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+2+0	speciality	optional	
Mathematics-Computer Science - in Hungarian	6	2+2+0	speciality	optional	
Information engineering  - in Hungarian	4	2+2+0		optional	

Teaching Staff in Charge	Assoc.Prof. SZANTO Csaba Lehel, Ph.D., szanto@math.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.	
Bibliography	[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.