Tre Amici e la Computer Algebra

Robbiano, Lorenzo

Bollettino della Unione matematica italiana, Série 8, 9A (2006) no. 1, pp. 1-23

Résumé

We listen in to some conversations of a dancer, a photographer, and a mathematical gardener. They speak of many things ranging from queens to oil wells, from logic problems to sundials with palindromes. We shall hear about colourful maps, CoCoA and gin, and short squares and magic squares. They even mention Hilbert functions and Groebner bases. All with the practicality of a gardener, the perspicacity of a photographer, and the delicacy of a dancer. And also a little knowledge of computational algebra. It is not a popular science article. It is a story, a tale around and about computer algebra. I often mention the two-volume book "Computational Commutative Algebra", which I wrote with Martin Kreuzer, because it explains the mathematics behind the various topics that appear in the story. I often mention the CoCoA program, lovingly crafted over the last twenty years by my research team in Genoa; it helps solve the mathematical conundrums we shall encounter. For those readers who have enjoyed the tale and are fascinated by the glimpses of mathematics, I have prepared an appendix and a short bibliography. The appendix explains some of the mathematical ideas and reasoning hidden behind the scenes. The bibliography contains a list of modern books about computer algebra and some of its vast palette of applications.