[Tex/LaTex] Best way to create an system of equations environment

Question

I am trying to write a few systems of equations, and I want the terms to be nicely spaced as below

2x  +   y  +  3z  =  10   \\ 
 x  +   y  +   z  =   6   \\
 x  +  3y  +  2z  =  13 

Now, using some very ugly code, I was able to produce the results above.

\documentclass[10pt,a4paper]{article}
\usepackage{mathtools}
\usepackage{amsmath}

\begin{document}

\begin{align*}
\begin{bmatrix}
\begin{tabular}{r c r c r c r }
$2x$ & $+$ & $ y$ & $+$ & $3z$ & $=$ & $10$ \\
$ x$ & $+$ & $ y$ & $+$ & $ z$ & $=$ & $ 6$ \\
$ x$ & $+$ & $3y$ & $+$ & $2z$ & $=$ & $13$
\end{tabular}
\end{bmatrix}
\end{align*}

\section{Another system of equations, now without the brackets}

\begin{table}[!htpb]
\centering
\begin{tabular}{r c r c r c r }
$2x$ & $+$ & $ y$ & $+$ & $3z$ & $=$ & $10$ \\
$ x$ & $+$ & $ y$ & $+$ & $ z$ & $=$ & $ 6$ \\
$ x$ & $+$ & $3y$ & $+$ & $2z$ & $=$ & $13$
\end{tabular}
\end{table}

\end{document}    

I would very much want a more automatic way to do this, and a simple method for controlling the spacing between elements. I have looked at earlier posts like

Multicol layout for systems of (linear) equations

It seems that I am looking for a simple version of this one. I have no need to use side-by-side equations, nor have numbers in front of them.

Using ideas from the post above, I guess the result is done by redefining commands such as - and + inside of the table? I tried to do something like this, but the code looked rather complex =(

To sum it up: Is there a way to define a simple System of Equations enviroment, with proper alignment and a optional command for defining the spacing?

Answer 1

You can try the package systeme. Its documentation is in French, but there are many examples to play with.

Your example would be input as

\systeme{
2x  +   y  +  3z  =  10,
 x  +   y  +   z  =   6,
 x  +  3y  +  2z  =  13}

To get right alignment in the column of right hand sides, one has to manually modify the package code:

\makeatletter
\def\SYS@makesyspreamble@i#1{%
  \ifnum#1<\SYS@preamblenum
    \SYS@addtotok\SYS@systempreamble{\hfil$##$&\hfil$##$&}% 
    \expandafter\SYS@makesyspreamble@i\expandafter{\number\numexpr#1+\@ne\expandafter}%
  \else
    \SYS@addtotok\SYS@systempreamble{\hfil$##$&$##$&\hfil$##$\null}% 
    \ifSYS@extracol
      \SYS@addtotok\SYS@systempreamble{&\SYS@extracolstart##\SYS@extracolend\hfil\null}% 
    \fi
    \SYS@addtotok\SYS@systempreamble{\cr\SYS@strutup}% 
  \fi
}
\makeatother

The patch is simply changing $##$\hfil into \hfil$##$ but, since this involves # it's not possible to use etoolbox's \patchcmd.

One can modify the distance between the lines by saying something like

\syslineskipcoeff{1.2}

and act on the column spacing with the parameter \tabskip; so, for example,

\[
\syslineskipcoeff{1.2}\setlength{\tabskip}{3pt}
\systeme{
2x  +   y  +  3z  =  10,
 x  +   y  +   z  =   6,
 x  +  3y  +  2z  =  13}
\]

will spread out the equations both vertically and horizontally. The \syslineskipcoeff can also be issued globally, in the preamble of the document; not the horizontal spacing, though, as \tabskip influences all TeX tables, tabular environments included.