COMPUTATIONAL ALGEBRA
Academic Year 2019/2020 - 1° Year - Curriculum APPLICATIVOCredit Value: 6
Scientific field: MAT/02 - Algebra
Taught classes: 35 hours
Exercise: 12 hours
Term / Semester: 2°
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.