Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Graduate

SUBJECT

Code
Subject
MML0012 Groebner Bases and Automated Proofs for Theorems in Geometry
Section
Semester
Hours: C+S+L
Category
Type
Computer Science - in Hungarian
4
2+1+0
speciality
optional
Information engineering - in Hungarian
4
2+1+0
complementary
optional
Teaching Staff in Charge
Assoc.Prof. SZANTO Csaba Lehel, Ph.D.,  szantomath.ubbcluj.ro
Aims
The aim of the course is to present the foundations of the theory of Groebner bases emphasizing its applications in different mathematical domains from coding theory to automated proofs for theorems in geometry
Content
The covered subjects include: introductory algebraic notions, definition of Groebner bases, construction of Groebner bases, Buchberger@s algorithm, Faugére F4 algorithm, Groebner bases in automated proofs for theorems in geometry, Groebner bases in the solution of a polynomial system of equations, Groebner bases in invariant theory and coding theory.
References
[1] B. Buchberger. Gröbner-Bases and System Theory.
Multidimensional Systems and Signal Processing, vol 12, nb 3-4,
July-October 2001, Springer
[2] B. Buchberger. Gröbner Bases: A Short Introduction for Systems
Theorists, http://www.risc.uni-linz.ac.at/people/buchberg/papers/2001-02-19-A.pdf
[3] W. W. Adams, P. Loustaunau. Introduction to Gröbner Bases.
Graduate Studies in Mathematics, American Mathematical Society,
Providence, R.I., 1994.
Assessment
Homework. Essays. Written exam.
Links: Syllabus for all subjects
Romanian version for this subject
Rtf format for this subject