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 - 3
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.