Csdrhrt

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?

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:

  
  
  

  $$left(frac{x}{raise0.35exhbox{$p$}}right)left(frac{p}{x}right)$$
  
  

  
  


• 
  

  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



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



$$Bigl(frac{x}{p}Bigr)Bigl(frac{p}{x}Bigr)$$

$$biggl(frac{x}{p}biggr)biggl(frac{p}{x}biggr)$$



$$left(frac{x}{raise0.35exhbox{$p$}}right)left(frac{p}{x}right)$$



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



$$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:

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}quadlegendre{p}{x}quad

legendre{x}{x}quadlegendre{d}{b}

]



end{document}

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

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}