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 59 articles , 1 standard article )

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  1. Dede, Mustafa; Ekici, Cumali; Goemans, Wendy; Ünlütürk, Yasin: Twisted surfaces with vanishing curvature in Galilean 3-space (2018)
  2. Kholodenko, Arkady L.; Kauffman, Louis H.: Huygens triviality of the time-independent Schrödinger equation. Applications to atomic and high energy physics (2018)
  3. Fukunaga, Tomonori; Takahashi, Masatomo: Existence conditions of framed curves for smooth curves (2017)
  4. López, Rafael; Kaya, Seher: New examples of maximal surfaces in Lorentz-Minkowski space (2017)
  5. Pengelley, David; Ramras, Daniel: How efficiently can one untangle a double-twist? Waving is believing! (2017)
  6. Takahashi, Masatomo: Envelopes of Legendre curves in the unit tangent bundle over the Euclidean plane (2017)
  7. Fukunaga, Tomonori; Takahashi, Masatomo: Involutes of fronts in the Euclidean plane (2016)
  8. Goemans, Wendy; Van de Woestyne, Ignace: Clelia curves, twisted surfaces and Plücker’s conoid in Euclidean and Minkowski 3-space (2016)
  9. Goemans, Wendy; Van de Woestyne, Ignace: Twisted surfaces with null rotation axis in Minkowski 3-space (2016)
  10. Honda, Shun’ichi; Takahashi, Masatomo: Framed curves in the Euclidean space (2016)
  11. Moruz, Marilena; Munteanu, Marian Ioan: Minimal translation hypersurfaces in $\mathbbE^4$ (2016)
  12. Takahashi, Masatomo: Legendre curves in the unit spherical bundle over the unit sphere and evolutes (2016)
  13. Armas, Jay; Blau, Matthias: Blackfolds, plane waves and minimal surfaces (2015)
  14. Fogg, Harold J.; Armstrong, Cecil G.; Robinson, Trevor T.: Automatic generation of multiblock decompositions of surfaces (2015)
  15. Fukunaga, Tomonori; Takahashi, Masatomo: Evolutes and involutes of frontals in the Euclidean plane (2015)
  16. Karakuş, Fatma; Yayli, Yusuf: The Fermi derivative in the hypersurfaces (2015)
  17. Yu, Haiou; Pei, Donghe; Cui, Xiupeng: Evolutes of fronts on Euclidean 2-sphere (2015)
  18. Athukorallage, Bhagya; Paragoda, Thanuja; Toda, Magdalena: Roulettes of conics, Delaunay surfaces and applications (2014)
  19. Fukunaga, T.; Takahashi, M.: Evolutes of fronts in the Euclidean plane (2014)
  20. Kassabov, Ognian: Transition to canonical principal parameters on minimal surfaces (2014)

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