CoCoA Tutorials
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)
  • 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