How to break apart a huge fraction resulting from a symbolic calculation?












2















I'm trying to use a Computer Algebra System to learn something about an algebraic expression, and this is what it gives me as a result in LaTex:



documentclass{article}

usepackage{breqn}



begin{document}



begin{dmath}

    frac{e_{0} n_{0} left(- n_{0} p_{0} + n_{0} r_{0} + n_{0} left(p_{0} - q_{0}right) - n_{1} p_{1} + n_{1} r_{1} + n_{1} left(p_{1} - q_{1}right) - n_{2} p_{2} + n_{2} r_{2} + n_{2} left(p_{2} - q_{2}right)right) + e_{1} n_{1} left(- n_{0} p_{0} + n_{0} r_{0} + n_{0} left(p_{0} - q_{0}right) - n_{1} p_{1} + n_{1} r_{1} + n_{1} left(p_{1} - q_{1}right) - n_{2} p_{2} + n_{2} r_{2} + n_{2} left(p_{2} - q_{2}right)right) - e_{10} left(left(- p_{1} + r_{1}right) left(n_{0} left(p_{0} - q_{0}right) + n_{1} left(p_{1} - q_{1}right) + n_{2} left(p_{2} - q_{2}right)right) + left(p_{1} - q_{1}right) left(n_{0} p_{0} - n_{0} r_{0} + n_{1} p_{1} - n_{1} r_{1} + n_{2} p_{2} - n_{2} r_{2}right)right) - e_{11} left(left(- p_{2} + r_{2}right) left(n_{0} left(p_{0} - q_{0}right) + n_{1} left(p_{1} - q_{1}right) + n_{2} left(p_{2} - q_{2}right)right) + left(p_{2} - q_{2}right) left(n_{0} p_{0} - n_{0} r_{0} + n_{1} p_{1} - n_{1} r_{1} + n_{2} p_{2} - n_{2} r_{2}right)right) + e_{2} n_{2} left(- n_{0} p_{0} + n_{0} r_{0} + n_{0} left(p_{0} - q_{0}right) - n_{1} p_{1} + n_{1} r_{1} + n_{1} left(p_{1} - q_{1}right) - n_{2} p_{2} + n_{2} r_{2} + n_{2} left(p_{2} - q_{2}right)right) - e_{9} left(left(- p_{0} + r_{0}right) left(n_{0} left(p_{0} - q_{0}right) + n_{1} left(p_{1} - q_{1}right) + n_{2} left(p_{2} - q_{2}right)right) + left(p_{0} - q_{0}right) left(n_{0} p_{0} - n_{0} r_{0} + n_{1} p_{1} - n_{1} r_{1} + n_{2} p_{2} - n_{2} r_{2}right)right) + left(e_{3} n_{0} + e_{4} n_{1} + e_{5} n_{2}right) left(n_{0} p_{0} - n_{0} r_{0} + n_{1} p_{1} - n_{1} r_{1} + n_{2} p_{2} - n_{2} r_{2}right) - left(e_{6} n_{0} + e_{7} n_{1} + e_{8} n_{2}right) left(n_{0} left(p_{0} - q_{0}right) + n_{1} left(p_{1} - q_{1}right) + n_{2} left(p_{2} - q_{2}right)right)}{left(n_{0} left(p_{0} - q_{0}right) + n_{1} left(p_{1} - q_{1}right) + n_{2} left(p_{2} - q_{2}right)right)^{2}}

end{dmath}



end{document}


It is a huge fraction, that gets cut when I try to compile this to PDF:



enter image description here



Is there an automagic way to cut this fraction in multiple lines in LaTex? If you look at the LaTex source code, searching for sensible break points to be manually inserted in such expressions will not be fun.



Edit: The fraction looks like this:



enter image description here



You can barely see it, but there is a single denominator, and the numerator is huge. Is there a way to write the numerator automatically across multiple lines?






amsmath fractions breqn







share|improve this question




















  • 3





    Well, this is not a TeX's problem. Tell us how the result should look like and there should be a way how to accomplish this. However, with my typography hat on, there is no good solution that keeps the fraction as a fraction.

    – yo'
    4 hours ago
















2















I'm trying to use a Computer Algebra System to learn something about an algebraic expression, and this is what it gives me as a result in LaTex:



documentclass{article}

usepackage{breqn}



begin{document}



begin{dmath}

    frac{e_{0} n_{0} left(- n_{0} p_{0} + n_{0} r_{0} + n_{0} left(p_{0} - q_{0}right) - n_{1} p_{1} + n_{1} r_{1} + n_{1} left(p_{1} - q_{1}right) - n_{2} p_{2} + n_{2} r_{2} + n_{2} left(p_{2} - q_{2}right)right) + e_{1} n_{1} left(- n_{0} p_{0} + n_{0} r_{0} + n_{0} left(p_{0} - q_{0}right) - n_{1} p_{1} + n_{1} r_{1} + n_{1} left(p_{1} - q_{1}right) - n_{2} p_{2} + n_{2} r_{2} + n_{2} left(p_{2} - q_{2}right)right) - e_{10} left(left(- p_{1} + r_{1}right) left(n_{0} left(p_{0} - q_{0}right) + n_{1} left(p_{1} - q_{1}right) + n_{2} left(p_{2} - q_{2}right)right) + left(p_{1} - q_{1}right) left(n_{0} p_{0} - n_{0} r_{0} + n_{1} p_{1} - n_{1} r_{1} + n_{2} p_{2} - n_{2} r_{2}right)right) - e_{11} left(left(- p_{2} + r_{2}right) left(n_{0} left(p_{0} - q_{0}right) + n_{1} left(p_{1} - q_{1}right) + n_{2} left(p_{2} - q_{2}right)right) + left(p_{2} - q_{2}right) left(n_{0} p_{0} - n_{0} r_{0} + n_{1} p_{1} - n_{1} r_{1} + n_{2} p_{2} - n_{2} r_{2}right)right) + e_{2} n_{2} left(- n_{0} p_{0} + n_{0} r_{0} + n_{0} left(p_{0} - q_{0}right) - n_{1} p_{1} + n_{1} r_{1} + n_{1} left(p_{1} - q_{1}right) - n_{2} p_{2} + n_{2} r_{2} + n_{2} left(p_{2} - q_{2}right)right) - e_{9} left(left(- p_{0} + r_{0}right) left(n_{0} left(p_{0} - q_{0}right) + n_{1} left(p_{1} - q_{1}right) + n_{2} left(p_{2} - q_{2}right)right) + left(p_{0} - q_{0}right) left(n_{0} p_{0} - n_{0} r_{0} + n_{1} p_{1} - n_{1} r_{1} + n_{2} p_{2} - n_{2} r_{2}right)right) + left(e_{3} n_{0} + e_{4} n_{1} + e_{5} n_{2}right) left(n_{0} p_{0} - n_{0} r_{0} + n_{1} p_{1} - n_{1} r_{1} + n_{2} p_{2} - n_{2} r_{2}right) - left(e_{6} n_{0} + e_{7} n_{1} + e_{8} n_{2}right) left(n_{0} left(p_{0} - q_{0}right) + n_{1} left(p_{1} - q_{1}right) + n_{2} left(p_{2} - q_{2}right)right)}{left(n_{0} left(p_{0} - q_{0}right) + n_{1} left(p_{1} - q_{1}right) + n_{2} left(p_{2} - q_{2}right)right)^{2}}

