LEADER 03269nam 2200601 450 001 996466644503316 005 20220304102629.0 010 $a3-540-46013-6 024 7 $a10.1007/BFb0089253 035 $a(CKB)1000000000437450 035 $a(SSID)ssj0000322057 035 $a(PQKBManifestationID)12069531 035 $a(PQKBTitleCode)TC0000322057 035 $a(PQKBWorkID)10281987 035 $a(PQKB)11258740 035 $a(DE-He213)978-3-540-46013-8 035 $a(MiAaPQ)EBC5594955 035 $a(Au-PeEL)EBL5594955 035 $a(OCoLC)1076253713 035 $a(MiAaPQ)EBC6842619 035 $a(Au-PeEL)EBL6842619 035 $a(OCoLC)864232473 035 $a(PPN)155198416 035 $a(EXLCZ)991000000000437450 100 $a20220304d1989 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aComputational synthetic geometry /$fJurgen Bokowski, Bernd Sturmfels 205 $a1st ed. 1989. 210 1$aBerlin ;$aHeidelberg :$cSpringer-Verlag,$d[1989] 210 4$dİ1989 215 $a1 online resource (VIII, 172 p.) 225 1 $aLecture Notes in Mathematics ;$v1355 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-50478-8 327 $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. 330 $aComputational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces. This research monograph considers a large class of problems from convexity and discrete geometry including constructing convex polytopes from simplicial complexes, vector geometries from incidence structures and hyperplane arrangements from oriented matroids. It turns out that algorithms for these constructions exist if and only if arbitrary polynomial equations are decidable with respect to the underlying field. Besides such complexity theorems a variety of symbolic algorithms are discussed, and the methods are applied to obtain new mathematical results on convex polytopes, projective configurations and the combinatorics of Grassmann varieties. Finally algebraic varieties characterizing matroids and oriented matroids are introduced providing a new basis for applying computer algebra methods in this field. The necessary background knowledge is reviewed briefly. The text is accessible to students with graduate level background in mathematics, and will serve professional geometers and computer scientists as an introduction and motivation for further research. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v1355. 606 $aGeometry$xData processing 615 0$aGeometry$xData processing. 676 $a516.00285 700 $aBokowski$b Ju?rgen$0441131 702 $aSturmfels$b Bernd$f1962- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466644503316 996 $aComputational synthetic geometry$91487124 997 $aUNISA