FI:M014 Geometric Algorithms II - Course Information

M014 Geometric Algorithms II

Faculty of Informatics
Spring 1998

Extent and Intensity

2/1. 3 credit(s). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).

Teacher(s)

prof. RNDr. Jan Slovák, DrSc. (lecturer)

Guaranteed by

Contact Person: prof. RNDr. Jan Slovák, DrSc.

Prerequisites

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

Syllabus

Basic course of Computational Algebraic Geometry, similar motivation as in the first part of the lectures, but for non-linear objects (given by systems of algebraic equations).
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).

Language of instruction

Czech

Teacher's information

http://www.math.muni.cz/~slovak/#1

The course is also listed under the following terms Spring 1996, Spring 1999, Spring 2001.