Subjects

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Computer Algebra - NMMB204

Title:	Počítačová algebra
Guaranteed by:	Department of Algebra (32-KA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2016 to 2016
Semester:	summer
E-Credits:	6
Hours per week, examination:	summer s.:3/1, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	doc. Mgr. et Mgr. Jan Žemlička, Ph.D.
Class:	M Bc. MMIB M Bc. MMIB > Povinně volitelné M Bc. MMIB > 2. ročník M Bc. MMIT M Bc. MMIT > Povinně volitelné
Classification:	Mathematics > Algebra
Incompatibility :	NMIB003
Interchangeability :	NMIB003
Is pre-requisite for:	NMMB349
Is interchangeable with:	NMIB003

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Annotation -

Last update: G_M (16.05.2012)

Required course for bachelor's program in Information security. The course contains description of algorithms used in computer systems for symbolic manipulation. It begins with analysis of the simplest algebraic algorithms and shows how to use theoretic results for their improvement. Algorithms for polynomials over integers, rational numbers or finite fields are emphasized.

Literature -

Last update: RNDr. Alexandr Kazda, Ph.D. (08.02.2019)

L.Barto, D. Stanovský: Počítačová algebra, Karolinum, 2011.

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

Knuth: The art of computer programming, vol. 1, Fundamental algorithms, Addison-Wesley, 3rd edition 1997.

Syllabus -

Last update: RNDr. Alexandr Kazda, Ph.D. (08.02.2019)

1. Data representation, basic operations with numbers and polynomials, Karacuba's and extended Euclid's algorithm.

2. Modular representation, algorithms for Chinese Remainder Theorem. Fast Fourier transform, fast multuiplication and division of polynomials.

3. Greatest common divisor: Primitive polynomials and Gauss' lemma, polynomial remainder sequences, modular algorithm.