COMPUTATIONAL ALGEBRA
Academic Year 2020/2021 - 1° Year - Curriculum APPLICATIVOCredit Value: 6
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. 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.
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.