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Computer Algebra 2 - NMMB403

Title:	Počítačová algebra 2
Form of teaching:	lecture+practicals
Guaranteed by:	Department of Algebra (32-KA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2026
Duration in semesters:	1
Semester:	winter
E-Credits:	6
Hours per week, examination:	winter s.:3/1, C+Ex [HT]
Capacity:	unlimited
Maximum number of enrolled students:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	not taught
Language:	English, Czech
Teaching methods:	full-time
Is provided by:	NMMB413
Additional information:	http://artax.karlin.mff.cuni.cz/~ppri7485/podivna_algebra
Repeated enrollment:	2 / 2 / 2 / 2

Classification:	Mathematics > Algebra
Incompatibility :	NMIB103
Interchangeability :	NMIB103, NMMB413
Is interchangeable with:	NMIB103

Opinion survey results Schedule Noticeboard

Annotation -

The main topics of the course are algorithms for polynomial factorization, Gröbner bases and Lenstra-Lenstra- Lovasz Algorithm. All the algorithms find many applications in computer algebra, geometry, cryptoanalysis, and in design of new cryptosystems.

Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (23.05.2019)

Course completion requirements -

3 homeworks.

Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (28.10.2019)

Literature -

F. Winkler: Polynomial Algorithms in Computer Algebra, Springer 1996.

Geddes, Czapor, Labahn: Algorithms for computer algebra, Kluwer Academic Publishers, 1992.

G. von zur Gathen: Modern computer algebra, Cambridge Univ. Press 1999.

Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (06.09.2013)

Course assessment methods and requirements for successful completion, grading scheme -

Students have to pass final test. The test consists of 3 parts, 2 problems are posed for

each topic of the lecture (factorization of polynomials, Groebner bases, lattices and LLL algorithm). It is

neccessary to get more than 50% of points in each part of the exam to pass.

Last update: Příhoda Pavel, doc. Mgr., Ph.D. (29.10.2019)

Syllabus -

1. Factorization of polynomials over finite fields, factorization of integral polynomials

2. Gröbner bases, applications, solving of systems of polynomial equation

3. Algorithm LLL, applications (factorization of polynomials over Z, cryptography).

Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (13.09.2013)