end{dmath}



end{document}


It is a huge fraction, that gets cut when I try to compile this to PDF:



enter image description here



Is there an automagic way to cut this fraction in multiple lines in LaTex? If you look at the LaTex source code, searching for sensible break points to be manually inserted in such expressions will not be fun.



Edit: The fraction looks like this:



enter image description here



You can barely see it, but there is a single denominator, and the numerator is huge. Is there a way to write the numerator automatically across multiple lines?






amsmath fractions breqn







share|improve this question




















  • 3





    Well, this is not a TeX's problem. Tell us how the result should look like and there should be a way how to accomplish this. However, with my typography hat on, there is no good solution that keeps the fraction as a fraction.

    – yo'
    4 hours ago














2












2








2








I'm trying to use a Computer Algebra System to learn something about an algebraic expression, and this is what it gives me as a result in LaTex:



documentclass{article}

usepackage{breqn}



begin{document}



begin{dmath}

    frac{e_{0} n_{0} left(- n_{0} p_{0} + n_{0} r_{0} + n_{0} left(p_{0} - q_{0}right) - n_{1} p_{1} + n_{1} r_{1} + n_{1} left(p_{1} - q_{1}right) - n_{2} p_{2} + n_{2} r_{2} + n_{2} left(p_{2} - q_{2}right)right) + e_{1} n_{1} left(- n_{0} p_{0} + n_{0} r_{0} + n_{0} left(p_{0} - q_{0}right) - n_{1} p_{1} + n_{1} r_{1} + n_{1} left(p_{1} - q_{1}right) - n_{2} p_{2} + n_{2} r_{2} + n_{2} left(p_{2} - q_{2}right)right) - e_{10} left(left(- p_{1} + r_{1}right) left(n_{0} left(p_{0} - q_{0}right) + n_{1} left(p_{1} - q_{1}right) + n_{2} left(p_{2} - q_{2}right)right) + left(p_{1} - q_{1}right) left(n_{0} p_{0} - n_{0} r_{0} + n_{1} p_{1} - n_{1} r_{1} + n_{2} p_{2} - n_{2} r_{2}right)right) - e_{11} left(left(- p_{2} + r_{2}right) left(n_{0} left(p_{0} - q_{0}right) + n_{1} left(p_{1} - q_{1}right) + n_{2} left(p_{2} - q_{2}right)right) + left(p_{2} - q_{2}right) left(n_{0} p_{0} - n_{0} r_{0} + n_{1} p_{1} - n_{1} r_{1} + n_{2} p_{2} - n_{2} r_{2}right)right) + e_{2} n_{2} left(- n_{0} p_{0} + n_{0} r_{0} + n_{0} left(p_{0} - q_{0}right) - n_{1} p_{1} + n_{1} r_{1} + n_{1} left(p_{1} - q_{1}right) - n_{2} p_{2} + n_{2} r_{2} + n_{2} left(p_{2} - q_{2}right)right) - e_{9} left(left(- p_{0} + r_{0}right) left(n_{0} left(p_{0} - q_{0}right) + n_{1} left(p_{1} - q_{1}right) + n_{2} left(p_{2} - q_{2}right)right) + left(p_{0} - q_{0}right) left(n_{0} p_{0} - n_{0} r_{0} + n_{1} p_{1} - n_{1} r_{1} + n_{2} p_{2} - n_{2} r_{2}right)right) + left(e_{3} n_{0} + e_{4} n_{1} + e_{5} n_{2}right) left(n_{0} p_{0} - n_{0} r_{0} + n_{1} p_{1} - n_{1} r_{1} + n_{2} p_{2} - n_{2} r_{2}right) - left(e_{6} n_{0} + e_{7} n_{1} + e_{8} n_{2}right) left(n_{0} left(p_{0} - q_{0}right) + n_{1} left(p_{1} - q_{1}right) + n_{2} left(p_{2} - q_{2}right)right)}{left(n_{0} left(p_{0} - q_{0}right) + n_{1} left(p_{1} - q_{1}right) + n_{2} left(p_{2} - q_{2}right)right)^{2}}

end{dmath}



end{document}


It is a huge fraction, that gets cut when I try to compile this to PDF:



enter image description here



Is there an automagic way to cut this fraction in multiple lines in LaTex? If you look at the LaTex source code, searching for sensible break points to be manually inserted in such expressions will not be fun.



Edit: The fraction looks like this:



enter image description here



You can barely see it, but there is a single denominator, and the numerator is huge. Is there a way to write the numerator automatically across multiple lines?






amsmath fractions breqn







share|improve this question
















I'm trying to use a Computer Algebra System to learn something about an algebraic expression, and this is what it gives me as a result in LaTex:



