of every \section in your document. This can be modified, of course:

\documentclass{article}
\usepackage{amsmath}% http://ctan.org/pkg/amsmath
\usepackage{chngcntr}% http://ctan.org/pkg/chngcntr

\newcounter{numrel}% Counter for numering relations
\counterwithin*{numrel}{section}% Counter resets at every section
\newcommand{\numrel}[1]{% Relation numbering
  \stepcounter{numrel}% Increment numrel counter
  \ensuremath{\stackrel{(\roman{numrel})}{#1}}% Print counter + relation
}
\begin{document}
\section{First section}
\begin{align*}
  P(x) &= ax^2+bx+c \\
       &\stackrel{(i)}{\leq} cx^3+dx^2+ex+f \\
       &\stackrel{(ii)}{<} gx^4+hx^3+ix^2+jx+k  
\end{align*}
\section{Second section}
\begin{align*}
  P(x) &= ax^2+bx+c \\
       &\numrel{\leq} cx^3+dx^2+ex+f \\
       &\numrel{<} gx^4+hx^3+ix^2+jx+k  
\end{align*}
\end{document}

In the example above, the first section uses \stackrel while the second uses the newly defined \numrel command, to show the similarities. It would also be possible to modify the code to accommodate for using references so that your document text will change according to the change of adding/removing a line in your equation. The chngcntr package was used for more flexibility in formatting the counter resetting.

---

In order to accommodate the possibility to reference the counter within your text, here's a modified minimal example that uses the etoolbox package to reset the counter at the end of the align* environment, as well as some amsmath counter manipulation using Multiply defined labels using hyperref. The \numrel{<rel>}{<lab>} now takes two mandatory arguments. The first is the relation <rel> while the second is the label <lab> that may be referenced elsewhere:

\documentclass{article}
\usepackage{amsmath}% http://ctan.org/pkg/amsmath
\usepackage{etoolbox}% http://ctan.org/pkg/etoolbox

\newcounter{numrel}% Counter for numering relations
\renewcommand{\thenumrel}{\roman{numrel}}% Counter numrel uses lowercase roman numerals
\let\textlabel\label% Use text \label rather than math \label
\newcommand{\numrel}[2]{% Relation numbering
  \begingroup%
  \refstepcounter{numrel}% Increment numrel counter and create correct reference hook
  \textlabel{#2}\endgroup% Label numrel counter
  \ensuremath{\stackrel{(\thenumrel)}{#1}}% Print counter + relation
}
\AfterEndEnvironment{align*}{\setcounter{numrel}{0}}% Resets numrel at the end of align*

\begin{document}
\section{First section}
\begin{align*}
  P(x) &= ax^2+bx+c \\
       &\stackrel{(i)}{\leq} cx^3+dx^2+ex+f \\
       &\stackrel{(ii)}{<} gx^4+hx^3+ix^2+jx+k  
\end{align*}
\section{Second section}
\begin{align*}
  P(x) &= ax^2+bx+c \\
       &\numrel{\leq}{rel1} cx^3+dx^2+ex+f \\
       &\numrel{<}{rel2} gx^4+hx^3+ix^2+jx+k  
\end{align*}
If you look at (\ref{rel1}), you will notice it is different from (\ref{rel2}).
\begin{align*}
  P(x) &= ax^2+bx+c \\
       &\numrel{\leq}{rel3} cx^3+dx^2+ex+f \\
       &\numrel{<}{rel4} gx^4+hx^3+ix^2+jx+k  
\end{align*}
If you look at (\ref{rel3}), you will notice it is different from (\ref{rel4}).

\end{document}