Computer algebra

The course deals with computer algebraic aspects of polynomial rings by means of the theory of Gröbner bases.

This course is offered as a reading course in the autumn 2026, and was most recently offered as a regular course in 2022.

The following topics and results are covered: ideals, Hilbert's basis theorem, affine varieties, Hilbert's nullstellensatz, monomial orderings, Gröbner bases, Buchberger's algorithm, elimination, quotient rings.

The course also includes an introduction to a modern computer algebra system (CAS) with focus on how to use it to solve applied problems from graph theory, theoretical computer science, and optimization.

The course consists of three elements: theory, practical exercises and project.


Teaching Format

Instruction consists of lectures, practical exercises and projects.


Assessment

The course is assessed through written examination, hand-in assignments and project work.

Examiner

A list of examiners can be found on

Exam information

The schedule will be available no later than one month before the start of the course. We do not recommend print-outs as changes can occur. At the start of the course, your department will advise where you can find your schedule during the course.


Note that the course literature can be changed up to two months before the start of the course.

Cox, Little, O'Shea; Ideal, varieties, and algorithms. Springer.

List of course literature Department of Mathematics

Course reports are displayed for the three most recent course instances.


New student
During your studies

Course web

You can find our course webpages on kurser.math.su.se.






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