M0140 Algorithms of Algebraic Geometry

Faculty of Science
Spring 2005
Extent and Intensity
2/0/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jan Slovák, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Jan Slovák, DrSc.
Timetable
Tue 17:00–18:50 N41
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
Basic course of Computational Algebraic Geometry. Solutions for algorithmic problems related to non-linear objects (given by systems of algebraic equations).
Syllabus
  • Afine varieties and polynomial ideals (implicit and parametric description of varieties, the relation of ideals and varieties, examples). & Gröbner bases (polynomial order, the division with remainder, Hilbert theorem, the existence of Gröbner bases). & Buchberger's algorithm (reduced Gröbner bases, simple algorithm, Buchberger's algorithm, examples of applications). & Elimination theory and decomposition of varieties (the elimination theorem, resultants, the extension theorem, implicitization of parametric description of varieties, indecomposable varieties). & Applications to algebraic curves (solvability of systems of equations, singular points of curves, envelopes of families, tangents and tangent cones). & Further applications (computerized proofs in plane geometry, Wu's method, kinematic problem for 'plane robots', the inverse problem, the singularities).
Literature
  • učební text na www.math.muni.cz/~slovak
  • COX, David A., John B. LITTLE and Donal O'SHEA. Ideals, varieties, and algorithms : an introduction to computational algebraic geometry and commutative algebra. 2nd ed. New York: Springer-Verlag, 1996, xiii, 536. ISBN 0387946802. info
Assessment methods (in Czech)
Zkouška formou nepříliš formální rozpravy o studované problematice.
Language of instruction
Czech
Further Comments
The course is taught once in two years.
Teacher's information
http://www.math.muni.cz/~slovak
The course is also listed under the following terms Spring 2003.
  • Enrolment Statistics (recent)
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