Mercurial Mercurial > wneuper > isa / file revision
summary | shortlog | changelog | graph | tags | bookmarks | branches | files | changeset | file | latest | revisions | annotate | diff | comparison | raw | help
doc-src/isac/dmeindl/proposal.tex
author Diana Meindl <meindl_diana@yahoo.com>
Tue, 06 Sep 2011 15:38:45 +0200
branchdecompose-isar
changeset 42265 36e7cd1b2b14
parent 42264 a58956d1f9d5
child 42266 eee328e06031
permissions -rwxr-xr-x
tuning 
     1 \documentclass[12pt,a4paper]{article}

     2 \usepackage{a4}

     3 \usepackage[naustrian]{babel}

     4 \usepackage[latin1]{inputenc}

     5 \usepackage{calc}

     6 \usepackage{amsmath}   

     7 \usepackage{epsfig}

     8 \usepackage{graphicx}

     9 \usepackage{xcolor}

    10 \usepackage{amsfonts}

    11 

    12 % Seitenräder einstellen und Höhe der Seitenzahlen

    13 \usepackage{geometry}

    14 \geometry{a4paper, left=2.5cm, right=2cm, top=3cm, bottom=2.8cm}

    15 \setlength{\footskip}{2cm}

    16 

    17 

    18 %Zähler definieren und Starwert setzen:

