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. Marszalek, Wieslaw: Autonomous models of self-crossing pinched hystereses for mem-elements (2018)
  2. Raffaelli, Matteo; Bohr, Jakob; Markvorsen, Steen: Cartan ribbonization and a topological inspection (2018)
  3. Zhang, N.: On bodies with congruent sections by cones or non-central planes (2018)
  4. Abd-Ellah, Hamdy N.; Omran, Abdelrahim Khalifa: Study on BCN and BAN ruled surfaces in (\mathbbE^3 ) (2017)
  5. Cadeddu, Lucio; Cannas, Sonia: Musical surfaces (2017)
  6. Fukunaga, Tomonori; Takahashi, Masatomo: Existence conditions of framed curves for smooth curves (2017)
  7. Georgiev, Georgi Hristov; Pavlov, Milen Dimov: Focal surfaces of hyperbolic cylinders (2017)
  8. López, Rafael; Kaya, Seher: New examples of maximal surfaces in Lorentz-Minkowski space (2017)
  9. Pengelley, David; Ramras, Daniel: How efficiently can one untangle a double-twist? Waving is believing! (2017)
  10. Takahashi, Masatomo: Envelopes of Legendre curves in the unit tangent bundle over the Euclidean plane (2017)
  11. Fukunaga, Tomonori; Takahashi, Masatomo: Involutes of fronts in the Euclidean plane (2016)
  12. Goemans, Wendy; Van de Woestyne, Ignace: Clelia curves, twisted surfaces and Plücker’s conoid in Euclidean and Minkowski 3-space (2016)
  13. Goemans, Wendy; Van de Woestyne, Ignace: Twisted surfaces with null rotation axis in Minkowski 3-space (2016)
  14. Honda, Shun’ichi; Takahashi, Masatomo: Framed curves in the Euclidean space (2016)
  15. Limacher, Eric; Morton, Chris; Wood, David: On the trajectory of leading-edge vortices under the influence of Coriolis acceleration (2016)
  16. Moruz, Marilena; Munteanu, Marian Ioan: Minimal translation hypersurfaces in (\mathbbE^4) (2016)
  17. Sánchez-Reyes, Javier: On the construction of minimal surfaces from geodesics (2016)
  18. Takahashi, Masatomo: Legendre curves in the unit spherical bundle over the unit sphere and evolutes (2016)
  19. Armas, Jay; Blau, Matthias: Blackfolds, plane waves and minimal surfaces (2015)
  20. Fogg, Harold J.; Armstrong, Cecil G.; Robinson, Trevor T.: Automatic generation of multiblock decompositions of surfaces (2015)