Applications of computational algebraic geometry. American Mathematical Society short course, San Diego, CA, USA, January 6–7, 1997.

*(English)*Zbl 0880.00039
Proceedings of Symposia in Applied Mathematics. 53. Providence, RI: American Mathematical Society (AMS). 172 p. (1998).

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Publisher’s description: This book introduces readers to key ideas and applications of computational algebraic geometry. Beginning with the discovery of Gröbner bases and fueled by the advent of modern computers and the rediscovery of resultants, computational algebraic geometry has grown rapidly in importance. The fact that “crunching equations” is now as easy as “crunching numbers” has had a profound impact in recent years. At the same time, the mathematics used in computational algebraic geometry is unusually elegant and accessible, which makes the subject easy to learn and easy to apply.

This book begins with an introduction to Gröbner bases and resultants, then discusses some of the more recent methods for solving systems of polynomial equations. A sampler of possible applications follows, including computer-aided geometric design, complex information systems, integer programming and algebraic coding theory. The lectures in the book assume no previous acquaintance with the material.

Indexed articles:

Cox, David A., Introduction to Gröbner bases, 1-24 [Zbl 0941.13018]

Sturmfels, Bernd, Introduction to resultants, 25-39 [Zbl 0916.13008]

Manocha, Dinesh, Numerical methods for solving polynomial equations, 41-66 [Zbl 0912.65044]

Sederberg, Thomas W., Applications to computer aided geometric design, 67-89 [Zbl 0885.68131]

Kramer, Xenia H.; Laubenbacher, Reinhard C., Combinatorial homotopy of simplicial complexes and complex information systems, 91-118 [Zbl 0886.05122]

Thomas, Rekha R., Applications to integer programming, 119-141 [Zbl 0888.90126]

Little, John B., Applications to coding theory, 143-167 [Zbl 1119.13305]

##### MSC:

00B25 | Proceedings of conferences of miscellaneous specific interest |

13-06 | Proceedings, conferences, collections, etc. pertaining to commutative algebra |

14-06 | Proceedings, conferences, collections, etc. pertaining to algebraic geometry |

68W30 | Symbolic computation and algebraic computation |

13P10 | Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) |

14Q99 | Computational aspects in algebraic geometry |

90C10 | Integer programming |

94B27 | Geometric methods (including applications of algebraic geometry) applied to coding theory |