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 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. Fukunaga, Tomonori; Takahashi, Masatomo: Evolutes and involutes of frontals in the Euclidean plane (2015)
  2. Karakuş, Fatma; Yayli, Yusuf: The Fermi derivative in the hypersurfaces (2015)
  3. Raviv, Dan; Kimmel, Ron: Affine invariant geometry for non-rigid shapes (2015)
  4. Sato, Masayuki; Shimizu, Yasuhiro: Log-aesthetic curves and Riccati equations from the viewpoint of similarity geometry (2015)
  5. Šukilović, Tijana: Curvature based shape detection (2015)
  6. Yu, Haiou; Pei, Donghe; Cui, Xiupeng: Evolutes of fronts on Euclidean 2-sphere (2015)
  7. Athukorallage, Bhagya; Paragoda, Thanuja; Toda, Magdalena: Roulettes of conics, Delaunay surfaces and applications (2014)
  8. Fukunaga, T.; Takahashi, Masatomo: Evolutes of fronts in the Euclidean plane (2014)
  9. Kassabov, Ognian: Transition to canonical principal parameters on minimal surfaces (2014)
  10. Munteanu, Marian Ioan: The Landau-Hall problem on canal surfaces (2014)
  11. Yeşiltaş, Özlem: Exact solutions of the Dirac Hamiltonian on the sphere under hyperbolic magnetic fields (2014)
  12. Aydin, M. Evren; Ergüt, Mahmut: The inverse surfaces of tangent developable of a timelike curve in Minkowski space (\mathbbE_1^3) (2013)
  13. Bayard, Pierre; Di Scala, Antonio J.; Castro, Osvaldo Osuna; Ruiz-Hernández, Gabriel: Surfaces in (\mathbbR^4) with constant principal angles with respect to a plane (2013)
  14. Ghomi, Mohammad: Vertices of closed curves in Riemannian surfaces (2013)
  15. Gielis, J.; Tavkhelidze, I.; Ricci, P. E.: About “bulky” links generated by generalized Möbius-Listing bodies (GML_2^n) (2013)
  16. Karakuş, Fatma; Yayli, Yusuf: The Fermi-Walker derivative in Lie groups (2013)
  17. Shah, Pratik; Chatterji, Samaresh: On the curve reconstruction in Riemannian manifolds (2013)
  18. Tavkhelidze, I.: On some properties of ribbon links generated by generalized Möbius-Listing surfaces (GML_m^n) (2013)
  19. Georgiev, Georgi Hristov: Rational generalized offsets of rational surfaces (2012)
  20. Munteanu, Marian Ioan; Nistor, Ana Irina: Surfaces in (\mathbbE^3) making constant angle with Killing vector fields (2012)