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doc-src/isac/dmeindl/proposal.tex
author Diana Meindl <meindl_diana@yahoo.com>
Tue, 06 Sep 2011 15:19:42 +0200
branchdecompose-isar
changeset 42263 5a2f4c554e1d
parent 42234 9914536834be
child 42264 a58956d1f9d5
permissions -rwxr-xr-x
tuned 
     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 %\usepackage{graphs}

    12 %\usepackage[all,dvips,arc,curve,color,frame]{xy}

    13 %% Declaring a new color for use in a XY graph.

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    15 % Eigene Nummerierung

    16 % Seitenräder einstellen und Höhe der Seitenzahlen

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

    19 \setlength{\footskip}{2cm}

    20 %Zähler definieren und Starwert setzen:

    21 

    22 \newcommand{\R}{\mathbb R}

    23 %\newcommand{\N}{\mathbb N}

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    25 %\newcommand{\C}{\mathbb C}

    26 

    27 

    28 \newcounter{ctr}

    29 \setcounter{ctr}{0}

    30 

    31 \newcounter{Teubner}

    32 \newcounter{Klingenberg}

    33 \newcounter{T}

    34 \newcounter{Vo}

    35 \newcounter{Se}

    36 \newcounter{E}

    37 \newcounter{Bwl}

    38 \newcounter{Int}

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    51 %BSP

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    63   {\end{list}

    64 }

    65 

    66 

    67 %Lemma

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   107 }

   108 

   109 

   110 %Proportion

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   123 }

   124 

   125 %Farben

   126 

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

   132 

   133 \usepackage{color}

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

   135 

   136 

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

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   142 

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   146 

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

   148 

   149 %------------------------------------------------------------- Beginn -----------------------------------------------------------------------

   150 

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

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

   153 \date{}

   154 

   155 \begin{document}

   156 \maketitle

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

   158 \begin{center}

   159 Presented to \\

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

   161 and\\

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

   163 \end{center}

   164 \newpage

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

   166 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).

   167 \section{Background}

   168 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.

   169  

   170 \section{Goal of the thesis}

   171 \subsection{Current situation}

   172 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.

   173 \subsection{Problem} 

   174 

   175 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.

   176 \subsection{Expected results}

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

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

   179 richtige implimentierung in isac basierend auf Isabelle.\\

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

   181 

   182 

   183 \section{State of the art}

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

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

   186 

   187 %\newpage

   188 \section{Thesis structure}

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

   190 \begin{enumerate}

   191 	\item Introduction (2-3 pages)

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

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

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

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

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

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

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

   199 	The basic idea of this programming languages.

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

   201 	\item Conclusion (2-3 pages)

   202 \end{enumerate}

   203 %\newpage

   204 

   205 \section{Timeline}

   206 %Werd nie fertig.\\

   207 \begin{center}

   208 		\begin{tabular}{|l|l|l|}

   209 		\hline

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

   211 			 \hline

   212 			 & Functional programming & Grundlagen Funktionales Programmieren\\

   213 			 \hline

   214 			 & Univariate Polynomials & Implimentation of the Algorithm\\

   215 			 & & for univariate Polynomials \\ \hline

   216 		   & Multivariate Polynomials &   \\ \hline

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

   218 			 & & for multivariate Polynomials \\ \hline

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

   220 			\hline

   221 		\end{tabular}

   222 	\end{center}

   223 		

   224 \section{Bibliography}

   225 mindestens 10

   226 \begin{enumerate}

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

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

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

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

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

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

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

   234  \item

   235  \item

   236  \item

   237 \end{enumerate} 

   238 

   239 \end{document}
wneuper/isa