03269nam 2200601 450 99646664450331620220304102629.03-540-46013-610.1007/BFb0089253(CKB)1000000000437450(SSID)ssj0000322057(PQKBManifestationID)12069531(PQKBTitleCode)TC0000322057(PQKBWorkID)10281987(PQKB)11258740(DE-He213)978-3-540-46013-8(MiAaPQ)EBC5594955(Au-PeEL)EBL5594955(OCoLC)1076253713(MiAaPQ)EBC6842619(Au-PeEL)EBL6842619(OCoLC)864232473(PPN)155198416(EXLCZ)99100000000043745020220304d1989 uy 0engurnn|008mamaatxtccrComputational synthetic geometry /Jurgen Bokowski, Bernd Sturmfels1st ed. 1989.Berlin ;Heidelberg :Springer-Verlag,[1989]©19891 online resource (VIII, 172 p.) Lecture Notes in Mathematics ;1355Bibliographic Level Mode of Issuance: Monograph3-540-50478-8 Preliminaries -- 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.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.Lecture notes in mathematics (Springer-Verlag) ;1355.GeometryData processingGeometryData processing.516.00285Bokowski Jürgen441131Sturmfels Bernd1962-MiAaPQMiAaPQMiAaPQBOOK996466644503316Computational synthetic geometry1487124UNISA01314nam 2200349 n 450 99639267320331620221108012543.0(CKB)1000000000683255(EEBO)2240935454(UnM)99866397(EXLCZ)99100000000068325519940401d1656 uy |engurbn#|||a|bb|Actæon and Diana[electronic resource] with a pastoral story of the nymph Oenone; followed by the several conceited humors of Bumpkin, the huntsman. Hobbinall, the shepheard. Singing Simpkin. And John Swabber, the sea-manPrinted at London by T. Newcomb, for the use of the author Robert Cox[1656][4], 40 pDate of Thomason purchase recorded in Thomason catalogue as 1 September 1656.Annotation on Thomason copy: "7ber 1st" [i.e. September 1st].Reproduction of the original in the British Library.eebo-0018English drama17th centuryEarly works to 1800English dramaCox Robert-1655.1010095Cu-RivESCu-RivESCStRLINWaOLNBOOK996392673203316Actæon and Diana2385389UNISA