\left and \right not working on parentheses within the same line when internal fractions are changed

Question

I'm trying to show the product of two Legendre symbols. When I compile the following

\documentclass{article}
\begin{document}
$$\left(\frac{x}{p}\right) \left(\frac{x}{p}\right)$$
\end{document}

it yields

as expected. However, when I switch the variables, i.e.

\documentclass{article}
\begin{document}
$$\left(\frac{x}{p}\right)\left(\frac{p}{x}\right)$$
\end{document}

it yields

How do I resolve this? Why do the values within the fractions matter?

Answer 1

This is somewhat similar to this question.

The values in the fractions matter because the boxes of the characters have different sizes. The p has a descender below the baseline which the x doesn't, thus when you swap them, the box of the denominator get a little bigger and TeX uses a larger delimiter to make that fit.

You have a few possibilities to work around that (basically the same ones I listed in the linked question):

• You can use a fixed delimiter size (\bigg or \Big, for instance):

  $$\Bigl(\frac{x}{p}\Bigr)\Bigl(\frac{p}{x}\Bigr)$$
  $$\biggl(\frac{x}{p}\biggr)\biggl(\frac{p}{x}\biggr)$$
  

• You can \raise the p so that TeX won't try to use a larger box:

  $$\left(\frac{x}{\raise0.35ex\hbox{$p$}}\right)\left(\frac{p}{x}\right)$$
  

• or you can add an invisible p next to the x so that the delimiter used will be the larger one:

  $$\left(\frac{x}{p}\right)\left(\frac{p}{\vphantom{p}x}\right)$$
  

• Or you can change change TeX's \delimiterfactor (and \delimitershortfall, which I didn't show here) and let TeX adjust the delimiters accordingly:

  $$\delimiterfactor=790
  \left(\frac{x}{p}\right)\left(\frac{p}{x}\right)$$
  
  $$\delimiterfactor=970
  \left(\frac{x}{p}\right)\left(\frac{p}{x}\right)$$
  

Full code:

\documentclass{article}
\begin{document}
% \delimitershortfall=5pt % Default
% \delimiterfactor=901    % Default

$$\left(\frac{x}{p}\right)\left(\frac{p}{x}\right)$$

$$\Bigl(\frac{x}{p}\Bigr)\Bigl(\frac{p}{x}\Bigr)$$
$$\biggl(\frac{x}{p}\biggr)\biggl(\frac{p}{x}\biggr)$$

$$\left(\frac{x}{\raise0.35ex\hbox{$p$}}\right)\left(\frac{p}{x}\right)$$

$$\left(\frac{x}{p}\right)\left(\frac{p}{\vphantom{p}x}\right)$$

$$\delimiterfactor=790
\left(\frac{x}{p}\right)\left(\frac{p}{x}\right)$$

$$\delimiterfactor=970
\left(\frac{x}{p}\right)\left(\frac{p}{x}\right)$$
\end{document}

Output:

Answer 2

Use \genfrac for this:

\documentclass{article}
\usepackage{amsmath}

\newcommand{\genlegendre}[3]{\genfrac{(}{)}{}{#1}{#2}{#3}}
\newcommand{\legendre}[2]{\genlegendre{}{#1}{#2}}
\newcommand{\dlegendre}[2]{\genlegendre{0}{#1}{#2}}
\newcommand{\tlegendre}[2]{\genlegendre{1}{#1}{#2}}

\begin{document}

\[
\legendre{x}{p}\quad\legendre{p}{x}\quad
\legendre{x}{x}\quad\legendre{d}{b}
\]

\end{document}

The variants \dlegendre and \tlegendre are analogous to \dfrac and \tfrac.

Answer 3

I like the unified syntax for this kind of stuff in the mathtools package.

\documentclass{article}

\usepackage{mathtools}
\DeclarePairedDelimiter{\paren}{\lparen}{\rparen}

\begin{document}

\begin{equation*}
  \paren*{\frac{x}{p} }\quad \paren*{\frac{p}{x}}
  \qquad
  \paren[\bigg]{\frac{x}{p}} \quad \paren[\bigg]{\frac{p}{x}}
\end{equation*}

\end{document}