documentclass{article}

usepackage{breqn}



begin{document}



begin{dmath}

    frac{e_{0} n_{0} left(- n_{0} p_{0} + n_{0} r_{0} + n_{0} left(p_{0} - q_{0}right) - n_{1} p_{1} + n_{1} r_{1} + n_{1} left(p_{1} - q_{1}right) - n_{2} p_{2} + n_{2} r_{2} + n_{2} left(p_{2} - q_{2}right)right) + e_{1} n_{1} left(- n_{0} p_{0} + n_{0} r_{0} + n_{0} left(p_{0} - q_{0}right) - n_{1} p_{1} + n_{1} r_{1} + n_{1} left(p_{1} - q_{1}right) - n_{2} p_{2} + n_{2} r_{2} + n_{2} left(p_{2} - q_{2}right)right) - e_{10} left(left(- p_{1} + r_{1}right) left(n_{0} left(p_{0} - q_{0}right) + n_{1} left(p_{1} - q_{1}right) + n_{2} left(p_{2} - q_{2}right)right) + left(p_{1} - q_{1}right) left(n_{0} p_{0} - n_{0} r_{0} + n_{1} p_{1} - n_{1} r_{1} + n_{2} p_{2} - n_{2} r_{2}right)right) - e_{11} left(left(- p_{2} + r_{2}right) left(n_{0} left(p_{0} - q_{0}right) + n_{1} left(p_{1} - q_{1}right) + n_{2} left(p_{2} - q_{2}right)right) + left(p_{2} - q_{2}right) left(n_{0} p_{0} - n_{0} r_{0} + n_{1} p_{1} - n_{1} r_{1} + n_{2} p_{2} - n_{2} r_{2}right)right) + e_{2} n_{2} left(- n_{0} p_{0} + n_{0} r_{0} + n_{0} left(p_{0} - q_{0}right) - n_{1} p_{1} + n_{1} r_{1} + n_{1} left(p_{1} - q_{1}right) - n_{2} p_{2} + n_{2} r_{2} + n_{2} left(p_{2} - q_{2}right)right) - e_{9} left(left(- p_{0} + r_{0}right) left(n_{0} left(p_{0} - q_{0}right) + n_{1} left(p_{1} - q_{1}right) + n_{2} left(p_{2} - q_{2}right)right) + left(p_{0} - q_{0}right) left(n_{0} p_{0} - n_{0} r_{0} + n_{1} p_{1} - n_{1} r_{1} + n_{2} p_{2} - n_{2} r_{2}right)right) + left(e_{3} n_{0} + e_{4} n_{1} + e_{5} n_{2}right) left(n_{0} p_{0} - n_{0} r_{0} + n_{1} p_{1} - n_{1} r_{1} + n_{2} p_{2} - n_{2} r_{2}right) - left(e_{6} n_{0} + e_{7} n_{1} + e_{8} n_{2}right) left(n_{0} left(p_{0} - q_{0}right) + n_{1} left(p_{1} - q_{1}right) + n_{2} left(p_{2} - q_{2}right)right)}{left(n_{0} left(p_{0} - q_{0}right) + n_{1} left(p_{1} - q_{1}right) + n_{2} left(p_{2} - q_{2}right)right)^{2}}

end{dmath}



end{document}


It is a huge fraction, that gets cut when I try to compile this to PDF:



enter image description here



Is there an automagic way to cut this fraction in multiple lines in LaTex? If you look at the LaTex source code, searching for sensible break points to be manually inserted in such expressions will not be fun.



Edit: The fraction looks like this:



enter image description here



You can barely see it, but there is a single denominator, and the numerator is huge. Is there a way to write the numerator automatically across multiple lines?






amsmath fractions breqn




amsmath fractions breqn






share|improve this question















share|improve this question













share|improve this question




share|improve this question








edited 5 mins ago









Cœur

1054




1054










asked 4 hours ago









tmarictmaric

4411416




4411416








  • 3





    Well, this is not a TeX's problem. Tell us how the result should look like and there should be a way how to accomplish this. However, with my typography hat on, there is no good solution that keeps the fraction as a fraction.

    – yo'
    4 hours ago














  • 3





    Well, this is not a TeX's problem. Tell us how the result should look like and there should be a way how to accomplish this. However, with my typography hat on, there is no good solution that keeps the fraction as a fraction.

    – yo'
    4 hours ago








3




3





Well, this is not a TeX's problem. Tell us how the result should look like and there should be a way how to accomplish this. However, with my typography hat on, there is no good solution that keeps the fraction as a fraction.

– yo'
4 hours ago





Well, this is not a TeX's problem. Tell us how the result should look like and there should be a way how to accomplish this. However, with my typography hat on, there is no good solution that keeps the fraction as a fraction.

– yo'
4 hours ago










2 Answers
2






active

oldest

votes


















3














Not automagically. I removed the left and right around long expressions, keeping them only for the differences pi – qi and similar.



documentclass{article}

usepackage{amsmath}



begin{document}



begin{equation}

begin{gathered}

frac{

  ;

  parbox{0.8displaywidth}{raggedrightleftskip=1emhspace{-1em}$

    e_{0} n_{0} (- n_{0} p_{0} + n_{0} r_{0} + n_{0} 

    left(p_{0} - q_{0}right) - n_{1} p_{1} + n_{1} r_{1} + n_{1} 

    left(p_{1} - q_{1}right) - n_{2} p_{2} + n_{2} r_{2} + n_{2}

    left(p_{2} - q_{2}right)) + e_{1} n_{1}

    (- n_{0} p_{0} + n_{0} r_{0} + n_{0} left(p_{0} - q_{0}right) 

    - n_{1} p_{1} + n_{1} r_{1} + n_{1} left(p_{1} - q_{1}right) - 

    n_{2} p_{2} + n_{2} r_{2} + n_{2} left(p_{2} - q_{2}right))

    - e_{10} (left(- p_{1} + r_{1}right) 

   (n_{0} left(p_{0} - q_{0}right) + n_{1} left(p_{1} - q_{1}right) 

   + n_{2} left(p_{2} - q_{2}right)) + left(p_{1} - q_{1}right)

   (n_{0} p_{0} - n_{0} r_{0} + n_{1} p_{1} - n_{1} r_{1} + 

   n_{2} p_{2} - n_{2} r_{2})) 

   - e_{11} (left(- p_{2} + r_{2}right)

   (n_{0} left(p_{0} - q_{0}right) + n_{1} left(p_{1} - q_{1}right)

   + n_{2} left(p_{2} - q_{2}right)) + left(p_{2} - q_{2}right) 

   (n_{0} p_{0} - n_{0} r_{0} + n_{1} p_{1} - n_{1} r_{1} + 

   n_{2} p_{2} - n_{2} r_{2})) + e_{2} n_{2} 

   (- n_{0} p_{0} + n_{0} r_{0} + n_{0} left(p_{0} - q_{0}right) 

   - n_{1} p_{1} + n_{1} r_{1} + n_{1} left(p_{1} - q_{1}right)

   - n_{2} p_{2} + n_{2} r_{2} + n_{2} left(p_{2} - q_{2}right))

   - e_{9} (left(- p_{0} + r_{0}right)

   (n_{0} left(p_{0} - q_{0}right) + n_{1} left(p_{1} - q_{1}right)

   + n_{2} left(p_{2} - q_{2}right))

   + left(p_{0} - q_{0}right) (n_{0} p_{0}

   - n_{0} r_{0} + n_{1} p_{1} - n_{1} r_{1} + n_{2} p_{2}

   - n_{2} r_{2})) + (e_{3} n_{0} + e_{4} n_{1}

   + e_{5} n_{2}) (n_{0} p_{0} - n_{0} r_{0}

   + n_{1} p_{1} - n_{1} r_{1} + n_{2} p_{2} - n_{2} r_{2})