    19 \newcommand{\R}{\mathbb R}

    20 %\newcommand{\N}{\mathbb N}

    21 %\newcommand{\Q}{\mathbb Q}

    22 %\newcommand{\C}{\mathbb C}

    23 

    24 

    25 \newcounter{ctr}

    26 \setcounter{ctr}{0}

    27 

    28 \newcounter{Teubner}

    29 \newcounter{Klingenberg}

    30 \newcounter{T}

    31 \newcounter{Vo}

    32 \newcounter{Se}

    33 \newcounter{E}

    34 \newcounter{Bwl}

    35 \newcounter{Int}

    36 \newcounter{Prim}

    37 \newcounter{Z}

    38 \setcounter{Z}{0}

    39 \setcounter{Teubner}{1}

    40 \setcounter{Klingenberg}{2}

    41 \setcounter{T}{1}

    42 \setcounter{Vo}{7}

    43 \setcounter{Se}{2}

    44 \setcounter{E}{3}

    45 \setcounter{Bwl}{4}

    46 \setcounter{Int}{5}

    47 \setcounter{Prim}{6}

    48 %BSP

    49 \newenvironment{myBsp}{

    50   \begin{list}{\textbf{\textsc{Bsp:}}}{

    51     \setlength{\labelwidth}{8Pc}

    52     \setlength{\labelsep}{0.5Pc}    

    53     \setlength{\rightmargin}{0Pc}

    54     \setlength{\leftmargin}{2Pc}

    55     \setlength{\parsep}{0ex plus 0.5ex}

    56     \setlength{\listparindent}{1em}

    57     \setlength{\itemsep}{1ex plus 0.5ex minus 0.2ex}

    58     \setlength{\topsep}{0.5Pc}

    59   }}

    60   {\end{list}

    61 }

    62 

    63 

    64 %Lemma

    65 \newenvironment{myLemma}{

    66   \begin{list}{\textsc{\textbf{Lemma:\ \ \ }}}{

    67    \setlength{\labelsep}{-0.5Pc}    

    68     \setlength{\leftmargin}{1Pc}

    69     \setlength{\parsep}{0ex plus 0.5ex}

    70     \setlength{\listparindent}{1em}

    71     \setlength{\itemsep}{1ex plus 0.5ex minus 0.2ex}

    72     \setlength{\topsep}{0.5Pc}

    73   }}

    74   {\end{list}

    75 }

    76 %Korollar

    77 \newenvironment{myKorollar}{

    78   \begin{list}{\textsc{\textbf{Korollar: }}}{

    79     \setlength{\labelwidth}{8Pc}

    80     \setlength{\labelsep}{0.5Pc}    

    81     \setlength{\rightmargin}{0Pc}

    82     \setlength{\leftmargin}{4Pc}

    83     \setlength{\parsep}{0ex plus 0.5ex}

    84     \setlength{\listparindent}{1em}

    85     \setlength{\itemsep}{1ex plus 0.5ex minus 0.2ex}

    86     \setlength{\topsep}{0.5Pc}

    87   }}

    88   {\end{list}

    89 }

    90 

    91 %Theorem

    92 \newenvironment{myTheorem}{

    93   \begin{list}{\textsc{\textbf{Theorem: }}}{

    94     \setlength{\labelwidth}{8Pc}

    95     \setlength{\labelsep}{0.5Pc}    

    96     \setlength{\rightmargin}{0Pc}

    97     \setlength{\leftmargin}{5Pc}

    98     \setlength{\parsep}{0ex plus 0.5ex}

    99     \setlength{\listparindent}{1em}

   100     \setlength{\itemsep}{1ex plus 0.5ex minus 0.2ex}

   101     \setlength{\topsep}{0.5Pc}

   102   }}

   103   {\end{list}

   104 }

   105 

   106 

   107 %Proportion

   108 \newenvironment{myProp}{

   109   \begin{list}{\textsc{\textbf{Proportion: }}}{

   110     \setlength{\labelwidth}{8Pc}

   111     \setlength{\labelsep}{0.5Pc}    

   112     \setlength{\rightmargin}{0Pc}

   113     \setlength{\leftmargin}{4Pc}

   114     \setlength{\parsep}{0ex plus 0.5ex}

   115     \setlength{\listparindent}{1em}

   116     \setlength{\itemsep}{1ex plus 0.5ex minus 0.2ex}

   117     \setlength{\topsep}{0.5Pc}

   118   }}

   119   {\end{list}

   120 }

   121 

   122 %Farben

   123 

   124 \newcommand{\red}[1]{\textcolor[rgb]{0.7,0,0}{\bf #1}}

   125 \newcommand{\rd}[1]{\color{red}{#1}}

   126 \newcommand{\white}[1]{\textcolor[rgb]{1,0,0}{\bf #1}}

   127 \newcommand{\w}[1]{\color{white}{#1}}

   128 \newcommand{\g}[1]{\color{myColor}{#1}}

   129 

   130 \usepackage{color}

   131 \definecolor{myColor}{rgb}{0.9,0.9,0.9}% Wir definieren im RGB-Farbraum

   132 

   133 

   134 \newcommand{\myDef}[1]{\parbox{\columnwidth}{\addtocounter{ctr}{1}{\w .}\\[-0.2cm]\textbf{Definition\ \Nummer:}\\#1}}

   135 \newcommand{\mySatz}[2]{\colorbox{myColor}{\parbox{\columnwidth}{\addtocounter{ctr}{1}{\g .}\\[-0.2cm]\textbf{Satz\ \Nummer:}\ #1\\ #2}}}

   136 \newcommand{\myBeweis}[1]{\textit{\textbf{Beweis:}\\ #1}}

   137 \newcommand{\myAlg}[2]{\parbox{\columnwidth}{\addtocounter{ctr}{1}\textbf{Algorithmus\ \Nummer:}\ \ #1\\#2}}

   138 \newcommand{\myProg}[1]{\fbox{\parbox{\columnwidth}{#1}}}

   139 

   140 \newcommand{\add}[1]{\addtocounter{#1}{1}}

   141 \newcommand{\zahl}[1]{\setcounter{#1}{Z}}

   142 \newcommand{\Q}[2]{\parbox{\columnwidth}{$^{[\arabic{#1}/#2]}$ }}

   143 

   144 \newcommand{\Nummer}{\thesection.\arabic{ctr}}

   145 

   146 %---------- --------------------------------------------------- Beginn -----------------------------------------------------------------------

   147 

   148 \title{Greates common divisor \\ for multivariable Polynomials}

   149 \author{By\\Diana Meindl\\meindl$_-$diana@yahoo.com}

   150 \date{}

   151 

   152 \begin{document}

   153 \maketitle

   154 {\w .}\\[12cm]

   155 \begin{center}

   156 Presented to \\

   157 A.Univ.Prof. Dipl.-Ing. Dr. Wolfgang Schreiner (RISC Insitute)\\

   158 and\\

   159 Dr. techn. Walther Neuper (Institut für Softwaretechnologie, TU Graz)

   160 \end{center}

   161 \newpage

   162 {\w .}\hspace{6.5cm}\textbf{Abstact}\\[0.5cm]

   163 Calculation with fractions is an importent part of Computer-Algebra-Systems (CAS). Therefor you need algorithms for canceling fractions, respectively for the greatest common divisor (GCD).

   164 \section{Background}

   165 The ISAC-project is a research and development project at the Institute for Software Technology of the Graz University of Technology. ISAC is an educational mathematics assistant, a single-stepping system for applied mathematics based on the computer theorem prover Isabelle. The novelty is given by the human-readable knowledge base including Isabelles HOL-theories and by the transparently working knowledge interpreter (a generalization of 'single stepping' algebra systems). The background to both, development and research, is given by actual needs in math education as well as by foundamental questions about 'the mechanization of thinking' as an essential aspect in mathematics and in technology. The ISAC-system under construction comprises a tutoring-system and an authoring-system. The latter provides for adaption to various needs of individual users and educational institutions and for extensions to arbitrary fields of applied mathematics.

