# LUP Student Papers

## LUND UNIVERSITY LIBRARIES

### Polynomial Computer Algebra and implementation of Wilf-Zeilberger's method

(2019) In Master's Thesis in Mathematical Sciences 2019:E65 FMAM05 20192
Mathematics (Faculty of Engineering)
Abstract
The purpose of the thesis is to get a better understanding of computer algebra in general, and polynomial computer algebra in particular. This is done by implementing a library for a polynomials and methods that are needed to be able to perform operations on the polynomials. Then this library is used to implement Wilf-Zeilberger’s method, which is a method that can be used to prove certain combinatorial identities involving summation. The thesis consists mostly of three parts; theory, implementation and examples. In the theory section, all the theoretical results used in the project are presented. The implementation section then treats the difﬁculties arising when turning theory into practice, and focuses in particular on when... (More)
The purpose of the thesis is to get a better understanding of computer algebra in general, and polynomial computer algebra in particular. This is done by implementing a library for a polynomials and methods that are needed to be able to perform operations on the polynomials. Then this library is used to implement Wilf-Zeilberger’s method, which is a method that can be used to prove certain combinatorial identities involving summation. The thesis consists mostly of three parts; theory, implementation and examples. In the theory section, all the theoretical results used in the project are presented. The implementation section then treats the difﬁculties arising when turning theory into practice, and focuses in particular on when theoretically easy methods and concepts become much more challenging in implementation. The program that is developed seems to work well, both on examples that were used throughout the project as testing and on validation examples that were found after all the implementation was done. This means that the program can solve and produce a paper proving that identities indeed are true. Therefore the thesis shows one example of how automated proofs can be generated, but mostly the thesis highlights the difﬁculties arising in computer algebra while implementing the speciﬁc example of Wilf-Zeilberger’s method. (Less)
author
supervisor
organization
course
FMAM05 20192
year
type
H2 - Master's Degree (Two Years)
subject
keywords
Computer Algebra, Wilf-Zeilberger's method, Automized proofs, Combinatorics, Proving identities
publication/series
Master's Thesis in Mathematical Sciences 2019:E65
report number
LUTFMA-3396-2019
ISSN
1404-6342
other publication id
2019:E65
language
English
id
9002117
2020-03-11 14:45:14
date last changed
2020-03-11 14:45:14
```@misc{9002117,
abstract     = {{The purpose of the thesis is to get a better understanding of computer algebra in general, and polynomial computer algebra in particular. This is done by implementing a library for a polynomials and methods that are needed to be able to perform operations on the polynomials. Then this library is used to implement Wilf-Zeilberger’s method, which is a method that can be used to prove certain combinatorial identities involving summation. The thesis consists mostly of three parts; theory, implementation and examples. In the theory section, all the theoretical results used in the project are presented. The implementation section then treats the difﬁculties arising when turning theory into practice, and focuses in particular on when theoretically easy methods and concepts become much more challenging in implementation. The program that is developed seems to work well, both on examples that were used throughout the project as testing and on validation examples that were found after all the implementation was done. This means that the program can solve and produce a paper proving that identities indeed are true. Therefore the thesis shows one example of how automated proofs can be generated, but mostly the thesis highlights the difﬁculties arising in computer algebra while implementing the speciﬁc example of Wilf-Zeilberger’s method.}},
author       = {{Åström, Lars}},
issn         = {{1404-6342}},
language     = {{eng}},
note         = {{Student Paper}},
series       = {{Master's Thesis in Mathematical Sciences 2019:E65}},
title        = {{Polynomial Computer Algebra and implementation of Wilf-Zeilberger's method}},
year         = {{2019}},
}

```