   - (e_{6} n_{0} + e_{7} n_{1} + e_{8} n_{2})

   (n_{0} left(p_{0} - q_{0}right) + n_{1}

   left(p_{1} - q_{1}right) + n_{2} left(p_{2} - q_{2}right))

  $};

}{

  (n_{0} (p_{0} - q_{0}) + n_{1} (p_{1} - q_{1}) + n_{2} (p_{2} - q_{2}))^{2}

}

end{gathered}

end{equation}



end{document}


enter image description here






share|improve this answer































    3














    Not automagically, I'm afraid. First and foremost, don't use left and right sizing directives: Not only do they not succeed in enlarging any of the parentheses, they also prevent TeX from inserting line breaks within the scope of left-right pairs. Second, use a parbox directive, and typeset the equation in inline-math mode (no frac terms) inside the parbox. Why inline-math mode? Because TeX allows line-breaking for inline-math material (as long as there are no left-right disturbances).



    To set off the start and end of the numerator and denominator term, use curly braces .



    Optionally, use square brackets -- [ and and ] -- instead of the "outer" round parentheses.



    That said, I'm not sure what your readers are supposed to take away -- let alone remember for more than three seconds -- from looking at the following expression...



    enter image description here



    documentclass{article}
    
begin{document}
    

    
[ 
    
parbox{0.8textwidth}{$bigl{
    
  e_0 n_0 [- n_0 (p_0 - r_0) + n_0 (p_0 - q_0) 
    
           - n_1 (p_1 - r_1) + n_1 (p_1 - q_1) 
    
           - n_2 (p_2 - r_2) + n_2 (p_2 - q_2)] 
    
+ e_1 n_1 [- n_0 (p_0 - r_0) + n_0 (p_0 - q_0) 
    
           - n_1 (p_1 - r_1) + n_1 (p_1 - q_1) 
    
           - n_2 (p_2 - r_2) + n_2 (p_2 - q_2)] 
    
- e_{10} [(- p_1 + r_1) [n_0 (p_0 - q_0) + n_1 (p_1 - q_1) + n_2 (p_2 - q_2)] 
    
          + (p_1 - q_1) [n_0 (p_0 - r_0) + n_1 (p_1 - r_1) + n_2 (p_2 - r_2)]] 
    
- e_{11} [(- p_2 + r_2) [n_0 (p_0 - q_0) + n_1 (p_1 - q_1) + n_2 (p_2 - q_2)] 
    
          + (p_2 - q_2) [n_0 (p_0 - r_0) + n_1 (p_1 - r_1) + n_2 (p_2 - r_2)]] 
    
+ e_2 n_2 [- n_0 (p_0 - r_0) + n_0 (p_0 - q_0) 
    
           - n_1 (p_1 - r_1) + n_1 (p_1 - q_1) 
    
           - n_2 (p_2 - r_2) + n_2 (p_2 - q_2)] 
    
- e_9 [(- p_0 + r_0) [n_0 (p_0 - q_0) + n_1 (p_1 - q_1) + n_2 (p_2 - q_2)] 
    
       + (p_0 - q_0) [n_0 (p_0 - r_0) + n_1 (p_1 - r_1) + n_2 (p_2 - r_2)]] 
    
+ [e_3 n_0 + e_4 n_1 + e_5 n_2] [n_0 (p_0 - r_0) + n_1 (p_1 - r_1) + n_2 (p_2 - r_2)] 
    
- [e_6 n_0 + e_7 n_1 + e_8 n_2] [n_0 (p_0 - q_0) + n_1 (p_1 - q_1) + n_2 (p_2 - q_2)]
    
bigr}big/bigl{
    
n_0 (p_0 - q_0) + n_1 (p_1 - q_1) + n_2 (p_2 - q_2)
    
bigr}^2 $}
    
]
    

    
end{document}





    share|improve this answer

























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      2 Answers
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      3














      Not automagically. I removed the left and right around long expressions, keeping them only for the differences pi – qi and similar.



      documentclass{article}
      
usepackage{amsmath}
      

      
begin{document}
      

      
begin{equation}
      
begin{gathered}
      
frac{
      
  ;
      
  parbox{0.8displaywidth}{raggedrightleftskip=1emhspace{-1em}$
      
    e_{0} n_{0} (- n_{0} p_{0} + n_{0} r_{0} + n_{0} 
      
    left(p_{0} - q_{0}right) - n_{1} p_{1} + n_{1} r_{1} + n_{1} 
      
    left(p_{1} - q_{1}right) - n_{2} p_{2} + n_{2} r_{2} + n_{2}
      
    left(p_{2} - q_{2}right)) + e_{1} n_{1}
      
    (- n_{0} p_{0} + n_{0} r_{0} + n_{0} left(p_{0} - q_{0}right) 
      
    - n_{1} p_{1} + n_{1} r_{1} + n_{1} left(p_{1} - q_{1}right) - 
      
    n_{2} p_{2} + n_{2} r_{2} + n_{2} left(p_{2} - q_{2}right))
      
    - e_{10} (left(- p_{1} + r_{1}right) 
      
   (n_{0} left(p_{0} - q_{0}right) + n_{1} left(p_{1} - q_{1}right) 
      
   + n_{2} left(p_{2} - q_{2}right)) + left(p_{1} - q_{1}right)
      
   (n_{0} p_{0} - n_{0} r_{0} + n_{1} p_{1} - n_{1} r_{1} + 
      
   n_{2} p_{2} - n_{2} r_{2})) 
      
   - e_{11} (left(- p_{2} + r_{2}right)
      
   (n_{0} left(p_{0} - q_{0}right) + n_{1} left(p_{1} - q_{1}right)
      
   + n_{2} left(p_{2} - q_{2}right)) + left(p_{2} - q_{2}right) 
      
   (n_{0} p_{0} - n_{0} r_{0} + n_{1} p_{1} - n_{1} r_{1} + 
      
   n_{2} p_{2} - n_{2} r_{2})) + e_{2} n_{2} 
      
   (- n_{0} p_{0} + n_{0} r_{0} + n_{0} left(p_{0} - q_{0}right) 
      
   - n_{1} p_{1} + n_{1} r_{1} + n_{1} left(p_{1} - q_{1}right)
      
   - n_{2} p_{2} + n_{2} r_{2} + n_{2} left(p_{2} - q_{2}right))
      
   - e_{9} (left(- p_{0} + r_{0}right)
      
