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 43 articles , 1 standard article )

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  1. Fukunaga, Tomonori; Takahashi, Masatomo: Involutes of fronts in the Euclidean plane (2016)
  2. Goemans, Wendy; Van de Woestyne, Ignace: Twisted surfaces with null rotation axis in Minkowski 3-space (2016)
  3. Moruz, Marilena; Munteanu, Marian Ioan: Minimal translation hypersurfaces in $\mathbbE^4$ (2016)
  4. Takahashi, Masatomo: Legendre curves in the unit spherical bundle over the unit sphere and evolutes (2016)
  5. Fukunaga, Tomonori; Takahashi, Masatomo: Evolutes and involutes of frontals in the Euclidean plane (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. Munteanu, Marian Ioan: The Landau-Hall problem on canal surfaces (2014)
  9. Aydin, M.Evren; Ergüt, Mahmut: The inverse surfaces of tangent developable of a timelike curve in Minkowski space $\mathbbE_1^3$ (2013)
  10. 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)
  11. Ghomi, Mohammad: Vertices of closed curves in Riemannian surfaces (2013)
  12. Gielis, J.; Tavkhelidze, I.; Ricci, P.E.: About “bulky” links generated by generalized Möbius-Listing bodies $GML_2^n$ (2013)
  13. Shah, Pratik; Chatterji, Samaresh: On the curve reconstruction in Riemannian manifolds (2013)
  14. Tavkhelidze, I.: On some properties of ribbon links generated by generalized Möbius-Listing surfaces $GML_m^n$ (2013)
  15. Georgiev, Georgi Hristov: Rational generalized offsets of rational surfaces (2012)
  16. Bas, E.; Erdogmus, D.: Connectivity of projected high dimensional data charts on one-dimensional curves (2011)
  17. Chen, C.: The order of local mobility of mechanisms (2011)
  18. Ersoy, Soley; Tosun, Murat: Lamarle formula in 3-dimensional Lorentz space (2011)
  19. Gemmer, John A.; Venkataramani, Shankar C.: Shape selection in non-Euclidean plates (2011)
  20. Mladenov, Ivaïlo M.; Hadzhilazova, Mariana Ts.; Djondjorov, Peter A.; Vassilev, Vassil M.: On some deformations of the Cassinian oval (2011)

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