000 | 03188nam a22004695i 4500 | ||
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001 | 978-3-540-46013-8 | ||
003 | DE-He213 | ||
005 | 20190213151233.0 | ||
007 | cr nn 008mamaa | ||
008 | 121227s1989 gw | s |||| 0|eng d | ||
020 |
_a9783540460138 _9978-3-540-46013-8 |
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024 | 7 |
_a10.1007/BFb0089253 _2doi |
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050 | 4 | _aQA440-699 | |
072 | 7 |
_aPBM _2bicssc |
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072 | 7 |
_aMAT012000 _2bisacsh |
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072 | 7 |
_aPBM _2thema |
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082 | 0 | 4 |
_a516 _223 |
100 | 1 |
_aBokowski, Jürgen. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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245 | 1 | 0 |
_aComputational Synthetic Geometry _h[electronic resource] / _cby Jürgen Bokowski, Bernd Sturmfels. |
264 | 1 |
_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg : _bImprint: Springer, _c1989. |
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300 |
_aVIII, 172 p. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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_acomputer _bc _2rdamedia |
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_aonline resource _bcr _2rdacarrier |
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_atext file _bPDF _2rda |
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490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1355 |
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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 | _aGeometry. | |
650 | 1 | 4 |
_aGeometry. _0http://scigraph.springernature.com/things/product-market-codes/M21006 |
700 | 1 |
_aSturmfels, Bernd. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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710 | 2 | _aSpringerLink (Online service) | |
773 | 0 | _tSpringer eBooks | |
776 | 0 | 8 |
_iPrinted edition: _z9783662168219 |
776 | 0 | 8 |
_iPrinted edition: _z9783540504788 |
830 | 0 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1355 |
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856 | 4 | 0 | _uhttps://doi.org/10.1007/BFb0089253 |
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912 | _aZDB-2-LNM | ||
912 | _aZDB-2-BAE | ||
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