Axel is an algebraic geometric modeler that aims at providing “algebraic modeling” tools for the manipulation and computation with curves, surfaces or volumes described by semi-algebraic representations. These include parametric and implicit representations of geometric objects. Axel also provides algorithms to compute intersection points or curves, singularities of algebraic curves or surfaces, certified topology of curves and surfaces, etc. A plugin mechanism allows to extend easily the data types and functions available in the plateform.

References in zbMATH (referenced in 22 articles , 1 standard article )

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  1. Jin, Kai; Cheng, Jinsan: Isotopic meshing of a real algebraic space curve (2020)
  2. Toth, Csaba D. (ed.); Goodman, Jacob E. (ed.); O’Rourke, Joseph (ed.): Handbook of discrete and computational geometry (2017)
  3. Clamond, Didier; Dutykh, Denys; Galligo, André: Computer algebra applied to a solitary waves study (2015)
  4. Cheng, Jin-San; Jin, Kai; Lazard, Daniel: Certified rational parametric approximation of real algebraic space curves with local generic position method (2013)
  5. Hodorog, Mădălina; Schicho, Josef: A regularization approach for estimating the type of a plane curve singularity (2013)
  6. Hodorog, Mădălina; Schicho, Josef: A symbolic-numeric algorithm for genus computation (2012)
  7. Alcazar, Juan Gerardo: On the different shapes arising in a family of plane rational curves depending on a parameter (2010)
  8. Hodorog, Mădălina; Mourrain, Bernard; Schicho, Josef: GENOM3CK: a library for genus computation of plane complex algebraic curves using knot theory (2010)
  9. Alberti, L.; Mourrain, B.; Wintz, J.: Topology and arrangement computation of semi-algebraic planar curves (2008)
  10. Berberich, Eric; Kerber, Michael; Sagraloff, Michael: Exact geometric-topological analysis of algebraic surfaces (2008)
  11. Daouda, Diatta Niang; Mourrain, Bernard; Ruatta, Olivier: On the computation of the topology of a non-reduced implicit space curve (2008)
  12. Dokken, Tor: The GAIA project on intersection and implicitization (2008)
  13. El Kahoui, M’hammed: Topology of real algebraic space curves (2008)
  14. Liang, Chen; Mourrain, Bernard; Pavone, Jean-Pascal: Subdivision methods for the topology of 2d and 3d implicit curves (2008)
  15. Mourrain, Bernard; Pavone, Jean-Pascal; Trebuchet, Philippe; Tsigaridas, Elias P.; Wintz, Julien: SYNAPS: a library for dedicated applications in symbolic numeric computing (2008)
  16. Alcazar, Juan Gerardo; Schicho, Josef; Sendra, Juan Rafael: A delineability-based method for computing critical sets of algebraic surfaces (2007)
  17. Bartoň, Michael; Jüttler, Bert: Computing roots of polynomials by quadratic clipping (2007)
  18. Boissonnat, Jean-Daniel (ed.); Teillaud, Monique (ed.): Effective computational geometry for curves and surfaces (2007)
  19. Jüttler, Bert; Chalmovianský, Pavel: A predictor-corrector-type technique for the approximate parameterization of intersection curves (2007)
  20. Cheng, Jin-San; Gao, Xiao-Shan; Li, Ming: Determining the topology of real algebraic surfaces (2005)

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