Course: Algoritms of computer algebra

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Course title Algoritms of computer algebra
Course code KMA/XAPAL
Organizational form of instruction no contact
Level of course Doctoral
Year of study not specified
Semester Winter and summer
Number of ECTS credits 30
Language of instruction Czech
Status of course Compulsory-optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
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..


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
Faculty: Faculty of Education Study plan (Version): Theory of Mathematics Education (2) Category: Pedagogy, teacher training and social care - Recommended year of study:-, Recommended semester: -
Faculty: Faculty of Education Study plan (Version): Theory of Mathematics Education (2) Category: Pedagogy, teacher training and social care - Recommended year of study:-, Recommended semester: -