Computational Algebra

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.

Practical exercises will be assigned to be solved on the computer using software; if solved with at least a sufficient score, you will move on to an oral exam. The results of the exercises carried out during the course will not be taken into account.Verification of learning can also be carried out electronically, should conditions require it.

Characterization theorem of Groebner bases. Applications of Groebner Bases to Algebra and Algebraic Geometry. Calculation of the modulus of the syzygies of an ideal.