From 007f67a693e4d031fd3d792df8e4d5f43e2cb2e7 Mon Sep 17 00:00:00 2001 From: Karl Berry Date: Mon, 9 Jan 2006 00:49:07 +0000 Subject: doc/latex git-svn-id: svn://tug.org/texlive/trunk@84 c570f23f-e606-0410-a88d-b1316a301751 --- Master/texmf-dist/doc/latex/gauss/gauss-ex.tex | 66 ++++++++++++++++++++++++++ Master/texmf-dist/doc/latex/gauss/readme.txt | 21 ++++++++ 2 files changed, 87 insertions(+) create mode 100644 Master/texmf-dist/doc/latex/gauss/gauss-ex.tex create mode 100644 Master/texmf-dist/doc/latex/gauss/readme.txt (limited to 'Master/texmf-dist/doc/latex/gauss') diff --git a/Master/texmf-dist/doc/latex/gauss/gauss-ex.tex b/Master/texmf-dist/doc/latex/gauss/gauss-ex.tex new file mode 100644 index 00000000000..35a6bafaf5b --- /dev/null +++ b/Master/texmf-dist/doc/latex/gauss/gauss-ex.tex @@ -0,0 +1,66 @@ +% +% 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 new file mode 100644 index 00000000000..3aa9b67027a --- /dev/null +++ b/Master/texmf-dist/doc/latex/gauss/readme.txt @@ -0,0 +1,21 @@ + +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 -- cgit v1.2.3