COMPUTATIONAL ALGEBRA

MAT/02 - 6 CFU - 2° Semester

Teaching Staff

VINCENZO MICALE


Learning Objectives

The objective of the second module of the course is to introduce the theory of Groebner bases , in order to begin the computational student to algebra and its applications


Course Structure

Teaching is done on the blackboard in a traditional way. The exercises also include using the computer



Detailed Course Content

I. Basic Theory of Groebner Bases. The linear case. The case of a single variable. Monomial orders. The division algorithm. Definition of Groebner Bases. S - polynomials and Buchberger algorithm. Reduced Groebner bases .

II . Applications of Groebner Bases. Elementary applications of Groebner Bases. Theory of elimination. Polynomial maps. Some applications to Algebraic Geometry .

III . Modules. Groebner bases and Syzygies. Calculation of the module of syzygy of an ideal.



Textbook Information

W.W. Adams, P. Loustaunau, An introduction to Groebner Bases, American Math. Soc, 1994.




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