157 A.Univ.Prof. Dipl.-Ing. Dr. Wolfgang Schreiner (RISC Insitute)\\ |
157 A.Univ.Prof. Dipl.-Ing. Dr. Wolfgang Schreiner (RISC Insitute)\\ |
158 and\\ |
158 and\\ |
159 Dr. techn. Walther Neuper (Institut für Softwaretechnologie, TU Graz) |
159 Dr. techn. Walther Neuper (Institut für Softwaretechnologie, TU Graz) |
160 \end{center} |
160 \end{center} |
161 \newpage |
161 \newpage |
162 {\w .}\hspace{6.5cm}\textbf{Abstact}\\[0.5cm] |
162 {\w .}\hspace{6.5cm}\textbf{Abstract}\\[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). |
163 Calculation with fractions is an important part of Computer-Algebra-Systems (CAS). Therefor you need algorithms for canceling fractions, respectively for the greatest common divisor (GCD). |
164 \section{Background} |
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. It is an educational mathematics assistant, a single-stepping system for applied mathematics based on the computer theorem prover Isabelle. The special is an easy readable knowledge base including Isabelles HOL-theories and a transparently working knowledge interpreter (a generalization of 'single stepping' algebra systems). |
165 The ISAC-project is a research and development project at the Institute for Software Technology of the Graz University of Technology. It is an educational mathematics assistant, a single-stepping system for applied mathematics based on the computer theorem prover Isabelle. The special is an easy readable knowledge base including Isabelles HOL-theories and a transparently working knowledge interpreter (a generalization of 'single stepping' algebra systems). |
166 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. |
166 The background to both, development and research, is given by actual needs in math education as well as by fundamental questions about 'the mechanization of thinking' as an essential aspect in mathematics and in technology. |
167 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. |
167 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. |
168 |
168 |
169 \section{Goal of the thesis} |
169 \section{Goal of the thesis} |
170 \subsection{Current situation} |
170 \subsection{Current situation} |
171 At the time there is no good implimentation for the problem of canceling fractions in Isac and or in Isabelle. But because canceling is important for calculating with fractions a new implimentation is necessary. |
171 At the time there is no good implementation for the problem of canceling fractions in Isac and or in Isabelle. But because canceling is important for calculating with fractions a new implementation is necessary. |
172 |
172 |
173 \subsection{Problem} |
173 \subsection{Problem} |
174 The wish is to handle fractions in Isac not only in one variable also in more. 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 into Isabelle. |
174 The wish is to handle fractions in Isac not only in one variable also in more. So the goal of this thesis is to find, assess and evaluate the existing algorithms and methods for finding the GCD. This will be an functional program with the possibility to include it into Isabelle. |
175 \subsection{Expected results} |
175 \subsection{Expected results} |
176 Find good algorithms for the different problems, and find out which one will be the best for the special problem.\\ |
176 Find good algorithms for the different problems, and find out which one will be the best for the special problem.\\ |
177 The program should handeling: |
177 The program should handling: |
178 \begin{itemize} |
178 \begin{itemize} |
179 \item[]real and rational coefficients. Maybe also imaginary coefficients. |
179 \item[]real and rational coefficients. Maybe also imaginary coefficients. |
180 \item[]Mulivariable polynomials canceling and adding, when they are in normalform. |
180 \item[]Multi variable polynomials canceling and adding, when they are in normal form. |
181 \end{itemize} |
181 \end{itemize} |
182 For the program should be used a functional programming language with good commentaries. And it should be based on Isabelle and works correctly in Isac. |
182 For the program should be used a functional programing language with good commentaries. And it should be based on Isabelle and works correctly in Isac. |
