publication . Preprint . 2017

CGAlgebra: a Mathematica package for conformal geometric algebra

Aragon, Jose L.;
Open Access English
  • Published: 03 Nov 2017
Abstract
A tutorial of the Mathematica package CGAlgebra, for conformal geometric algebra calculations is presented. Using rule-based programming, the 5-dimensional conformal geometric algebra is implemented and defined functions simplify the calculations of geometric, outer and inner products, as well as many other calculations related with geometric transformations. CGAlgebra is available from https://github.com/jlaragonvera/Geometric-Algebra
Subjects
free text keywords: Computer Science - Mathematical Software
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[1] D. Hestenes, Old wine in new bottles: A new algebraic framework for computational geometry. In: E. Bayro-Corrochano and G. Sobczyk (Editors), Geometric Algebra with Applications in Science and Engineering. (Birkauser, Boston, 2001). Ch. 1.

[2] H. Li, D. Hestenes, A. Rockwood, Generalized homogeneous coordinates for computational geometry. In: G. Sommer (Ed.), Geometric Computing with Cli ord Algebras (Springer-Verlag, Heidelberg, 2000). Ch. 2.

[3] L. Dorst, D. Fontijne and S. Mann, Geometric Algebra for Computer Science (Revised Edition), Morgan Kaufmann Publishers (Burlington, MA, 2009)

[4] C. Perwass, Geometric Algebra with Applications in Engineering. Springer-Verlag (Berlin, 2009).

[5] D. Hildenbrand, Foundations of Geometric Algebra Computing. Springer-Verlag (Berlin, 2013).

Abstract
A tutorial of the Mathematica package CGAlgebra, for conformal geometric algebra calculations is presented. Using rule-based programming, the 5-dimensional conformal geometric algebra is implemented and defined functions simplify the calculations of geometric, outer and inner products, as well as many other calculations related with geometric transformations. CGAlgebra is available from https://github.com/jlaragonvera/Geometric-Algebra
Subjects
free text keywords: Computer Science - Mathematical Software
Download from

[1] D. Hestenes, Old wine in new bottles: A new algebraic framework for computational geometry. In: E. Bayro-Corrochano and G. Sobczyk (Editors), Geometric Algebra with Applications in Science and Engineering. (Birkauser, Boston, 2001). Ch. 1.

[2] H. Li, D. Hestenes, A. Rockwood, Generalized homogeneous coordinates for computational geometry. In: G. Sommer (Ed.), Geometric Computing with Cli ord Algebras (Springer-Verlag, Heidelberg, 2000). Ch. 2.

[3] L. Dorst, D. Fontijne and S. Mann, Geometric Algebra for Computer Science (Revised Edition), Morgan Kaufmann Publishers (Burlington, MA, 2009)

[4] C. Perwass, Geometric Algebra with Applications in Engineering. Springer-Verlag (Berlin, 2009).

[5] D. Hildenbrand, Foundations of Geometric Algebra Computing. Springer-Verlag (Berlin, 2013).

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