productivity tools

Question

I am using latex to write a mathematically dense document which has several hundred differential forms and products. There must be better ways than just typing out the whole equations line by line. Can any body suggest me some better productivity techniques which could reduce some of the work of debugging some of the equations.

I am pasting a part of equations which I have to write.

\begin{equation}
\begin{aligned}
    Energy^{(i)} & =   U^{(i)}_{1} + U^{(i)}_{2} + U^{(i)}_{3}\\
    U^{(1)}_{1} & =  \int_{a}^{b} \int_{0}^{\sigma_{rr}^{(1)}} \Big(\frac{(1+\nu)(\sigma_{rr}^{(1)})}{E1} - \frac{\nu (2(\sigma_{rr}^{(1)})+ \sigma_{z})}{E1} \Big) d(\sigma_{rr}^{(1)}) r dr dz \\
    U^{(1)}_{2} & = \int_{a}^{b} \int_{0}^{\sigma_{rz}^{(1)}} (1+\nu)\frac{(\sigma_{rz}^{(1)})}{E1} d(\sigma_{rz}^{(1)}) r dr dz \\
    U^{(1)}_{3} & =  \int_{a}^{b} \int_{0}^{\sigma_{zz}^{(1)}} \Big(\frac{(1+\nu)\sigma_{zz}^{(1)}}{2E1} -  \frac{\nu ((\sigma_{zz}^{(1)})+ 2\sigma_{rr}^{(1)})}{2 E1} \Big) d(\sigma_{zz}^{(1)}) r dr dz \\
    %
    % End of 1
    %
    U^{(2)}_{1} & =  \int_{b}^{c} \int_{0}^{\sigma_{rr}^{(2)}} \Big(\frac{(1+\nu)(\sigma_{rr}^{(2)})}{E2} - \frac{\nu (2(\sigma_{rr}^{(2)})+ \sigma_{z})}{E2} \Big) d(\sigma_{rr}^{(2)}) r dr dz \\
    U^{(2)}_{2} & = \int_{b}^{c} \int_{0}^{\sigma_{rz}^{(2)}} (1+\nu)\frac{(\sigma_{rz}^{(2)})}{E2} d(\sigma_{rz}^{(2)}) r dr dz \\
    U^{(2)}_{3} & =  \int_{b}^{c} \int_{0}^{\sigma_{zz}^{(2)}} \Big(\frac{(1+\nu)\sigma_{zz}^{(2)}}{2E2} -  \frac{\nu ((\sigma_{zz}^{(2)})+ 2\sigma_{rr}^{(2)})}{2 E2} \Big) d(\sigma_{zz}^{(2)}) r dr dz \\
    %
    % End of 2
    %
    U^{(3)}_{1} & =  \int_{c}^{d} \int_{0}^{\sigma_{rr}^{(3)}} \Big(\frac{(1+\nu)(\sigma_{rr}^{(3)})}{E3} - \frac{\nu (2(\sigma_{rr}^{(3)})+ \sigma_{z})}{E3} \Big) d(\sigma_{rr}^{(3)}) r dr dz \\
    U^{(3)}_{2} & = \int_{c}^{d} \int_{0}^{\sigma_{rz}^{(3)}} (1+\nu)\frac{(\sigma_{rz}^{(3)})}{E3} d(\sigma_{rz}^{(3)}) r dr dz \\
    U^{(3)}_{3} & =  \int_{c}^{d} \int_{0}^{\sigma_{zz}^{(3)}} \Big(\frac{(1+\nu)\sigma_{zz}^{(3)}}{2E3} -  \frac{\nu ((\sigma_{zz}^{(3)})+ 2\sigma_{rr}^{(3)})}{2 E3} \Big) d(\sigma_{zz}^{(3)}) r dr dz \\
    %
    % End of 3
    %   
\end{aligned}
\end{equation}

Answer 1

I would define some macros to handle the parts of the code that don't change.

Here's an example of something you can do:

\documentclass{article}
\usepackage{amsmath,amssymb}

\makeatletter

%% user macro translated into internal control sequence
%% to test whether short or long form.
\newcommand\intU{\ae@intU}
%% short form is flagged by a `*` immediately following
%% the control sequence.
\def\ae@intU{%%
  \@ifstar{\ae@intU@short}
          {\ae@intU@long}}

\def\ae@intU@short#1(#2){U^{(#2)}_{#1}}
%% There are three different forms the integral can take in the        
%% long form.  By testing on the first argument, we can determine      
%% which integral form to use.  This could have been handled using     
%% \ifcase.  I chose not to use \ifcase because it only works          
%% on numbers.  If you have integrals somehow indexed by some of token 
%% then this approach *should* work.                                   
\def\ae@intU@long#1(#2)_#3^#4{%%
  \if#11\ae@intUa{#2}{#3}{#4}\fi
  \if#12\ae@intUb{#2}{#3}{#4}\fi
  \if#13\ae@intUc{#2}{#3}{#4}\fi}

%% #1 superscript (<num>)
%% #2 lower bound of integration
%% #3 upper bound of integration
\def\ae@intUa#1#2#3{  \int_{#2}^{#3} \int_{0}^{\sigma_{rr}^{(#1)}} \Big(\frac{(1+\nu)(\sigma_{rr}^{(#1)})}{E#1} - \frac{\nu (2(\sigma_{rr}^{(#1)})+ \sigma_{z})}{E#1} \Big) d(\sigma_{rr}^{(#1)}) r dr dz }
\def\ae@intUb#1#2#3{  \int_{#2}^{#3} \int_{0}^{\sigma_{rz}^{(#1)}} (1+\nu)\frac{(\sigma_{rz}^{(#1)})}{E#1} d(\sigma_{rz}^{(#1)}) r dr dz  }
\def\ae@intUc#1#2#3{  \int_{#2}^{#3} \int_{0}^{\sigma_{zz}^{(#1)}} \Big(\frac{(1+\nu)\sigma_{zz}^{(#1)}}{2E#1} -  \frac{\nu ((\sigma_{zz}^{(#1)})+ 2\sigma_{rr}^{(#1)})}{2 E#1} \Big) d(\sigma_{zz}^{(#1)}) r dr dz }

\makeatother

\begin{document}

\begin{equation}
  \begin{aligned}
    Energy^{(i)} & =  \intU*1(i) + \intU*2(i) + \intU*3(i) \\
    \intU*1(1)   & = \intU1(1)_{a}^{b}                     \\
    \intU*2(1)   & = \intU2(1)_{a}^{b}                     \\
    \intU*3(1)   & = \intU3(1)_{a}^{b}                     \\
    %
    % End of 1
    %
    \intU*1(2)   & = \intU1(2)_{b}^{c}                     \\
    \intU*2(2)   & = \intU2(2)_{b}^{c}                     \\
    \intU*3(2)   & = \intU3(2)_{b}^{c}                     \\
  \end{aligned}
\end{equation}

\end{document}

Since the integrands change and I don't really know what all of this is about, there could be a better way to write this, but I think the above example conveys the general idea.

I'm using a few TeX tricks here. At a minimum I'm trying to let the syntax of command sequence match what's needed: the superscripting with (<num>) and the bounds of integration.

Answer 2

I've found the mathpix is great for boosting latex productivity as it enables you to derive latex from an image and then that can be used as a template for further copy/pasting.

https://mathpix.com/docs/snip/overview