183 \newpage |
183 \newpage |
184 |
184 |
185 \section{State of the art} |
185 \section{State of the art} |
186 Was ist vorhanden, was kann ich aus welchen Büchern für meine Arbeit verwenden |
186 Was ist vorhanden, was kann ich aus welchen Büchern für meine Arbeit verwenden |
187 Es gibt verschiedene CAS die bereits einen Algrotihmus implimentiert haben, wie haben die das gemacht, und welcher ist für mich am besten. |
187 Es gibt verschiedene CAS die bereits einen Algrotihmus implimentiert haben, wie haben die das gemacht, und welcher ist für mich am besten. |
190 \section{Thesis structure} |
190 \section{Thesis structure} |
191 The proposed table of contents of the thesis on the chapter level is as follows: |
191 The proposed table of contents of the thesis on the chapter level is as follows: |
192 \begin{enumerate} |
192 \begin{enumerate} |
193 \item Introduction (2-3 pages) |
193 \item Introduction (2-3 pages) |
194 \item Computer Algebra Systems (CAS) (5 - 7 pages)\\ |
194 \item Computer Algebra Systems (CAS) (5 - 7 pages)\\ |
195 Which different CAS exists and whats the foucus of them. |
195 Which different CAS exists and whats the focus of them. |
196 \item The \textit{ISAC}-Project (5 - 7 pages)\\ |
196 \item The \textit{ISAC}-Project (5 - 7 pages)\\ |
197 This chapter will describe the \textit{ISAC}-Project and the goals of the project. |
197 This chapter will describe the \textit{ISAC}-Project and the goals of the project. |
198 \item Univariate Polynomials (15-20 pages)\\ |
198 \item Univariate Polynomials (15-20 pages)\\ |
199 This chapter will describe different Algorithms for univariate polynomials, with different coefficients. |
199 This chapter will describe different Algorithms for univariate polynomials, with different coefficients. |
200 \item Multivariate Polynomials (20-25 pages)\\ |
200 \item Multivariate Polynomials (20-25 pages)\\ |
201 This chapter will describe different Algorithms for multivariate polynomials, with different coefficients |
201 This chapter will describe different Algorithms for multivariate polynomials, with different coefficients |
202 \item Functional programming and SML(2-5 pages)\\ |
202 \item Functional programing and SML(2-5 pages)\\ |
203 The basic idea of this programming languages. |
203 The basic idea of this programing languages. |
204 \item Implimentation in \textit{ISAC}-Project (15-20 pages) |
204 \item Implementation in \textit{ISAC}-Project (15-20 pages) |
205 \item Conclusion (2-3 pages) |
205 \item Conclusion (2-3 pages) |
206 \end{enumerate} |
206 \end{enumerate} |
207 %\newpage |
207 %\newpage |
208 |
208 |
209 \section{Timeline} |
209 \section{Time line} |
210 %Werd nie fertig.\\ |
210 %Werd nie fertig.\\ |
211 \begin{center} |
211 \begin{center} |
212 \begin{tabular}{|l|l|l|} |
212 \begin{tabular}{|l|l|l|} |
213 \hline |
213 \hline |
214 \textbf{Time}&\textbf{Thesis}&\textbf{Project}\\ |
214 \textbf{Time}&\textbf{Thesis}&\textbf{Project}\\ |
215 \hline |
215 \hline |
216 & Functional programming & Learning the basics and the idea\\ |
216 & Functional programing & Learning the basics and the idea\\ |
217 & & of funcional programming\\ |
217 & & of functional programing\\ |
218 \hline |
218 \hline |
219 & Different CAS & Can they handle the problem \\ |
219 & Different CAS & Can they handle the problem \\ |
220 & &and which algorithm do they use?\\ \hline |
220 & &and which algorithm do they use?\\ \hline |
221 & Univariate Polynomials & Implimentation of the Algorithm\\ |
221 & Univariate Polynomials & Implementation of the Algorithm\\ |
222 & & for univariate Polynomials \\ \hline |
222 & & for univariate Polynomials \\ \hline |
223 & Multivariate Polynomials & Implimentation of the Algorithm\\ |
223 & Multivariate Polynomials & Implementation of the Algorithm\\ |
224 & & for multivariate Polynomials \\ \hline |
224 & & for multivariate Polynomials \\ \hline |
225 & The Isac-Project &\\ \hline |
225 & The Isac-Project &\\ \hline |
226 & Conclusion and Introduction & Find good examples for testing\\ |
226 & Conclusion and Introduction & Find good examples for testing\\ |
227 \hline |
227 \hline |
228 \end{tabular} |
228 \end{tabular} |