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How can I write a linear equation system that uses circles and arrows to indicate what should be added on each line.

This is what I have so far:

$S = \begin{cases}
    x_1+2x_2 - 2x_3 = 1 \\
    2x_1 - x_2 + x_3 = 3 \\
    x_1 + 3x_2 + x_3 = 1
\end{cases}$

enter image description here

And it should look like this:

enter image description here

Oskar Persson
  • 573
  • This is related (http://tex.stackexchange.com/questions/140529/graphics-equations-put-text-on-equations/140547#140547) only insofar as placing such notes below equations. Placing notes to the side presents a slightly different challenge. – Steven B. Segletes Jan 21 '14 at 17:50
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    Do you want to illustrate row operations in the system of equations? Then the gauss package might do the job: http://www.ctan.org/pkg/gauss – Robert Jan 21 '14 at 21:40
  • @Robert How can I write what I want in Gauss? I can only find how to write parentheses and

    not S = {...

     – Oskar Persson Jan 22 '14 at 09:45
  • You can define a new matrix with only the left delimiter {: \newmatrix{{}{.}{A} and use it with \begin{gmatrix}[A] ... \end{gmatrix} Maybe I was too hasty when I suggested gauss: It's only for matrices and I don't think it's possible to write equations. Sorry about that! – Robert Jan 23 '14 at 09:04

1 Answers1

14

One option using TikZ:

New version:

\documentclass{article}
\usepackage{amsmath}
\usepackage{systeme}
\usepackage{tikz}

\newcounter{tmp}


\newcommand\tikzmark[1]{%
\tikz[remember picture,baseline=-0.65ex]
  \node[inner sep=0,outer sep=0] (#1){};%
}


\newcommand\mess[4][25pt]{%
\stepcounter{tmp}%
\begin{tikzpicture}[remember picture,overlay,>=latex,xshift=#1,cyan]
  \node[circle,draw,cyan,inner sep=2pt] at ([xshift=#1]#2) (a\thetmp) {$#4$};
  \draw[->] (a\thetmp.south) |- (#3);
\end{tikzpicture}%
}


\begin{document}


[
S = 
\systeme{x_1+2x_2 - 2x_3 = 1 \tikzmark{a},
    2x_1 - x_2 + x_3 = 3 \tikzmark{b},
    x_1 + 3x_2 + x_3 = 1 \tikzmark{c}}
]


\mess{a}{b}{-2}
\mess[55pt]{a}{c}{-1}


\end{document}

Explanation:

First, you place some marks for the relevant lines using \tikzmark, then you use the \mess command to add the circles with their arrows; the three mandatory arguments for \mess are the string for the initial mark, the string for the final mark, and the text to be used inside the circle. The optional argument gives control over the length of the horizontal separation.

Notice also the use of the systeme package, so that the system of equations gets nicely typeset.

Since the code requires some internal calculation, two or three runs will be needed for the elements to stabilize.

enter image description here

First version

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}

\newcommand\mess[2][20pt]{%
\begin{tikzpicture}[overlay,>=latex,yshift=22pt,xshift=#1,cyan]
  \node[circle,draw,cyan,inner sep=2pt] (a) {$#2$};
  \draw[->,shorten >= 3pt] (a.south) |- ([yshift=-9pt,xshift=-#1]a.south);
\end{tikzpicture}%
}


\begin{document}


[
S = \begin{cases}
    \phantom{0}x_1+2x_2 - 2x_3 = 1 \
    2x_1 - \phantom{0}x_2 + \phantom{0}x_3 = 3 \mess{-2}\
    \phantom{0}x_1 + 3x_2 + \phantom{0}x_3 = 1 \mess[40pt]{-1}
\end{cases}
]


\end{document}

enter image description here

The mandatory argument for \mess will be written in the circular node; the optional argument allows control over the length of the horizontal part of the arrow.

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Gonzalo Medina
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