This project a reimplementation of CLICAL. The original CLICAL was created in Helsinki University of Technology in 1987. From the original documentation:
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.
I think Geometric Algebras and Clifford Algebras are the neatest way of explaining many physical phenomena. For example, replacing the concept of the axis of rotation with a plane of rotation gives you information about the orientation of rotation. This means that even when you switch from right-handed coordinate system to a left-handed system, there will be no unphysical axis reversal.
This project is my attempt at bringing geometric algebra to a wider audience. CLICAL had a pleasant syntax, but running it in a modern computer can be a bit underwhelming. On the Web it can be used from anywhere on the world. Also the output can be a lot prettier. To emphasize the last point, here's a quote from the GUIDE file distributed with the original:
If you have a color monitor and a color card, you can write colored files.
Indeed I have a color monitor!
The primary goal is to provide an easily accessible tool for people not familiar with Clifford algebras. Specifically, performance is a bit of a non-concern. It is for exploration, for toying and for
For "production use," whatever that may mean, this is probably not a good tool. Consider other tools, such as:
It can do sums! That's end-to-end functionality from input to output. This means we are at version 0.0.1. See it in action at http://arsatiki.github.com/clical.js/
(Try 1 + 2e1 or e1 + e12 + e21 or whatever.)
For more detailed future plans, see the Github issues list and the file CONTRIBUTING.md.
Target environment is HTML5 compatible browser.
Some initial prototyping is done with Python.