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Computations with algebraic curves

  • Algebraic Geometry
  • Conference paper
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Symbolic and Algebraic Computation (ISSAC 1988)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 358))

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Abstract

We present a variety of computational techniques dealing with algebraic curves both in the plane and in space. Our main results are polynomial time algorithms (1) to compute the genus of plane algebraic curves, (2) to compute the rational parametric equations for implicitly defined rational plane algebraic curves of arbitrary degree, (3) to compute birational mappings between points on irreducible space curves and points on projected plane curves and thereby to compute the genus and rational parametric equations for implicitly defined rational space curves of arbitrary degree, (4) to check for the faithfulness (one to one) of parameterizations.

Supported in part by ONR contract N00014-86-0689 under URI, ARO contract DAAG29-85-C-0018 under Cornell MSI and ONR contract N00014-88-K-0402

Supported in part by NSF Grant MIP 85-21356, ARO Contract DAAG29-85-C0018 under Cornell MSI and ONR contract N00014-88-K-0402

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Author information

Authors and Affiliations

  1. Department of Mathematics, Purdue University, 47907, West Lafayette, IN

    Shreeram S. Abhyankar

  2. Department of Computer Science, Purdue University, 47907, West Lafayette, IN

    Chanderjit L. Bajaj

Authors
  1. Shreeram S. Abhyankar
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  2. Chanderjit L. Bajaj
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P. Gianni

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© 1989 Springer-Verlag Berlin Heidelberg

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Abhyankar, S.S., Bajaj, C.L. (1989). Computations with algebraic curves. In: Gianni, P. (eds) Symbolic and Algebraic Computation. ISSAC 1988. Lecture Notes in Computer Science, vol 358. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51084-2_26

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  • DOI: https://doi.org/10.1007/3-540-51084-2_26

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  • Print ISBN: 978-3-540-51084-0

  • Online ISBN: 978-3-540-46153-1

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