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 85 articles , 1 standard article )

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  1. Alcázar, Juan Gerardo; Quintero, Emily: Affine equivalences, isometries and symmetries of ruled rational surfaces (2020)
  2. Honda, Shun’ichi; Takahashi, Masatomo: Evolutes and focal surfaces of framed immersions in the Euclidean space (2020)
  3. Li, Siran: On the existence of (C^1,1)-isometric immersions of several classes of negatively curved surfaces into (\mathbbR^3) (2020)
  4. Müller, Marius; Spener, Adrian: On the convergence of the elastic flow in the hyperbolic plane (2020)
  5. Shipman, Barbara A.; Shipman, Patrick D.: Weierstrass representations for triply orthogonal and conformal Euclidean and Lorentzian systems (2020)
  6. Várady, Tamás; Salvi, Péter; Vaitkus, Márton; Sipos, Ágoston: Multi-sided Bézier surfaces over curved, multi-connected domains (2020)
  7. Ateş, Osman; Munteanu, Marian Ioan; Nistor, Ana Irina: Dynamics on (\mathbbS^3) and the Hopf fibration (2019)
  8. Bestuzheva, Ksenia; Hijazi, Hassan: Invex optimization revisited (2019)
  9. Fukunaga, Tomonori; Takahashi, Masatomo: Framed surfaces in the Euclidean space (2019)
  10. Pei, Donghe; Takahashi, Masatomo; Yu, Haiou: Envelopes of one-parameter families of framed curves in the Euclidean space (2019)
  11. Soliman, M. A.; Mahmoud, W. M.; Solouma, E. M.; Bary, M.: The new study of some characterization of canal surfaces with Weingarten and linear Weingarten types according to Bishop frame (2019)
  12. Takahashi, Masatomo: Envelopes of families of Legendre mappings in the unit tangent bundle over the Euclidean space (2019)
  13. Babalic, Elena Mirela; Lazaroiu, Calin Iuliu: Generalized (\alpha)-attractor models from elementary hyperbolic surfaces (2018)
  14. Dede, Mustafa; Ekici, Cumali; Goemans, Wendy; Ünlütürk, Yasin: Twisted surfaces with vanishing curvature in Galilean 3-space (2018)
  15. Dölz, Jürgen; Harbrecht, Helmut: Hierarchical matrix approximation for the uncertainty quantification of potentials on random domains (2018)
  16. Güler, Erhan: Family of Enneper minimal surfaces (2018)
  17. Güler, Erhan; Kişi, Ömer; Konaxis, Christos: Implicit equations of the Henneberg-type minimal surface in the four-dimensional Euclidean space (2018)
  18. Kholodenko, Arkady L.; Kauffman, Louis H.: Huygens triviality of the time-independent Schrödinger equation. Applications to atomic and high energy physics (2018)
  19. Marszalek, Wieslaw: Autonomous models of self-crossing pinched hystereses for mem-elements (2018)
  20. Raffaelli, Matteo; Bohr, Jakob; Markvorsen, Steen: Cartan ribbonization and a topological inspection (2018)

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