\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - Algebraic Kernel

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Bibliographic References

[1]

  J. Abbott. Quadratic interval refinement for real roots, 2006. Poster presented at the 2006 Int. Symp. on Symb. and Alg. Comp. (ISSAC 2006).

[2]

  Eric Berberich, Arno Eigenwillig, Michael Hemmer, Susan Hert, Lutz Kettner, Kurt Mehlhorn, Joachim Reichel, Susanne Schmitt, Elmar Schömer, and Nicola Wolpert. Exacus: Efficient and exact algorithms for curves and surfaces. In Gerth S. Brodal and Stefano Leonardi, editors, 13th Annual European Symposium on Algorithms (ESA 2005), volume 3669 of Lecture Notes in Computer Science, pages 155–166, Palma de Mallorca, Spain, October 2005. European Association for Theoretical Computer Science (EATCS), Springer.

[3]

  Eric Berberich, Michael Hemmer, Menelaos I. Karavelas, and Monique Teillaud. Revision of the interface specification of algebraic kernel. Technical Report ACS-TR-243301-01, INRIA Sophia-Antipolis, Max Planck Institut für Informatik, National University of Athens, 2007.

[4]

  Arno Eigenwillig and Michael Kerber. Exact and efficient 2d-arrangements of arbitrary algebraic curves. In Proceedings of the Nineteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA08), 2008. 122–131.

[5]

  Arno Eigenwillig, Michael Kerber, and Nicola Wolpert. Fast and exact geometric analysis of real algebraic plane curves. In Christopher W. Brown, editor, Proocedings of the 2007 International Symposium on Symbolic and Algebraic Computation (ISSAC 2007), pages 151–158, 2007.

[6]

  Arno Eigenwillig. Real Root Isolation for Exactand Approximate Polynomials Using Descartes ' Rule of Signs. PhD thesis, Universität des Saarlandes, Saarbrücken, Germany, 2008.

[7]

  L. Gonzalez-Vega, T. Recio, H. Lombardi, and M.-F. Roy. Sturm-habicht sequences, determinants and real roots of univariate polynomials. In B.F. Caviness and J.R. Johnson, editors, Quantifier Elimination and Cylindrical Algebraic Decomposition, Texts and Monographs in Symbolic Computation, pages 300–316. Springer, 1998.

[8]

  Michael Kerber. Geometric Algorithms for Algebraic Curves and Surfaces. PhD thesis, Universität des Saarlandes, Saarbrücken, Germany, 2009.

[9]

  Sylvain Lazard, Luis Peñaranda, and Elias Tsigaridas. Univariate algebraic kernel and application to arrangements. In Jan Vahrenhold, editor, SEA, volume 5526 of Lecture Notes in Computer Science, pages 209–220. Springer, 2009.

[10]

  MPFI - the multiple precision floating-point interval library. Revol, Nathalie and Rouillier, Fabrice.

[11]

  MPFR - the multiple precision floating-point reliable library. The MPFR Team.

[12]

  Fabrice Rouillier and Paul Zimmermann. Efficient isolation of polynomial's real roots. Journal of Computational and Applied Mathematics, 162(1):33–50, 2004.

[13]

  RS - A software for real solving of algebraic systems. Rouillier, Fabrice.