   (n_{0} left(p_{0} - q_{0}right) + n_{1} left(p_{1} - q_{1}right)
      
   + n_{2} left(p_{2} - q_{2}right))
      
   + left(p_{0} - q_{0}right) (n_{0} p_{0}
      
   - n_{0} r_{0} + n_{1} p_{1} - n_{1} r_{1} + n_{2} p_{2}
      
   - n_{2} r_{2})) + (e_{3} n_{0} + e_{4} n_{1}
      
   + e_{5} n_{2}) (n_{0} p_{0} - n_{0} r_{0}
      
   + n_{1} p_{1} - n_{1} r_{1} + n_{2} p_{2} - n_{2} r_{2})
      
   - (e_{6} n_{0} + e_{7} n_{1} + e_{8} n_{2})
      
   (n_{0} left(p_{0} - q_{0}right) + n_{1}
      
   left(p_{1} - q_{1}right) + n_{2} left(p_{2} - q_{2}right))
      
  $};
      
}{
      
  (n_{0} (p_{0} - q_{0}) + n_{1} (p_{1} - q_{1}) + n_{2} (p_{2} - q_{2}))^{2}
      
}
      
end{gathered}
      
end{equation}
      

      
end{document}


      enter image description here






      share|improve this answer




























        3














        Not automagically. I removed the left and right around long expressions, keeping them only for the differences pi – qi and similar.



        documentclass{article}
        
usepackage{amsmath}
        

        
begin{document}
        

        
begin{equation}
        
begin{gathered}
        
frac{
        
  ;
        
  parbox{0.8displaywidth}{raggedrightleftskip=1emhspace{-1em}$
        
    e_{0} n_{0} (- n_{0} p_{0} + n_{0} r_{0} + n_{0} 
        
    left(p_{0} - q_{0}right) - n_{1} p_{1} + n_{1} r_{1} + n_{1} 
        
    left(p_{1} - q_{1}right) - n_{2} p_{2} + n_{2} r_{2} + n_{2}
        
    left(p_{2} - q_{2}right)) + e_{1} n_{1}
        
    (- n_{0} p_{0} + n_{0} r_{0} + n_{0} left(p_{0} - q_{0}right) 
        
    - n_{1} p_{1} + n_{1} r_{1} + n_{1} left(p_{1} - q_{1}right) - 
        
    n_{2} p_{2} + n_{2} r_{2} + n_{2} left(p_{2} - q_{2}right))
        
    - e_{10} (left(- p_{1} + r_{1}right) 
        
   (n_{0} left(p_{0} - q_{0}right) + n_{1} left(p_{1} - q_{1}right) 
        
   + n_{2} left(p_{2} - q_{2}right)) + left(p_{1} - q_{1}right)
        
   (n_{0} p_{0} - n_{0} r_{0} + n_{1} p_{1} - n_{1} r_{1} + 
        
   n_{2} p_{2} - n_{2} r_{2})) 
        
   - e_{11} (left(- p_{2} + r_{2}right)
        
   (n_{0} left(p_{0} - q_{0}right) + n_{1} left(p_{1} - q_{1}right)
        
   + n_{2} left(p_{2} - q_{2}right)) + left(p_{2} - q_{2}right) 
        
   (n_{0} p_{0} - n_{0} r_{0} + n_{1} p_{1} - n_{1} r_{1} + 
        
   n_{2} p_{2} - n_{2} r_{2})) + e_{2} n_{2} 
        
   (- n_{0} p_{0} + n_{0} r_{0} + n_{0} left(p_{0} - q_{0}right) 
        
   - n_{1} p_{1} + n_{1} r_{1} + n_{1} left(p_{1} - q_{1}right)
        
   - n_{2} p_{2} + n_{2} r_{2} + n_{2} left(p_{2} - q_{2}right))
        
   - e_{9} (left(- p_{0} + r_{0}right)
        
   (n_{0} left(p_{0} - q_{0}right) + n_{1} left(p_{1} - q_{1}right)
        
   + n_{2} left(p_{2} - q_{2}right))
        
   + left(p_{0} - q_{0}right) (n_{0} p_{0}
        
   - n_{0} r_{0} + n_{1} p_{1} - n_{1} r_{1} + n_{2} p_{2}
        
   - n_{2} r_{2})) + (e_{3} n_{0} + e_{4} n_{1}
        
   + e_{5} n_{2}) (n_{0} p_{0} - n_{0} r_{0}
        
   + n_{1} p_{1} - n_{1} r_{1} + n_{2} p_{2} - n_{2} r_{2})
        
   - (e_{6} n_{0} + e_{7} n_{1} + e_{8} n_{2})
        
   (n_{0} left(p_{0} - q_{0}right) + n_{1}
        
   left(p_{1} - q_{1}right) + n_{2} left(p_{2} - q_{2}right))
        
  $};
        
}{
        
  (n_{0} (p_{0} - q_{0}) + n_{1} (p_{1} - q_{1}) + n_{2} (p_{2} - q_{2}))^{2}
        
}
        
end{gathered}
        
end{equation}
        

        
end{document}


        enter image description here






        share|improve this answer


























          3












          3








          3







          Not automagically. I removed the left and right around long expressions, keeping them only for the differences pi – qi and similar.



          documentclass{article}
          
usepackage{amsmath}
          

          
begin{document}
          

          
begin{equation}
          
begin{gathered}
          
frac{
          
  ;
          
  parbox{0.8displaywidth}{raggedrightleftskip=1emhspace{-1em}$
          
    e_{0} n_{0} (- n_{0} p_{0} + n_{0} r_{0} + n_{0} 
          
    left(p_{0} - q_{0}right) - n_{1} p_{1} + n_{1} r_{1} + n_{1} 
          
    left(p_{1} - q_{1}right) - n_{2} p_{2} + n_{2} r_{2} + n_{2}
          
    left(p_{2} - q_{2}right)) + e_{1} n_{1}
          
    (- n_{0} p_{0} + n_{0} r_{0} + n_{0} left(p_{0} - q_{0}right) 
          
    - n_{1} p_{1} + n_{1} r_{1} + n_{1} left(p_{1} - q_{1}right) - 
          
    n_{2} p_{2} + n_{2} r_{2} + n_{2} left(p_{2} - q_{2}right))
          
    - e_{10} (left(- p_{1} + r_{1}right) 
          
   (n_{0} left(p_{0} - q_{0}right) + n_{1} left(p_{1} - q_{1}right) 
          
   + n_{2} left(p_{2} - q_{2}right)) + left(p_{1} - q_{1}right)
          