   166  

   167 \section{Goal of the thesis}

   168 \subsection{Current situation}

   169 Zur Zeit ist keine gute Implimentierung vorhanden. Um polynomiale Brüche zu kürzen, darum besteht die Notwendigkeit eienr Implimentierung in Isabelle, auf die von Isac zugegriffen wird.

   170 \subsection{Problem} 

   171 

   172 In Isac möchte man gerne Brüche kürzen können und dies nicht nur mit einer Variablel sondern auch mit mehrern Variablen. So the goal of this thesis ist to find, assess and evaluate the existing algorithms and methods for finding the GCD. This will be an functional programm with the posibility to include it in Isabelle.

   173 \subsection{Expected results}

   174 Polynome kürzen und addieren ( wenn sie in Normalform sind)\\

   175 Für reale koeffizienten eventuell auch für imaginäre oder rationale.\\

   176 richtige implimentierung in isac basierend auf Isabelle.\\

   177 Funktional programmiert mit guten Beschreibungen, was gerade gemacht wird.\\

   178 

   179 

   180 \section{State of the art}

   181 Was ist vorhanden, was kann ich aus welchen Büchern für meine Arbeit verwenden

   182 Es gibt verschiedene CAS die bereits einen Algrotihmus implimentiert haben, wie haben die das gemacht, und welcher ist für mich am besten.

   183 

   184 %\newpage

   185 \section{Thesis structure}

   186 the proposed table of contents of the thesis on the chapter level is as follows:

   187 \begin{enumerate}

   188 	\item Introduction (2-3 pages)

   189 	\item The \textit{ISAC}-Project (5 - 7 pages)\\

   190 	This chapter will describe the \textit{ISAC}-Project and the goals of the project.

   191 	\item Univariate Polynomials (15-20 pages)\\

   192 	This chapter will describe different Algorithms for univariate polynomials, with different coefficients.

   193 	\item Multivariate Polynomials (20-25 pages)\\

   194 	This chapter will describe different Algorithms for multivariate polynomials,  with different coefficients

   195 	\item Functional programming and SML(2-5 pages)\\

   196 	The basic idea of this programming languages.

   197 	\item Implimentation in \textit{ISAC}-Project (15-20 pages)

   198 	\item Conclusion (2-3 pages)

   199 \end{enumerate}

   200 %\newpage

   201 

   202 \section{Timeline}

   203 %Werd nie fertig.\\

   204 \begin{center}

   205 		\begin{tabular}{|l|l|l|}

   206 		\hline

   207 			 \textbf{Time}&\textbf{Thesis}&\textbf{Project}\\

   208 			 \hline

   209 			 & Functional programming & Grundlagen Funktionales Programmieren\\

   210 			 \hline

   211 			 & Univariate Polynomials & Implimentation of the Algorithm\\

   212 			 & & for univariate Polynomials \\ \hline

   213 		   & Multivariate Polynomials &   \\ \hline

   214 		   & The Isac-Project &Implimentation of the Algorithm\\

   215 			 & & for multivariate Polynomials \\ \hline

   216 		   & Conclusion and Introduction & Summary and Conclusions of Experiments\\

   217 			\hline

   218 		\end{tabular}

   219 	\end{center}

   220 		

   221 \section{Bibliography}

   222 mindestens 10

   223 \begin{enumerate}

   224  \item Franz Winkler, \textit{Polynomial Algorithms in Computer Algebra}, Springer,1996

   225  \item M. Mignotte, \textit{An inequality about factors of polynomial}

   226  \item M. Mignotte, \textit{Some useful bounds}

   227  \item W. S. Brown and J. F. Traub. \textit{On euclid's algorithm and the theory of subresultans}, Journal of the ACM (JACM), 1971

   228  \item Bruno Buchberger, \textit{Algorhimic mathematics: Problem types, data types, algorithm types}, Lecture notes, RISC Jku A-4040 Linz, 1982

   229  \item Bird/Wadler, \textit{Einführung in die funktionale Programmierung}, Carl Hanser and Prentice-Hall International, 1992

   230  \item Tateaki Sasaki and Masayuki Suzuki, \textit{Thre new algorithms for multivariate polynomial GCD}, J. Symbolic Combutation, 1992

   231  \item

   232  \item

   233  \item

   234 \end{enumerate} 

   235 

   236 \end{document}
wneuper/isa