2026

Computational Algebra

Name: Computational Algebra
Code: MAT10146D
6 ECTS
Duration: 15 weeks/156 hours
Scientific Area: Mathematics

Teaching languages: Portuguese
Languages of tutoring support: Portuguese

Sustainable Development Goals

Learning Goals

This course aims to provide the student an introdution to Computational Algebra, by studying algorithms
related to Commutative Algebra and Semigroup Theory.

Contents

Introduction. Polynomials and affine space. Affine varieties. Parametrizations of affine varieties. Ideals.
Polynomials of one variable. Monomial orderings in k[x_1,...,x_n]. A division algorithm in k[x_1,...,x_n].
Monomial ideals and Dickson's Lemma. Hilbert Beses Theorem Gröbner bases. Buchberger's algorithm.
Some applicatuons of Gröbner bases. Rewriting Systems. Knuth Bendix procedure.

Teaching Methods

Guided readings. Evaluation throughout the semester: essays and oral presentation.