   (n_{0} p_{0} - n_{0} r_{0} + n_{1} p_{1} - n_{1} r_{1} + 
          
   n_{2} p_{2} - n_{2} r_{2})) 
          
   - e_{11} (left(- p_{2} + r_{2}right)
          
   (n_{0} left(p_{0} - q_{0}right) + n_{1} left(p_{1} - q_{1}right)
          
   + n_{2} left(p_{2} - q_{2}right)) + left(p_{2} - q_{2}right) 
          
   (n_{0} p_{0} - n_{0} r_{0} + n_{1} p_{1} - n_{1} r_{1} + 
          
   n_{2} p_{2} - n_{2} r_{2})) + e_{2} n_{2} 
          
   (- n_{0} p_{0} + n_{0} r_{0} + n_{0} left(p_{0} - q_{0}right) 
          
   - n_{1} p_{1} + n_{1} r_{1} + n_{1} left(p_{1} - q_{1}right)
          
   - n_{2} p_{2} + n_{2} r_{2} + n_{2} left(p_{2} - q_{2}right))
          
   - e_{9} (left(- p_{0} + r_{0}right)
          
   (n_{0} left(p_{0} - q_{0}right) + n_{1} left(p_{1} - q_{1}right)
          
   + n_{2} left(p_{2} - q_{2}right))
          
   + left(p_{0} - q_{0}right) (n_{0} p_{0}
          
   - n_{0} r_{0} + n_{1} p_{1} - n_{1} r_{1} + n_{2} p_{2}
          
   - n_{2} r_{2})) + (e_{3} n_{0} + e_{4} n_{1}
          
   + e_{5} n_{2}) (n_{0} p_{0} - n_{0} r_{0}
          
   + n_{1} p_{1} - n_{1} r_{1} + n_{2} p_{2} - n_{2} r_{2})
          
   - (e_{6} n_{0} + e_{7} n_{1} + e_{8} n_{2})
          
   (n_{0} left(p_{0} - q_{0}right) + n_{1}
          
   left(p_{1} - q_{1}right) + n_{2} left(p_{2} - q_{2}right))
          
  $};
          
}{
          
  (n_{0} (p_{0} - q_{0}) + n_{1} (p_{1} - q_{1}) + n_{2} (p_{2} - q_{2}))^{2}
          
}
          
end{gathered}
          
end{equation}
          

          
end{document}


          enter image description here






          share|improve this answer













          Not automagically. I removed the left and right around long expressions, keeping them only for the differences pi – qi and similar.



          documentclass{article}
          
usepackage{amsmath}
          

          
begin{document}
          

          
begin{equation}
          
begin{gathered}
          
frac{
          
  ;
          
  parbox{0.8displaywidth}{raggedrightleftskip=1emhspace{-1em}$
          
    e_{0} n_{0} (- n_{0} p_{0} + n_{0} r_{0} + n_{0} 
          
    left(p_{0} - q_{0}right) - n_{1} p_{1} + n_{1} r_{1} + n_{1} 
          
    left(p_{1} - q_{1}right) - n_{2} p_{2} + n_{2} r_{2} + n_{2}
          
    left(p_{2} - q_{2}right)) + e_{1} n_{1}
          
    (- n_{0} p_{0} + n_{0} r_{0} + n_{0} left(p_{0} - q_{0}right) 
          
    - n_{1} p_{1} + n_{1} r_{1} + n_{1} left(p_{1} - q_{1}right) - 
          
    n_{2} p_{2} + n_{2} r_{2} + n_{2} left(p_{2} - q_{2}right))
          
    - e_{10} (left(- p_{1} + r_{1}right) 
          
   (n_{0} left(p_{0} - q_{0}right) + n_{1} left(p_{1} - q_{1}right) 
          
   + n_{2} left(p_{2} - q_{2}right)) + left(p_{1} - q_{1}right)
          
   (n_{0} p_{0} - n_{0} r_{0} + n_{1} p_{1} - n_{1} r_{1} + 
          
   n_{2} p_{2} - n_{2} r_{2})) 
          
   - e_{11} (left(- p_{2} + r_{2}right)
          
   (n_{0} left(p_{0} - q_{0}right) + n_{1} left(p_{1} - q_{1}right)
          
   + n_{2} left(p_{2} - q_{2}right)) + left(p_{2} - q_{2}right) 
          
   (n_{0} p_{0} - n_{0} r_{0} + n_{1} p_{1} - n_{1} r_{1} + 
          
   n_{2} p_{2} - n_{2} r_{2})) + e_{2} n_{2} 
          
   (- n_{0} p_{0} + n_{0} r_{0} + n_{0} left(p_{0} - q_{0}right) 
          
   - n_{1} p_{1} + n_{1} r_{1} + n_{1} left(p_{1} - q_{1}right)
          
   - n_{2} p_{2} + n_{2} r_{2} + n_{2} left(p_{2} - q_{2}right))
          
   - e_{9} (left(- p_{0} + r_{0}right)
          
   (n_{0} left(p_{0} - q_{0}right) + n_{1} left(p_{1} - q_{1}right)
          
   + n_{2} left(p_{2} - q_{2}right))
          
   + left(p_{0} - q_{0}right) (n_{0} p_{0}
          
   - n_{0} r_{0} + n_{1} p_{1} - n_{1} r_{1} + n_{2} p_{2}
          
   - n_{2} r_{2})) + (e_{3} n_{0} + e_{4} n_{1}
          
   + e_{5} n_{2}) (n_{0} p_{0} - n_{0} r_{0}
          
   + n_{1} p_{1} - n_{1} r_{1} + n_{2} p_{2} - n_{2} r_{2})
          
   - (e_{6} n_{0} + e_{7} n_{1} + e_{8} n_{2})
          
   (n_{0} left(p_{0} - q_{0}right) + n_{1}
          
   left(p_{1} - q_{1}right) + n_{2} left(p_{2} - q_{2}right))
          
  $};
          
}{
          
  (n_{0} (p_{0} - q_{0}) + n_{1} (p_{1} - q_{1}) + n_{2} (p_{2} - q_{2}))^{2}
          
}
          
end{gathered}
          
end{equation}
          

          
end{document}


          enter image description here







          share|improve this answer












          share|improve this answer



          share|improve this answer










          answered 4 hours ago









          egregegreg

          714k8618973184




          714k8618973184























              3














              Not automagically, I'm afraid. First and foremost, don't use left and right sizing directives: Not only do they not succeed in enlarging any of the parentheses, they also prevent TeX from inserting line breaks within the scope of left-right pairs. Second, use a parbox directive, and typeset the equation in inline-math mode (no frac terms) inside the parbox. Why inline-math mode? Because TeX allows line-breaking for inline-math material (as long as there are no left-right disturbances).



