mjhjmtu

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

documentclassarticle
begindocument
$$left(fracxpright) left(fracxpright)$$
enddocument

it yields

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

documentclassarticle
begindocument
$$left(fracxpright)left(fracpxright)$$
enddocument

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):

  
  
  

  $$Bigl(fracxpBigr)Bigl(fracpxBigr)$$
  $$biggl(fracxpbiggr)biggl(fracpxbiggr)$$
  

  
  


• 
  

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

  
  
  

  $$left(fracxraise0.35exhbox$p$right)left(fracpxright)$$
  

  
  


• 
  

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

  
  
  

  $$left(fracxpright)left(fracpvphantompxright)$$
  

  
  


• 
  

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

  
  
  

  $$delimiterfactor=790
  left(fracxpright)left(fracpxright)$$
  
  $$delimiterfactor=970
  left(fracxpright)left(fracpxright)$$
  

  
  

Full code:

documentclassarticle
begindocument
% delimitershortfall=5pt % Default
% delimiterfactor=901 % Default

$$left(fracxpright)left(fracpxright)$$

$$Bigl(fracxpBigr)Bigl(fracpxBigr)$$
$$biggl(fracxpbiggr)biggl(fracpxbiggr)$$

$$left(fracxraise0.35exhbox$p$right)left(fracpxright)$$

$$left(fracxpright)left(fracpvphantompxright)$$

$$delimiterfactor=790
left(fracxpright)left(fracpxright)$$

$$delimiterfactor=970
left(fracxpright)left(fracpxright)$$
enddocument

Output:

Use genfrac for this:

documentclassarticle
usepackageamsmath

newcommandgenlegendre[3]genfrac()#1#2#3
newcommandlegendre[2]genlegendre#1#2
newcommanddlegendre[2]genlegendre0#1#2
newcommandtlegendre[2]genlegendre1#1#2

begindocument

[
legendrexpquadlegendrepxquad
legendrexxquadlegendredb
]

enddocument

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.

documentclassarticle

usepackagemathtools
DeclarePairedDelimiterparenlparenrparen

begindocument

beginequation*
 paren*fracxp quad paren*fracpx
 qquad
 paren[bigg]fracxp quad paren[bigg]fracpx
endequation*

enddocument