Subjects

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Computer Algebra II - NMIB103

Title:	Počítačová algebra II
Guaranteed by:	Department of Algebra (32-KA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2018
Semester:	winter
E-Credits:	3
Hours per week, examination:	winter s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	cancelled
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time
Additional information:	http://www.karlin.mff.cuni.cz/~stanovsk/vyuka/palg.htm

Guarantor:	doc. Mgr. Jan Šaroch, Ph.D.
Classification:	Mathematics > Algebra
Interchangeability :	NMMB403
Is incompatible with:	NMMB403
Is interchangeable with:	NMMB403

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Annotation -

Last update: T_KA (16.05.2008)

The main topics of the course are two advanced algorithms: Gröbner bases and Lenstra-Lenstra-Lovasz Algorithm. Both the algorithms find many applications in computer algebra, geometry, cryptoanalysis, and in design of new cryptosystems.

Literature -

Last update: T_KA (16.05.2008)

D. Stanovský: Počítačová algebra na

http://www.karlin.mff.cuni.cz/~stanovsk/vyuka/palg.htm

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.

Syllabus -

Last update: STANOVSK/MFF.CUNI.CZ (12.05.2009)

1. Gröbner bases, Buchberger's algorithm, applications (including in cryptoanalysis).

2. Theory of lattices, and algorithm LLL, applications (factorization of polynomials over Z, cryptography).

3. Other topics depending on interests of participants.

Basic knowledge of subjects taught in the course NMIB003 Computer algebra is expected.