## CLICAL

swMATH ID: | 20733 |

Software Authors: | Lounesto, P., Mikkola, R., Vierros, V. |

Description: | 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. |

Homepage: | https://users.aalto.fi/~ppuska/mirror/Lounesto/CLICAL.htm |

Related Software: | CLIFFORD; Maple; BIGEBRA; GABLE; Gaigen; LUCY; Mathematica; Quaternion; GluCat; AXIOM; CLUCalc; Clifford Multivector Toolbox; Gaalet; Octave; Matlab; Gaalop; cmulWpar; cmulW; cmulRS; cmulNUM |

Cited in: | 17 Publications |

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### Cited by 22 Authors

### Cited in 4 Serials

5 | Advances in Applied Clifford Algebras |

2 | Computer Physics Communications |

1 | Applied Mathematics and Computation |

1 | International Journal of Computer Vision |

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