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Cylinders Through Five Points: Complex and Real Enumerative Geometry

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Automated Deduction in Geometry (ADG 2006)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4869))

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Abstract

It is known that five points in ℝ3 generically determine a finite number of cylinders containing those points. We discuss ways in which it can be shown that the generic (complex) number of solutions, with multiplicity, is six, of which an even number will be real valued and hence correspond to actual cylinders in ℝ3. We partially classify the case of no real solutions in terms of the geometry of the five given points. We also investigate the special case where the five given points are coplanar, as it differs from the generic case for both complex and real valued solution cardinalities.

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Authors and Affiliations

  1. Wolfram Research, Inc., 100 Trade Center Dr., Champaign, IL 61820, USA

    Daniel Lichtblau

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  1. Daniel Lichtblau
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Francisco Botana Tomas Recio

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© 2007 Springer-Verlag Berlin Heidelberg

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Lichtblau, D. (2007). Cylinders Through Five Points: Complex and Real Enumerative Geometry. In: Botana, F., Recio, T. (eds) Automated Deduction in Geometry. ADG 2006. Lecture Notes in Computer Science(), vol 4869. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77356-6_6

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  • DOI: https://doi.org/10.1007/978-3-540-77356-6_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-77355-9

  • Online ISBN: 978-3-540-77356-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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