Subjects

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Algorithms in Computer Algebra - NALG078

Title:	Algoritmy počítačové algebry
Guaranteed by:	Department of Algebra (32-KA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2011
Semester:	winter
E-Credits:	9
Hours per week, examination:	winter s.:2/2, C [HT] summer 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

Guarantor:	doc. RNDr. Jiří Tůma, DrSc.
Class:	Algebra v informatice Algebra v přírodních vědách
Classification:	Informatics > Theoretical Computer Science Mathematics > Algebra
Pre-requisite :	NALG027

Annotation -

Description and analysis of fundamental algorithms for polynomial and number arithmetics. Modular arithmetics. Fast algorithms.

Last update: T_KA (14.05.2002)

Syllabus -

Fundamental algorithms for addition and multiplication of numbers and polynomials.

Extended Euclidean algorithm and its applications.

Modular arithmetics, evaluation and interpolation, secret sharing.

Chinese reminder theorem, modular calculation of determinants.

Algorithms for fast multiplication, Karatsuba's algorithm, discrete and fast Fourier transform.

Fast algorithm for Chinese reminder theorem.

Fast Euclidean algorithm for polynomials.

Fast matrix multiplication.

Factorization of polynomials over finite fields and over integers.

Last update: T_KA (14.05.2002)