Computations in Algebraic Geometry with Macaulay 2: v. 2 (Algorithms and Computation in Mathematics) [Englisch] [Gebundene Ausgabe]

"... Fazit: das Buch ist kein Lehrbuch im traditionellen Sinn. Sicherlich ist Teil I eine gelungene Einführung, wenn man schon die elementaren Grundlagen der Algebraischen oder Analytischen Geometrie kennt. In Teil II ist das Buch aber eher wie ein Tagungsband, in dem einzelne Spezialisten ihre Themen vorstellen. Hier kann man sich etwas aussuchen, denn die Artikel sind unabhängig voneinander. ... Ich habe beim Lesen viele interessante Stellen gefunden, die man beim flüchtigen Durchblättern übersehen kann. Man muss sich Zeit nehmen, dann wird der Band wirklich zum Gewinn für alle, die Interesse an Algebraischer Geometrie haben." S.Müller-Stach, Jahresberichte der DMV 2002, Bd. 104, Heft 4

This book presents algorithmic tools for algebraic geometry, with experimental applications. It also introduces Macaulay 2, a computer algebra system supporting research in algebraic geometry, commutative algebra, and their applications. The algorithmic tools presented here are designed to serve readers wishing to bring such tools to bear on their own problems. The first part of the book covers Macaulay 2 using concrete applications; the second emphasizes details of the mathematics.

This book presents algorithmic tools for algebraic geometry and experimental applications of them. It also introduces a software system in which the tools have been implemented and with which the experiments can be carried out. Macaulay 2 is a computer algebra system devoted to supporting research in algebraic geometry, commutative algebra, and their applications. The reader of this book will encounter Macaulay 2 in the context of concrete applications and practical computations in algebraic geometry. The expositions of the algorithmic tools presented here are designed to serve as a useful guide for those wishing to bring such tools to bear on their own problems. These expositions will be valuable to both the users of other programs similar to Macaulay 2 (for example, Singular and CoCoA) and those who are not interested in explicit machine computations at all. The first part of the book is primarily concerned with introducing Macaulay2, whereas the second part emphasizes the mathematics.