| 书目名称 | Computational Synthetic Geometry |
| 编辑 | Jürgen Bokowski,Bernd Sturmfels |
| 视频video | http://file.papertrans.cn/234/233164/233164.mp4 |
| 丛书名称 | Lecture Notes in Mathematics |
| 图书封面 |  |
| 描述 | Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces. This research monograph considers a large class of problems from convexity and discrete geometry including constructing convex polytopes from simplicial complexes, vector geometries from incidence structures and hyperplane arrangements from oriented matroids. It turns out that algorithms for these constructions exist if and only if arbitrary polynomial equations are decidable with respect to the underlying field. Besides such complexity theorems a variety of symbolic algorithms are discussed, and the methods are applied to obtain new mathematical results on convex polytopes, projective configurations and the combinatorics of Grassmann varieties. Finally algebraic varieties characterizing matroids and oriented matroids are introduced providing a new basis for applying computer algebra methods in this field. The necessary background knowledge is reviewed briefly. The text is accessible to students with graduate level background in mathematics, and will serve professional geometers and computer scientists as an introduction and motivation for further research. |
| 出版日期 | Book 1989 |
| 关键词 | Mathematica; Microsoft Access; Processing; Vector space; boundary element method; complexity; computer alg |
| 版次 | 1 |
| doi | https://doi.org/10.1007/BFb0089253 |
| isbn_softcover | 978-3-540-50478-8 |
| isbn_ebook | 978-3-540-46013-8Series ISSN 0075-8434 Series E-ISSN 1617-9692 |
| issn_series | 0075-8434 |
| copyright | Springer-Verlag Berlin Heidelberg 1989 |
|Archiver|手机版|小黑屋|
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