CandS

Originally the software consisted of 17 Mathematica Packages written by Alfred Gray (1939 - 1998) in connection with his book ”Modern Differential Geometry of Curves and Surfaces” and collected in a directory named CandS. These packages are written in Mathematica version 2.2 or 3.0. Clearly, to be used today, they need an adaption to Mathematica version 9.0. For the four most important of Gray`s packages this adaption has been done by Rolf Sulanke. Thus now, with the software CandS, we have more than 200 functions (or ”miniprograms”), applicable to calculate the basic Euclidean differential invariants of curves and surfaces and to present these graphically. A catalog of 200 parameter presentations of curves, and a catalog of 200 parameter representations of surfaces collected by Alfred Gray complete the software as a useful tool for Mathematica users in education and engineering. Examples of applications of the miniprograms are given in the notebook CandS-1.nb of Rolf Sulanke which can be used as a starting point for working in Euclidean differential geometry with Mathematica. This notebook, the adapted and Gray`s not adapted packages are packed into the zip-file gray1.zip which can be downloaded from the URL of the software, where also a detailed description of the software can be seen.


References in zbMATH (referenced in 109 articles , 1 standard article )

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  1. Bas, E.; Erdogmus, D.: Connectivity of projected high dimensional data charts on one-dimensional curves (2011)
  2. Chen, C.: The order of local mobility of mechanisms (2011)
  3. Ersoy, Soley; Tosun, Murat: Lamarle formula in 3-dimensional Lorentz space (2011)
  4. Gemmer, John A.; Venkataramani, Shankar C.: Shape selection in non-Euclidean plates (2011)
  5. Mladenov, Ivaïlo M.; Hadzhilazova, Mariana Ts.; Djondjorov, Peter A.; Vassilev, Vassil M.: On some deformations of the Cassinian oval (2011)
  6. Nistor, Ana-Irina: Certain constant angle surfaces constructed on curves (2011)
  7. Sym, Antoni; Szereszewski, Adam: On Darboux’s approach to (R)-separability of variables (2011)
  8. Yamasaki, K.; Yajima, T.; Iwayama, T.: Differential geometric structures of stream functions: incompressible two-dimensional flow and curvatures (2011)
  9. Arimoto, Suguru; Yoshida, Morio: Modeling and control of 2D grasping under rolling contact constraints between arbitrary shapes: a Riemannian-geometry approach (2010) ioport
  10. Ganchev, Georgi; Mihova, Vesselka: On the invariant theory of Weingarten surfaces in Euclidean space (2010)
  11. Hoveijn, I.; Kirillov, O. N.: Singularities on the boundary of the stability domain near 1:1-resonance (2010)
  12. Jiao, Xiangmin; Colombi, Andrew; Ni, Xinlai; Hart, John: Anisotropic mesh adaptation for evolving triangulated surfaces (2010) ioport
  13. Jiao, Xiangmin; Einstein, Daniel R.; Dyedov, Vladimir: Local orthogonal cutting method for computing medial curves and its biomedical applications (2010)
  14. Kadianakis, N.: Evolution of surfaces and the kinematics of membranes (2010)
  15. Staicu, Ana-Maria; Fraser, Donald A. S.: The second order ancillary is rotation based (2010)
  16. Yoshida, Norimasa; Fukuda, Ryo; Saito, Takafumi: Logarithmic curvature and torsion graphs (2010)
  17. Barros, Manuel; Ferrández, Angel: A conformal variational approach for helices in nature (2009)
  18. Ginoux, Jean-Marc: Differential geometry applied to dynamical systems. With CD-ROM (2009)
  19. Olver, Peter J.: Differential invariants of maximally symmetric submanifolds (2009)
  20. Treyssède, Fabien; Ben Tahar, Mabrouk: Jump conditions for unsteady small perturbations at fluid-solid interfaces in the presence of initial flow and prestress (2009)