# Computational Algebra

## Objectives

This course is an introduction for some basic concepts of computational algebra and its applications. It is intended that students be able to:

solve elementary problems occurring in computer algebra, preferentially with the help of a computer algebra system;

understand major algorithms of computational algebra such as the euclidean algorithm, some modular algorithms, and the Karatsuba algorithm for multiplication;

understand some algorithms of experimental mathematics;

understand some algorithms used in for automated theorem provers;

ackowledge some tools of experimental mathematics and their use in modelling and discovery of mathematical results.

## General characterization

##### Code

10986

##### Credits

3.0

##### Responsible teacher

Available soon

##### Hours

Weekly - Available soon

Total - 42

##### Teaching language

Português

### Prerequisites

Available soon

### Bibliography

1. J. Gathen e J. Gerhard, Modern Computer Algebra, Cambridge University Press, 2003

2. K.O. Geddes, S.R. Czapor e G. Labahn, Algorithms for computer algebra, Kluwer Academic Publishers, 1992

3. C.C. Sims, Computation with finitely presented groups, Cambridge University Press, 1994

4. H. Cohen, A course in computational algebraic number theory, Springer-Verlag, 1993

### Teaching method

Available soon

### Evaluation method

Available soon

## Subject matter

1. Introduction. Computer algebra systems.

2. Applications of the Euclidean algorithm.

3. Modular algorithms and interpolation.

4. Fast multiplication: Karatsuba''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''s algorithm.

5. Factorization of integers and cryptography. RSA system.

6. Rewriting systems: Knuth-Bendix procedure.

7. Algorithms involving finitely presented groups.