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Finding a Deterministic Generic Position for an Algebraic Space Curve

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Computer Algebra in Scientific Computing (CASC 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8660))

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Abstract

Checking whether an algebraic space curve is in a generic position or not is an important step for computing the topology of real algebraic space curve. In this paper, we present an algorithm to find a deterministic generic position for an algebraic space curve.

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References

  1. Alcázar, J.G., Sendra, J.R.: Computation of the topology of real algebraic space curves. Journal of symbolic Computation 39, 719–744 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bouzidi, Y., Lazard, S., Pouget, M., Rouillier, F.: Rational Univariate Representations of bivariate systems and applications. In: Preceeding of ISSAC. ACM (2013)

    Google Scholar 

  3. Cheng, J.S., Gao, X.S., Guo, L.: Root Isolation of Zero-dimensional Polynomial Systems with Linear Univariate Representation. Journal of Symbolic Computation 47(7), 843–858 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  4. Cheng, J.-S., Gao, X.-S., Li, M.: Determining the topology of real algebraic surfaces. In: Martin, R., Bez, H.E., Sabin, M.A. (eds.) IMA 2005. LNCS, vol. 3604, pp. 121–146. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  5. Jin, K., Cheng, J.S.: Isotopic ε-Meshing of Real Algebraic Space Curves. In: SNC 2014 (to appear, 2014) (preprint)

    Google Scholar 

  6. Cheng, J.S., Jin, K., Lazard, D.: Certified Rational Parametric Approximation of Real Algebraic Space Curves with Local Generic Position Method. Journal of Symbolic Computation 58, 18–40 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  7. Cheng, J.S., Jin, K.: A Generic Position Method For Real Roots Isolation Of Zero-Dimensional Polynomial System, arXiv:1312.0462

    Google Scholar 

  8. Diatta, D.N., Mourrain, B., Ruatta, O.: On the computation of the topology of a non-reduced implicit space curve. In: ISSAC 2008, pp. 47–54 (2008)

    Google Scholar 

  9. Diatta, D.N., Mourrain, B., Ruatta, O.: On the isotopic meshing of an algebraic implicit surface. Journal Symbolic Computation 47, 903–925 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  10. Diochnos, D.I., Emiris, I.Z., Tsigaridas, E.P.: On the asymptotic and practical complexity of solving bivariate systems over the reals. Journal Symbolic Computation, Special issue for ISSAC 2007 44(7), 818–835 (2009)

    MATH  MathSciNet  Google Scholar 

  11. González-Vega, L., El Kahoui, M.: An improved upper complexity bound for the topology computation of a real algebraic plane curve. Journal of Complexity 12(4), 527–544 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  12. El Kahoui, M.: Topology of real algebraic space curves. Journal of Symbolic Computation 43, 235–258 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  13. González-Vega, L., Necula, I.: Efficient topology determination of implicitly defined algebraic plane curves. Computer Aided Geometric Design 19, 719–743 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  14. Sakkalis, T., Farouki, R.: Singular points of algebraic curves. Journal of Symbolic Computation 9(4), 405–421 (1990)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Key Lab of Mathematics Mechanization ,Institute of Systems Science, AMSS, Chinese Academy of Sciences, China

    Jin-San Cheng & Kai Jin

Authors
  1. Jin-San Cheng
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  2. Kai Jin
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Editor information

Editors and Affiliations

  1. Laboratory of Information Technologies (LIT), Joint Institute for Nuclear Research, 141980, Dubna, Russia

    Vladimir P. Gerdt

  2. Institut für Mathematik, Universität Kassel, Heinrich-Plett-Straße 40, 34132, Kassel, Germany

    Wolfram Koepf

  3. Institut für Mathematik, Universität Kassel, 34132, Kassel, Germany

    Werner M. Seiler

  4. Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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© 2014 Springer International Publishing Switzerland

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Cheng, JS., Jin, K. (2014). Finding a Deterministic Generic Position for an Algebraic Space Curve. In: Gerdt, V.P., Koepf, W., Seiler, W.M., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2014. Lecture Notes in Computer Science, vol 8660. Springer, Cham. https://doi.org/10.1007/978-3-319-10515-4_6

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  • DOI: https://doi.org/10.1007/978-3-319-10515-4_6

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-10514-7

  • Online ISBN: 978-3-319-10515-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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