Lesson 1: Introduction to CoCoA
Using CoCoA to implement Euclid's Algorithm (for integers and for univariate polynomials)
01-EuclideanAlgm.cocoa5
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.
02-factorization.cocoa5
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.
03-MonomialIdeals.cocoa5
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.
04-TermOrdering.cocoa5
Lesson 5: Division Algorithm
We look at the division algorithm which lies at the heart of Groebner bases.
05-DivisionAlgm.cocoa5
Lesson 6: Leading term ideal
We consider how to compute LT(I), and the utility of doing so.
06-LeadingTerm.cocoa5
Lesson 7: Buchberger's Algorithm
Presentazione dell'Algoritmo di Buchberger; esempi ed esercizi.
07-BuchbergerAlgm.cocoa5
Lesson 8: Elimination
Algorithms and exercises related to elimination ideals
08-elimination.cocoa5
Lesson 9: Polynomial system solving
We look at exact (algebraic) techniques for solving systems of polynomial equations
09-SystemSolving.cocoa5
Lesson 10: Graph colouring
We look at an application of polynomial system solving to colouring graphs.
10-BuchbergerMoeller.cocoa5
10-GraphColouring.cocoa5