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Course, academic year 2023/2024
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Computer Algebra 2 - NMMB403
Title: Počítačová algebra 2
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2020
Semester: winter
E-Credits: 6
Hours per week, examination: winter s.:3/1, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: not taught
Language: English, Czech
Teaching methods: full-time
Teaching methods: full-time
Is provided by: NMMB413
Additional information:
Guarantor: doc. Mgr. Jan Šaroch, Ph.D.
Class: M Mgr. MMIB
M Mgr. MMIB > Povinné
Classification: Mathematics > Algebra
Incompatibility : NMIB103
Interchangeability : NMIB103, NMMB413
Is interchangeable with: NMIB103
Annotation -
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)
Course completion requirements -

3 homeworks.

Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (28.10.2019)
Literature -

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)
Requirements to the exam -

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)
Syllabus -

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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