              To set off the start and end of the numerator and denominator term, use curly braces .



              Optionally, use square brackets -- [ and and ] -- instead of the "outer" round parentheses.



              That said, I'm not sure what your readers are supposed to take away -- let alone remember for more than three seconds -- from looking at the following expression...



              enter image description here



              documentclass{article}
              
begin{document}
              

              
[ 
              
parbox{0.8textwidth}{$bigl{
              
  e_0 n_0 [- n_0 (p_0 - r_0) + n_0 (p_0 - q_0) 
              
           - n_1 (p_1 - r_1) + n_1 (p_1 - q_1) 
              
           - n_2 (p_2 - r_2) + n_2 (p_2 - q_2)] 
              
+ e_1 n_1 [- n_0 (p_0 - r_0) + n_0 (p_0 - q_0) 
              
           - n_1 (p_1 - r_1) + n_1 (p_1 - q_1) 
              
           - n_2 (p_2 - r_2) + n_2 (p_2 - q_2)] 
              
- e_{10} [(- p_1 + r_1) [n_0 (p_0 - q_0) + n_1 (p_1 - q_1) + n_2 (p_2 - q_2)] 
              
          + (p_1 - q_1) [n_0 (p_0 - r_0) + n_1 (p_1 - r_1) + n_2 (p_2 - r_2)]] 
              
- e_{11} [(- p_2 + r_2) [n_0 (p_0 - q_0) + n_1 (p_1 - q_1) + n_2 (p_2 - q_2)] 
              
          + (p_2 - q_2) [n_0 (p_0 - r_0) + n_1 (p_1 - r_1) + n_2 (p_2 - r_2)]] 
              
+ e_2 n_2 [- n_0 (p_0 - r_0) + n_0 (p_0 - q_0) 
              
           - n_1 (p_1 - r_1) + n_1 (p_1 - q_1) 
              
           - n_2 (p_2 - r_2) + n_2 (p_2 - q_2)] 
              
- e_9 [(- p_0 + r_0) [n_0 (p_0 - q_0) + n_1 (p_1 - q_1) + n_2 (p_2 - q_2)] 
              
       + (p_0 - q_0) [n_0 (p_0 - r_0) + n_1 (p_1 - r_1) + n_2 (p_2 - r_2)]] 
              
+ [e_3 n_0 + e_4 n_1 + e_5 n_2] [n_0 (p_0 - r_0) + n_1 (p_1 - r_1) + n_2 (p_2 - r_2)] 
              
- [e_6 n_0 + e_7 n_1 + e_8 n_2] [n_0 (p_0 - q_0) + n_1 (p_1 - q_1) + n_2 (p_2 - q_2)]
              
bigr}big/bigl{
              
n_0 (p_0 - q_0) + n_1 (p_1 - q_1) + n_2 (p_2 - q_2)
              
bigr}^2 $}
              
]
              

              
end{document}





              share|improve this answer






























                3














                Not automagically, I'm afraid. First and foremost, don't use left and right sizing directives: Not only do they not succeed in enlarging any of the parentheses, they also prevent TeX from inserting line breaks within the scope of left-right pairs. Second, use a parbox directive, and typeset the equation in inline-math mode (no frac terms) inside the parbox. Why inline-math mode? Because TeX allows line-breaking for inline-math material (as long as there are no left-right disturbances).



                To set off the start and end of the numerator and denominator term, use curly braces .



                Optionally, use square brackets -- [ and and ] -- instead of the "outer" round parentheses.



                That said, I'm not sure what your readers are supposed to take away -- let alone remember for more than three seconds -- from looking at the following expression...



                enter image description here



                documentclass{article}
                
begin{document}
                

                
[ 
                
parbox{0.8textwidth}{$bigl{
                
  e_0 n_0 [- n_0 (p_0 - r_0) + n_0 (p_0 - q_0) 
                
           - n_1 (p_1 - r_1) + n_1 (p_1 - q_1) 
                
           - n_2 (p_2 - r_2) + n_2 (p_2 - q_2)] 
                
+ e_1 n_1 [- n_0 (p_0 - r_0) + n_0 (p_0 - q_0) 
                
           - n_1 (p_1 - r_1) + n_1 (p_1 - q_1) 
                
           - n_2 (p_2 - r_2) + n_2 (p_2 - q_2)] 
                
- e_{10} [(- p_1 + r_1) [n_0 (p_0 - q_0) + n_1 (p_1 - q_1) + n_2 (p_2 - q_2)] 
                
          + (p_1 - q_1) [n_0 (p_0 - r_0) + n_1 (p_1 - r_1) + n_2 (p_2 - r_2)]] 
                
- e_{11} [(- p_2 + r_2) [n_0 (p_0 - q_0) + n_1 (p_1 - q_1) + n_2 (p_2 - q_2)] 
                
          + (p_2 - q_2) [n_0 (p_0 - r_0) + n_1 (p_1 - r_1) + n_2 (p_2 - r_2)]] 
                
+ e_2 n_2 [- n_0 (p_0 - r_0) + n_0 (p_0 - q_0) 
                
           - n_1 (p_1 - r_1) + n_1 (p_1 - q_1) 
                
           - n_2 (p_2 - r_2) + n_2 (p_2 - q_2)] 
                
- e_9 [(- p_0 + r_0) [n_0 (p_0 - q_0) + n_1 (p_1 - q_1) + n_2 (p_2 - q_2)] 
                
       + (p_0 - q_0) [n_0 (p_0 - r_0) + n_1 (p_1 - r_1) + n_2 (p_2 - r_2)]] 
                
+ [e_3 n_0 + e_4 n_1 + e_5 n_2] [n_0 (p_0 - r_0) + n_1 (p_1 - r_1) + n_2 (p_2 - r_2)] 
                
- [e_6 n_0 + e_7 n_1 + e_8 n_2] [n_0 (p_0 - q_0) + n_1 (p_1 - q_1) + n_2 (p_2 - q_2)]
                
bigr}big/bigl{
                
n_0 (p_0 - q_0) + n_1 (p_1 - q_1) + n_2 (p_2 - q_2)
                
bigr}^2 $}
                
]
                

                
end{document}





                share|improve this answer




























                  3












                  3








                  3







                  Not automagically, I'm afraid. First and foremost, don't use left and right sizing directives: Not only do they not succeed in enlarging any of the parentheses, they also prevent TeX from inserting line breaks within the scope of left-right pairs. Second, use a parbox directive, and typeset the equation in inline-math mode (no frac terms) inside the parbox. Why inline-math mode? Because TeX allows line-breaking for inline-math material (as long as there are no left-right disturbances).



