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authorKarl Berry <karl@freefriends.org>2006-01-09 00:49:07 +0000
committerKarl Berry <karl@freefriends.org>2006-01-09 00:49:07 +0000
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tree90d17e00e572ecb1e24764b6f29c80e098b08d29 /Master/texmf-dist/doc/latex/gauss
parent950209b26f70aa87ed07c54f82a95b6f03b7c3a0 (diff)
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git-svn-id: svn://tug.org/texlive/trunk@84 c570f23f-e606-0410-a88d-b1316a301751
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diff --git a/Master/texmf-dist/doc/latex/gauss/gauss-ex.tex b/Master/texmf-dist/doc/latex/gauss/gauss-ex.tex
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+%
+% This file is part of the gauss package by Manuel Kauers.
+% Its purpose is to demonstrate the usage of the package.
+% See the gauss-doc.dvi file for further information.
+%
+\documentclass{article}
+\usepackage{amsmath}
+\usepackage{gauss}
+\usepackage{amssymb} % to import \leadsto
+
+\begin{document}
+
+ \section{An Example for Gaussian Elimination}
+
+ Consider the real matrix
+ \[
+ A(t):=\begin{pmatrix}
+ 1 & 1 & 1 \\
+ t & 2t & 2 \\
+ t+1 & 0 & 2t
+ \end{pmatrix},
+ \]
+ which depends on a real valued parameter~$t$.
+ We want to find all solutions of the homogenous linear system defined by $A$
+ depending on the parameter~$t$.
+
+ Therefore, we use the Algorithm Gauss:
+ \begin{alignat*}1
+ A(t)=\begin{gmatrix}[p]
+ 1 & 1 & 1 \\
+ t & 2t & 2 \\
+ t+1 & 0 & 2t
+ \rowops
+ \add[-t]{0}{1}
+ \add[-(t+1)]{0}{2}
+ \end{gmatrix}\kern-6.23pt\leadsto&
+ \begin{gmatrix}[p]
+ 1 & 1 & 1 \\
+ 0 & t & 2-t \\
+ 0 & -t-1 & t-1
+ \rowops
+ \add12
+ \mult{2}{\cdot(-1)}
+ \end{gmatrix}\\
+ \leadsto&\begin{gmatrix}[p]
+ 1 & 1 & 1 \\
+ 0 & t & 2-t \\
+ 0 & 1 & -1
+ \rowops
+ \swap12
+ \add[-t]12
+ \mult2{:2}
+ \end{gmatrix}\\
+ \leadsto&\begin{pmatrix}
+ 1 & 1 & 1 \\
+ 0 & 1 & -1 \\
+ 0 & 0 & 1
+ \end{pmatrix}.
+ \end{alignat*}
+
+ \subsection*{Conclusion}
+
+ We have learned that the matrix $A$ defined above is regular for all real
+ valued~$t$, and we hopefully also have learned how to use the gauss package.
+
+\end{document} \ No newline at end of file
diff --git a/Master/texmf-dist/doc/latex/gauss/readme.txt b/Master/texmf-dist/doc/latex/gauss/readme.txt
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+
+gauss.sty -- A Package for Typesetting Matrix Operations
+--------------------------------------------------------
+
+To use the package, just place the gauss.sty file at a
+location where TeX will find it, and insert
+
+ \usepackage{gauss}
+
+to your document's preamble. This will define a new
+environment gmatrix whose usage is well explained in
+the gauss-doc.dvi file.
+
+This program may be distributed and/or modified under the
+conditions of the LaTeX Project Public License, either
+version 1.1 of this license or (at your option) any later
+version.
+
+---
+
+(c) 2001, 2002 by Manuel Kauers <manuel@kauers.de>