https://github.com/davidedc/Algebrite

CoffeeScript
Computer Algebra System in Javascript (Coffeescript)

Algebrite is a Javascript library for symbolic mathematics (actually, mostly coffeescript resulting in Javascript) keeping the code as simple as possible in order to be comprehensible and easily extensible.

Why Algebrite

Algebrite is...

• lightweight: made to be simple to comprehend and extend, it only depends on BigInteger.js by Peter Olson.
• self-contained: doesn't need connection to servers or another "backend" CAS
• a library: beyond use as an interactive tool, algebrite can be embedded in your applications and extended with custom functions.
• free: MIT-Licenced

Features

Algebrite supports: arbitrary-precision arithmetic, complex quantities, simplification, expansion , substitution, symbolic and numeric roots, units of measurement, derivatives and gradients, tensors, integrals, multi-integrals, computing integrals and much more!

Examples and manual

Please refer to http://algebrite.org/

How to build it

To recompile the tables (this should almost never be needed):

coffee --compile --bare tables/itab.coffee

coffee --compile --bare tables/primetab.coffee

...to recompile the actual sources as soon as they change:

coffee --watch -c --bare --join algebrite-0.1.0.js *.coffee

References

The EigenMath CAS by George Weigt. Also you might want to check another fork of EigenMath: SMIB by Philippe Billet.

Another CAS of similar nature is SymPy made in Python.

Three other Javascript CAS are

• javascript-cas by Anthony Foster supporting "differentiation, complex numbers, sums, vectors (dot products, cross products, gradient/curl etc)"
• Coffeequate by Matthew Alger supporting "quadratic and linear equations, simplification of most algebraic expressions, uncertainties propagation, substitutions, variables, constants, and symbolic constants".
• Algebra.js by Nicole White which among other things can build and solve equations via a "chainable" API.

The MIT License (MIT)

Copyright © 2016 all algebrite contributors

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the “Software”), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.