# How would you create syntax for variable substitutions

I'm using the following syntax a lot for defining variable substitutions in my calculations:

\left [ \begin{array}{rcl}
t &=& \sqrt{x+5}\\
x &=& t^2 - 5\\
dx &=& 2tdt\\
\end{array} \right ]


It looks (almost!) exactly the way I want, but it is a lot of garbage to write everytime I'm making a substitution. How can I create new Latex syntax so that instead of the above, I would instead write:

\begin{vars}
t &=& \sqrt{x+5}\\
x &=& t^2 - 5\\
dx &=& 2tdt
\end{vars}


And it would render to the same? Even better would be if I could write something like:

\defvars{t, {\sqrt{x+5}}{x, {t^2 - 5}}{dx, {2tdt}}

• firs step: \left[ \begin{aligned} t & = \sqrt{x+5}\\ x & = t^2 - 5\\ dx & = 2tdt \end{aligned}\; \right], second step: \newcommand\defvars[6]{\left[ \begin{aligned} #1 & = #2 \\ #3 & = #4 \\ #5 & = #6 \end{aligned}\; \right]} and than use as \defvars{t}{\sqrt{x+5}}{x}{t^2-5}{dx}{2tdt}. Is this what looking for? – Zarko Mar 14 '17 at 20:28
• @Zarko: I think you should turn your comment into an answer. Edit: If I may suggest it, I prefer using \newcommand* in these situations. – GuM Mar 14 '17 at 20:32
• @GustavoMezzetti, I was not sure, id I correctly understand OP question ... I can't manage showed desired syntax of command. And, yes, beter is use \newcommand*. Thank you for encouragement. I will convert my comment to answer. – Zarko Mar 14 '17 at 20:36
• @Zarko: Thanks, but that is hardcoded to three variables. I want the syntax to work for an arbitrary number. – Björn Lindqvist Mar 14 '17 at 20:39
• @BjörnLindqvist, this you not mentioned in your question ... since I didn't understood it well, I first wrote comment, which I later convert into answer. Meanwhile you receive solution which better fit your expectations. – Zarko Mar 14 '17 at 20:49

Here's an idea using etoolbox's \docsvlist:

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

\makeatletter
\newcommand*\dovar{}
\def\@dovar#1=#2\q@stop{#1&{}={}&#2\\}
\newrobustcmd*\vars[1]{%
\renewcommand*\do[1]{\@dovar##1\q@stop}%
\left[
\begin{array}{r@{}c@{}l}
\docsvlist{#1}
\end{array}
\right]
}
\makeatother

\begin{document}

$\vars{ t = \sqrt{x+5} , x = t^2 - 5 , dx = 2tdt }$

\end{document}

• +1, but I really think that using aligned, as @Zarko suggests, is much better! :-) – GuM Mar 14 '17 at 20:44
• Perfect thanks! I'll absolutely research the difference between aligned and array – Björn Lindqvist Mar 14 '17 at 20:46
• @GustavoMezzetti nothing against aligned but why do you think that it is much better? – cgnieder Mar 14 '17 at 20:59
• @BjörnLindqvist I improved the answer a bit with regard to spacing – cgnieder Mar 14 '17 at 20:59
• @clemens: Well, it is well known that amsmath’s alignments provide the exact spacing that is required around the “=” sign—that is, exactly the same amount that is used in all math formulas… :-) – GuM Mar 14 '17 at 22:32

Let me convert my comment into answer:

I assumed that you can add package amsmath or mathtool . With them you can simplify typing of your equation array to:

\left[ \begin{aligned}
t & = \sqrt{x+5}\\
x & = t^{2} - 5\\
dx & = 2tdt
\end{aligned}\; \right]


this can use in in definition of new command:

\newcommand*\defvars[6]{\left[ \begin{aligned}
#1 & = #2   \\
#3 & = #4   \\
#5 & = #6
\end{aligned}\; \right]}


and then use for example as follows:

$\defvars{t}{\sqrt{x+5}}{x}{t^{2}-5}{dx}{2tdt}$


In both case (direct use of code or it use as command) the result is the same:

You can use xparse:

\documentclass{article}
\usepackage{amsmath}
\usepackage{xparse}

\newcommand{\diff}{\mathop{}\!d}

\ExplSyntaxOn
\NewDocumentCommand{\vars}{m}
{
\left[\, % this opens a group
\tl_clear:N \l_tmpa_tl
\seq_set_split:Nnn \l_tmpa_seq { \\ } { #1 }
\seq_map_inline:Nn \l_tmpa_seq
{
\bjorn_vars_line:n { ##1 }
}
\begin{aligned}
\tl_use:N \l_tmpa_tl
\end{aligned}
\,\right]
}
\cs_new_protected:Nn \bjorn_vars_line:n
{
\seq_set_split:Nnn \l_tmpb_seq { = } { #1 }
\tl_put_right:Nx \l_tmpa_tl
{
\seq_item:Nn \l_tmpb_seq {1}
&=
\seq_item:Nn \l_tmpb_seq {2}
\exp_not:N \\
}
}
\ExplSyntaxOff

\begin{document}

$\vars{ t = \sqrt{x+5} \\ x = t^2 - 5 \\ \diff x = 2t\diff t }$

\end{document}


• Any advantage to that over clemens method? – Björn Lindqvist Mar 15 '17 at 14:26
• @BjörnLindqvist Simplicity? ;-) – egreg Mar 15 '17 at 17:40