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