"Babes-Bolyai" University of Cluj-Napoca
Faculty of Mathematics and Computer Science

Computational algebra
Code
Semes-
ter
Hours: C+S+L
Credits
Type
Section
MA261
1
2+2+0
9
compulsory
Matematică Computaţională - în limba maghiară
Teaching Staff in Charge
Prof. MARCUS Andrei, Ph.D.,  marcusmath.ubbcluj.ro
Aims
We present some of the most important algorithms with applications to problems in abstract algebra but not only. We also discuss the complexity of these algorithms.
Content
Finite fields. Discrete logarithm. Factorization of polynomials over finite fields. Berlakamp's algorithm. Fast adding. Fast Fourier transform. Groebner basis. Buchberger's algorithm. Generators and relations in groups. The Todd-Coxeter algorithm. Lattice reduction and the LLL-algorithm. Factorization of polynomials over the rationals.
References
1. W. BOSMA, A. VAN DER PORTEN: Computational Algebra and Number Theory, Kluwer 1995.
2. D. BRESSOUD, S. WAGON: A Course in Computational Number Theory, Springer-Verlag 2000.
3. H. COHEN: A Course in Computational Algebraic Number Theory, Springer-Verlag 2001.
4. R.LIDL, G. PILZ : Applied Abstract Algebra, Springer-Verlag, Berlin1998.
5. A. M. COHEN, H. CUYPERS, H. STERK: Some Tapas of Computer Algebra, Springer-Verlag 1999
6. THE GAP GROUP: GAP - Groups, Algorithms, and Programming. Version 4.4.3. [http://www.gap-system.org]
7. T.H. CORMEN, C.E. LEISERSON, R.L. RIVEST: Introduction to Algorithms. MIT 1990.
8. D.E. KNUTH: The Art of Computer Programming, Addison Wesley Longman 1998.
Assessment
Homework. Essays. Exam.