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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.
Last update: T_KA (10.05.2006)
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D. Stanovský: Počítačová algebra, 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
Knuth: The art of computer programming, vol. 1, Fundamental algorithms, Addison-Wesley, 3rd edition 1997. Last update: T_KA (21.05.2009)
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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. 4. Factorization of polynomials: square-free factorization, Berlekamp-Hensel's algorithm.
Last update: T_KA (12.05.2009)
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