Lecturer(s)


Hora Jaroslav, doc. RNDr. CSc.

Course content

Representation of polynomials, Computation of the greatest common divisor in Z, Computation of the greatest common divisor for polynomials, Chinese theorem on remainders, Resultant of polynomials, Factorization of polynomials, Integration of rational functions, Number series', Computer methods of determination of the sum, Gosper's algorithm.

Learning activities and teaching methods

Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming), Monitoring

Learning outcomes

Representation of polynomials. Computation of the greatest common divisor of integers and polynomials. The Chinese reminder theorem. Resultant of polynomials. Polynomial factorization and the rational functions integration. Number series, computer methods of summation. The Gosper's algorithm. Elimination of quantifiers in R. The cylindrical algebraic decomposition. Examples of application. Inequality theorems proving.
Knowledge of basic algorithms of computer algebra and their application.

Prerequisites

Knowledge of algebra of the basic university course.

Assessment methods and criteria

Oral examination, Written examination
Understanding of basic notions of the theory, knowledge of definitions, theorems and basic proofs. Ability to solve typical problems of a given theory. Written part of the exam is particularly oriented to verification whether a student can solve individual problems which come from a given theory. The aim of the oral part of the exam is to verify student's understanding of the theory and his/her ability to apply it.

Recommended literature


Davenport, J. H. , Siret, Y. and Tournier. E. Computer Algebra, Systems and Algorithms for Algebraic Computation. London: Academic Press, 1988..

von zur Gathen, G, Bernard, J. Modern Computer Algebra. Cambridge Univ. Press, 1999..

Winkler, F. Polynomial Algorithms in Computer Algebra. Springer, 1996..
