000 03036nam a22004695i 4500
001 978-3-540-46013-8
003 DE-He213
005 20160624101822.0
007 cr nn 008mamaa
008 121227s1989 gw | s |||| 0|eng d
020 _a9783540460138
_9978-3-540-46013-8
024 7 _a10.1007/BFb0089253
_2doi
050 4 _aQA440-699
072 7 _aPBM
_2bicssc
072 7 _aMAT012000
_2bisacsh
082 0 4 _a516
_223
100 1 _aBokowski, Jürgen.
_eauthor.
245 1 0 _aComputational Synthetic Geometry
_h[electronic resource] /
_cby Jürgen Bokowski, Bernd Sturmfels.
260 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c1989.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c1989.
300 _aVIII, 172 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1355
505 0 _aPreliminaries -- On the existence of algorithms -- Combinatorial and algebraic methods -- Algebraic criteria for geometric realizability -- Geometric methods -- Recent topological results -- Preprocessing methods -- On the finding of polyheadral manifolds -- Matroids and chirotopes as algebraic varieties.
520 _aComputational 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.
650 0 _aMathematics.
650 0 _aGeometry.
650 1 4 _aMathematics.
650 2 4 _aGeometry.
700 1 _aSturmfels, Bernd.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540504788
786 _dSpringer
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1355
856 4 0 _uhttp://dx.doi.org/10.1007/BFb0089253
942 _2EBK1372
_cEBK
999 _c30666
_d30666