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 108 articles , 1 standard article )

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  1. Dede, Mustafa: Helical extension curve of a space curve (2021)
  2. Johnson, Emily L.; Laurence, Devin W.; Xu, Fei; Crisp, Caroline E.; Mir, Arshid; Burkhart, Harold M.; Lee, Chung-Hao; Hsu, Ming-Chen: Parameterization, geometric modeling, and isogeometric analysis of tricuspid valves (2021)
  3. Malkoun, Joseph; Olver, Peter J.: Continuous maps from spheres converging to boundaries of convex hulls (2021)
  4. Müller, Christian; Vaxman, Amir: Discrete curvature and torsion from cross-ratios (2021)
  5. Pulov, Vladimir I.; Mladenov, Ivaïlo M.: A plethora of non-bending surfaces of revolution: classifications and explicit parameterizations (2021)
  6. Rangamani, P.; Behzadan, A.; Holst, M.: Local sensitivity analysis of the “Membrane shape equation” derived from the Helfrich energy (2021)
  7. Takahashi, Masatomo; Yu, Haiou: Envelopes of families of framed surfaces and singular solutions of first-order partial differential equations (2021)
  8. Abdel-Baky, Rashad A.; Unluturk, Yasin: Normal developable surfaces of a surface along a direction curve (2020)
  9. Alcázar, Juan Gerardo; Quintero, Emily: Affine equivalences, isometries and symmetries of ruled rational surfaces (2020)
  10. Cariow, Aleksandr; Cariowa, Galina; Majorkowska-Mech, Dorota: An algorithm for quaternion-based 3D rotation (2020)
  11. Dölz, Jürgen: A higher order perturbation approach for electromagnetic scattering problems on random domains (2020)
  12. Gabrielides, Nikolaos C.; Sapidis, Nickolas S.: Inflection points on 3D curves (2020)
  13. Honda, Shun’ichi; Takahashi, Masatomo: Evolutes and focal surfaces of framed immersions in the Euclidean space (2020)
  14. Karacan, Murat Kemal; Tunçer, Yilmaz; Yüksel, Nural: Classifications of conformal rotational surfaces in Euclidean 3-space (2020)
  15. Li, Siran: On the existence of (C^1,1)-isometric immersions of several classes of negatively curved surfaces into (\mathbbR^3) (2020)
  16. Lotay, Jason D.: Calibrated submanifolds (2020)
  17. Müller, Marius; Spener, Adrian: On the convergence of the elastic flow in the hyperbolic plane (2020)
  18. Ören, İdris; Khadjiev, Djavvat: Recognition of paths and curves in the 2-dimensional Euclidean geometry (2020)
  19. Pulov, Vladimir I.; Mladenov, Ivaïlo M.: Explicit parameterizations of non-bending torus-like surfaces (2020)
  20. Shipman, Barbara A.; Shipman, Patrick D.: Weierstrass representations for triply orthogonal and conformal Euclidean and Lorentzian systems (2020)

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