Computational Algebra

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

Teaching is done on the blackboard in a traditional way. The exercises also include using the computer. If the teaching is given in mixed or remote mode, they can be introduced the necessary changes with respect to what was previously stated, in order to comply the planned program and reported in the syllabus.

Information for students with disabilities and / or SLD. To guarantee equal opportunities 
and in compliance with the laws in force, interested students can ask for a personal interview 
in order to plan any compensatory and / or dispensatory measures, based on the didactic objectives
 and specific needs. It is also possible to contact the referent teacher CInAP (Center for Active
 and Participated Integration - Services for Disabilities and / or SLD) of our Department,
 prof. Filippo Stanco.

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.

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