Software for Algebraic GeometryMichael E. Stillman, Nobuki Takayama, Jan Verschelde Algorithms in algebraic geometry go hand in hand with software packages that implement them. Together they have established the modern field of computational algebraic geometry which has come to play a major role in both theoretical advances and applications. Over the past fifteen years, several excellent general purpose packages for computations in algebraic geometry have been developed, such as, CoCoA, Singular and Macaulay 2. While these packages evolve continuously, incorporating new mathematical advances, they both motivate and demand the creation of new mathematics and smarter algorithms. This volume reflects the workshop “Software for Algebraic Geometry” held in the week from 23 to 27 October 2006, as the second workshop in the thematic year on Applications of Algebraic Geometry at the IMA. The papers in this volume describe the software packages Bertini, PHClab, Gfan, DEMiCs, SYNAPS, TrIm, Gambit, ApaTools, and the application of Risa/Asir to a conjecture on multiple zeta values. They offer the reader a broad view of current trends in computational algebraic geometry through software development and applications. |
Contents
1 | |
A MATLABOctave interface to PHCpack | 15 |
Computing Grobner fans and tropical varieties in Gfan | 33 |
On a conjecture for the dimension of the space | 47 |
SYNAPS a library for dedicated applications | 81 |
Tropical implicitization and mixed fiber polytopes | 110 |
A software toolbox for approximate | 149 |
List of workshop participants | 169 |
Other editions - View all
Software for Algebraic Geometry Michael E. Stillman,Nobuki Takayama,Jan Verschelde No preview available - 2010 |
Software for Algebraic Geometry Michael E. Stillman,Nobuki Takayama,Jan Verschelde No preview available - 2008 |