Strange behaviour of binomial coefficient's delimiters

Question

This question led to a new package:
fixcmex

While writing down my Combinatorics exercises I found that the binomial coefficient's delimiters weren't displayed as indicated inside the amsmath documentation.

By subsequent trials and errors I was able to reduce the volume of my document to this simpler and fully compilable MWE:

\documentclass[11pt]{article}
%
\usepackage{amsmath}
%
\makeatletter
%
\usepackage{lmodern}
\usepackage{lipsum}
%
\makeatother
%
\begin{document}
%
\lipsum[1]
\begin{equation}
2^k-\binom{k}{1}2^{k-1}+\binom{k}{2}2^{k-2}
\end{equation}
\lipsum[1]
%
\end{document}

Which gives (using TeXworks 0.44 on MikTeX 2.9.4521 updated 09/10/13) this un-expected result:

While the amsmath doc shows that with the loaded packages inside the MWE the result would actually be like this:

From here we can see that the delimiters on the first example are a little bit stretched vertically as they surpass the arguments inside the binom. coeff.

The more strange event is that when I comment the line \usepackage{lmodern} the result on delimiter's shape in my example looks exactly as the amsmath doc:

\documentclass[11pt]{article}
%
\usepackage{amsmath}
%
\makeatletter
%
%\usepackage{lmodern}
\usepackage{lipsum}
%
\makeatother
%
\begin{document}
%
\lipsum[1]
\begin{equation}
2^k-\binom{k}{1}2^{k-1}+\binom{k}{2}2^{k-2}
\end{equation}
\lipsum[1]
%
\end{document}

Output:

From here I deduce that the problem lies inside lmodern, but I'd like to keep using this package and fix this wierd "issue" with the math mode. Is there some clue that I've missed or this is in fact an update-process bug infecting amsmath's delimiter control?

Answer 1

This is a problem in how lmodern sets up the math extensions font, by saying

\DeclareFontShape{OMX}{lmex}{m}{n}{%
   <->sfixed*lmex10%
   }{}

which is utterly wrong, in my opinion, because it destroys the settings made by amsmath which would solve the problem. The fonts, unfortunately, do not provide for optical sizes different from 10pt, so you have a few strategies

Let amsmath do the main work

\documentclass[11pt]{article}

\usepackage{amsmath}
\usepackage{lmodern}

\DeclareSymbolFont{largesymbols}{OMX}{cmex}{m}{n} % use cmex rather than lmex

\usepackage{lipsum}

\begin{document}

\lipsum[1]
\begin{equation}
2^k-\binom{k}{1}2^{k-1}+\binom{k}{2}2^{k-2}
\end{equation}
\lipsum[1]

\end{document}

Load exscale or, better, the fonts defined by it

\documentclass[11pt]{article}

\usepackage{amsmath}
\usepackage{lmodern}

\DeclareFontShape{OMX}{cmex}{m}{n}{%
      <-7.5> cmex7
      <7.5-8.5> cmex8
      <8.5-9.5> cmex9
      <9.5-> cmex10
       }{}
\DeclareSymbolFont{largesymbols}{OMX}{cmex}{m}{n} % use cmex rather than lmex

\usepackage{lipsum}

\begin{document}

\lipsum[1]
\begin{equation}
2^k-\binom{k}{1}2^{k-1}+\binom{k}{2}2^{k-2}
\end{equation}
\lipsum[1]

\end{document}

Make lmex10 scalable

\documentclass[11pt]{article}

\usepackage{amsmath}
\usepackage{lmodern}
\DeclareFontFamily{OMX}{lmex}{}
\DeclareFontShape{OMX}{lmex}{m}{n}{%
   <-> lmex10
   }{}

\usepackage{lipsum}

\begin{document}

\lipsum[1]
\begin{equation}
2^k-\binom{k}{1}2^{k-1}+\binom{k}{2}2^{k-2}
\end{equation}
\lipsum[1]

\end{document}

With all strategies the computation for the delimiter's sizes gives a better result. Strategy one and two are rather similar; the difference is that the second one scales all fonts even at non standard sizes, while the first uses only fixed sizes 7, 8, 9, 10, 11 (10.95), 12, 14 (14.4) and 17 (17.28).

Answer 2

This answer relies on redefining \binom to use features of the scalerel and stackengine packages. The \scaleleftright macro will make the paren delimiters exactly match the height of the binomial contents, which are stacked using \stackanchor.

The vertical gap between the components of the binomial coefficient is an optional argument to \stackanchor (currently set at 1.8ex), and the horizontal limiting width of the parens of the coefficient are given as an optional argument to \scaleleftright (currently set to 1.5ex).

\documentclass[11pt]{article}
%
\usepackage{amsmath}
\usepackage{scalerel}
\usepackage{stackengine}
%
\makeatletter
%
\usepackage{lmodern}
\usepackage{lipsum}
%
\makeatother
%
\begin{document}
%
\lipsum[1]
\begin{equation}
2^k-\binom{k}{1}2^{k-1}+\binom{k}{2}2^{k-2}
\end{equation}
\renewcommand\binom[2]{\stackMath\mathop{%
  \scaleleftright[1.5ex]{(}{\stackanchor[1.8ex]{#1}{#2}}{)}}}
\begin{equation}
2^k-\binom{k}{1}2^{k-1}+\binom{k}{2}2^{k-2}
\end{equation}
\lipsum[1]

%
\end{document}

The top image is the original that you posted, while the lower one is the fix proposed here.