                  To set off the start and end of the numerator and denominator term, use curly braces .



                  Optionally, use square brackets -- [ and and ] -- instead of the "outer" round parentheses.



                  That said, I'm not sure what your readers are supposed to take away -- let alone remember for more than three seconds -- from looking at the following expression...



                  enter image description here



                  documentclass{article}
                  
begin{document}
                  

                  
[ 
                  
parbox{0.8textwidth}{$bigl{
                  
  e_0 n_0 [- n_0 (p_0 - r_0) + n_0 (p_0 - q_0) 
                  
           - n_1 (p_1 - r_1) + n_1 (p_1 - q_1) 
                  
           - n_2 (p_2 - r_2) + n_2 (p_2 - q_2)] 
                  
+ e_1 n_1 [- n_0 (p_0 - r_0) + n_0 (p_0 - q_0) 
                  
           - n_1 (p_1 - r_1) + n_1 (p_1 - q_1) 
                  
           - n_2 (p_2 - r_2) + n_2 (p_2 - q_2)] 
                  
- e_{10} [(- p_1 + r_1) [n_0 (p_0 - q_0) + n_1 (p_1 - q_1) + n_2 (p_2 - q_2)] 
                  
          + (p_1 - q_1) [n_0 (p_0 - r_0) + n_1 (p_1 - r_1) + n_2 (p_2 - r_2)]] 
                  
- e_{11} [(- p_2 + r_2) [n_0 (p_0 - q_0) + n_1 (p_1 - q_1) + n_2 (p_2 - q_2)] 
                  
          + (p_2 - q_2) [n_0 (p_0 - r_0) + n_1 (p_1 - r_1) + n_2 (p_2 - r_2)]] 
                  
+ e_2 n_2 [- n_0 (p_0 - r_0) + n_0 (p_0 - q_0) 
                  
           - n_1 (p_1 - r_1) + n_1 (p_1 - q_1) 
                  
           - n_2 (p_2 - r_2) + n_2 (p_2 - q_2)] 
                  
- e_9 [(- p_0 + r_0) [n_0 (p_0 - q_0) + n_1 (p_1 - q_1) + n_2 (p_2 - q_2)] 
                  
       + (p_0 - q_0) [n_0 (p_0 - r_0) + n_1 (p_1 - r_1) + n_2 (p_2 - r_2)]] 
                  
+ [e_3 n_0 + e_4 n_1 + e_5 n_2] [n_0 (p_0 - r_0) + n_1 (p_1 - r_1) + n_2 (p_2 - r_2)] 
                  
- [e_6 n_0 + e_7 n_1 + e_8 n_2] [n_0 (p_0 - q_0) + n_1 (p_1 - q_1) + n_2 (p_2 - q_2)]
                  
bigr}big/bigl{
                  
n_0 (p_0 - q_0) + n_1 (p_1 - q_1) + n_2 (p_2 - q_2)
                  
bigr}^2 $}
                  
]
                  

                  
end{document}





                  share|improve this answer















                  Not automagically, I'm afraid. First and foremost, don't use left and right sizing directives: Not only do they not succeed in enlarging any of the parentheses, they also prevent TeX from inserting line breaks within the scope of left-right pairs. Second, use a parbox directive, and typeset the equation in inline-math mode (no frac terms) inside the parbox. Why inline-math mode? Because TeX allows line-breaking for inline-math material (as long as there are no left-right disturbances).



                  To set off the start and end of the numerator and denominator term, use curly braces .



                  Optionally, use square brackets -- [ and and ] -- instead of the "outer" round parentheses.



                  That said, I'm not sure what your readers are supposed to take away -- let alone remember for more than three seconds -- from looking at the following expression...



                  enter image description here



                  documentclass{article}
                  
begin{document}
                  

                  
[ 
                  
parbox{0.8textwidth}{$bigl{
                  
  e_0 n_0 [- n_0 (p_0 - r_0) + n_0 (p_0 - q_0) 
                  
           - n_1 (p_1 - r_1) + n_1 (p_1 - q_1) 
                  
           - n_2 (p_2 - r_2) + n_2 (p_2 - q_2)] 
                  
+ e_1 n_1 [- n_0 (p_0 - r_0) + n_0 (p_0 - q_0) 
                  
           - n_1 (p_1 - r_1) + n_1 (p_1 - q_1) 
                  
           - n_2 (p_2 - r_2) + n_2 (p_2 - q_2)] 
                  
- e_{10} [(- p_1 + r_1) [n_0 (p_0 - q_0) + n_1 (p_1 - q_1) + n_2 (p_2 - q_2)] 
                  
          + (p_1 - q_1) [n_0 (p_0 - r_0) + n_1 (p_1 - r_1) + n_2 (p_2 - r_2)]] 
                  
- e_{11} [(- p_2 + r_2) [n_0 (p_0 - q_0) + n_1 (p_1 - q_1) + n_2 (p_2 - q_2)] 
                  
          + (p_2 - q_2) [n_0 (p_0 - r_0) + n_1 (p_1 - r_1) + n_2 (p_2 - r_2)]] 
                  
+ e_2 n_2 [- n_0 (p_0 - r_0) + n_0 (p_0 - q_0) 
                  
           - n_1 (p_1 - r_1) + n_1 (p_1 - q_1) 
                  
           - n_2 (p_2 - r_2) + n_2 (p_2 - q_2)] 
                  
- e_9 [(- p_0 + r_0) [n_0 (p_0 - q_0) + n_1 (p_1 - q_1) + n_2 (p_2 - q_2)] 
                  
       + (p_0 - q_0) [n_0 (p_0 - r_0) + n_1 (p_1 - r_1) + n_2 (p_2 - r_2)]] 
                  
+ [e_3 n_0 + e_4 n_1 + e_5 n_2] [n_0 (p_0 - r_0) + n_1 (p_1 - r_1) + n_2 (p_2 - r_2)] 
                  
- [e_6 n_0 + e_7 n_1 + e_8 n_2] [n_0 (p_0 - q_0) + n_1 (p_1 - q_1) + n_2 (p_2 - q_2)]
                  
bigr}big/bigl{
                  
n_0 (p_0 - q_0) + n_1 (p_1 - q_1) + n_2 (p_2 - q_2)
                  
bigr}^2 $}
                  
]
                  

                  
end{document}






                  share|improve this answer














                  share|improve this answer



                  share|improve this answer








                  edited 3 hours ago

























                  answered 4 hours ago









                  MicoMico

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                  276k30374763






























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