CLICAL is a stand-alone calculator-type computer program for geometric algebras of multivectors, called Clifford algebras. CLICAL evaluates elementary functions with arguments in complex numbers, and their generalizations: quaternions, octonions and multivectors in Clifford algebras. CLICAL works directly on intrinsic geometric objects: lines, planes and volumes, represented by vectors, bivectors and multivectors. Oriented volume elementes, or segments of subspaces, are represented by simple multivectors, which are homogeneous and decomposable elements in the exterior algebra. CLICAL works on Clifford algebras Clp,q of real non-degenerate quadratic spaces Rp,q. Clifford algebras are used to handle rotations and oriented subspaces. Clifford algebra is a user interface, which provides geometrical insight. However, the actual numerical computations are faster in matrix images of Clifford algebras. CLICAL computer program was developed to enable input-output in Clifford algebras (and fast internal computation in matrices). CLICAL is intended for researchers and teachers of Clifford algebras and spinors. In research, CLICAL has been applied to verify and falsify conjectures about Clifford algebras. With the help of CLICAL, I have found counterexamples to conjectures and theorems about Clifford algebras. I have used CLICAL to solve problems presented in Usenet newsgroups, for instance about rotations of the 4D Euclidean space R4. In teaching, CLICAL has been used in mathematics and physics courses in the USA, Mexico, Finland and Spain. Take a look at a course delivered with CLICAL. There are competing projects, most notably an online geometric calculator, two symbolic computer algebra packages for MapleV5, one for Mathematica, MatLab geometric algebra tutotial, and C++ Template Classes for Geometric Algebras.

References in zbMATH (referenced in 17 articles )

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  1. Sangwine, Stephen J.; Hitzer, Eckhard: Clifford multivector toolbox (for MATLAB) (2017)
  2. Abłamowicz, Rafał; Fauser, Bertfried: On parallelizing the Clifford algebra product for \textttCLIFFORD (2014)
  3. Zamora-Esquivel, Julio: (G_6,3) geometric algebra; description and implementation (2014)
  4. Sangwine, Stephen J.; Ell, Todd A.: Complex and hypercomplex discrete Fourier transforms based on matrix exponential form of Euler’s formula (2012)
  5. Abłamowicz, Rafał: Computations with Clifford and Grassmann algebras (2009)
  6. Reyes, Leo; Medioni, Gerard; Bayro, Eduardo: Registration of 3D points using geometric algebra and tensor voting (2007) ioport
  7. Ablamowicz, Rafal; Fauser, Bertfried: Mathematics of Clifford -- a Maple package for Clifford and Graßmann algebras (2005)
  8. Abłamowicz, Rafał (ed.); Sobczyk, Garret (ed.): Lectures on Clifford (geometric) algebras and applications (2004)
  9. Perwass, Christian; Gebken, Christian; Sommer, Gerald: Implementation of a Clifford algebra co-processor design on a field programmable gate array (2004)
  10. Fauser, Bertfried; Abłamowicz, Rafał: On the decomposition of Clifford algebras of arbitrary bilinear form (2000)
  11. Abłamowicz, Rafał: Spinor representations of Clifford algebras: A symbolic approach (1998)
  12. Dray, Tevian; Manogue, Corinne A.: Finding octonionic eigenvectors using Mathematica (1998)
  13. Abłamowicz, Rafał: Clifford algebra computations with Maple (1996)
  14. Abłamowicz, Rafał (ed.); Lounesto, Pertti (ed.); Parra, Josep M. (ed.): Clifford algebras with numeric and symbolic computations (1996)
  15. Abłamowicz, Rafał; Lounesto, Pertti: On Clifford algebras of a bilinear form with an antisymmetric part (1996)
  16. Schmeikal, Bernd: The generative process of space-time and strong interaction quantum numbers of orientation (1996)
  17. Ablamowicz, Rafal: Algebraic spinors for (R^9,1) (1992)