Computer Algebra Course in Genoa
John Abbott - 2014
Lesson 1: Introduction to CoCoA
Using CoCoA to implement Euclid's Algorithm (for integers and for univariate polynomials)
Lesson 2: Advanced use of CoCoA
Using polynomial factorization as the main topic, we shall see how to define and use polynomial rings, homomorphisms, records, and matrices.
Lesson 3: Operations on monomial ideals
Monomial ideals are a simple yet useful subclass of general (polynomial) ideals. We look at various operations on monomial ideals; a first encounter between algebra and algorithmics, and also a foretaste of what is to come.
Lesson 4: Term orderings
Terms orderings lie at the core of Groebner basis theory.
We see how to create and use term orderings in CoCoA; also some special properties of certain orderings.
Lesson 5: Division Algorithm
We look at the division algorithm which lies at the heart of Groebner bases.
Lesson 6: Leading term ideal
We consider how to compute LT(I), and the utility of doing so.
Lesson 7: Buchberger's Algorithm
Presentazione dell'Algoritmo di Buchberger; esempi ed esercizi.
Lesson 8: Elimination
Algorithms and exercises related to elimination ideals
Lesson 9: Polynomial system solving
We look at exact (algebraic) techniques for solving systems of polynomial equations
Lesson 10: Graph colouring
We look at an application of polynomial system solving to colouring graphs.