Algex - a collection of Go packages for performing basic symbolic algebra

Overview

Algex is a collection of interdependent Go packages for performing basic algebra. The core functionality was developed to solve the inverse kinematics of a 6-axis robot. However, structuring it as a set of stand alone packages provided a motivation for expanding its capabilities.

How to use

The documentation for each of the packages can be found on go.dev via this top-level search: zappem.net/pub/math/algex.

The basic command line example is built as follows:

$ go build examples/algex.go
$ ./algex
> x:=a+b
> y:=a-b
> x*y
 a^2-b^2
> fn(x,y):=x-y
> list
 fn(x,y) := x-y
 x := a+b
 y := a-b
> fn(a,b)
 a-b
> fn(y,x)
 -2*b
> exit
exiting

Other included examples

The other included example is examples/ik.go which is the mentioned inverse kinematics algebra for the saxis robot:

$ go run examples/ik.go
... a lot of formulas (investigated and solved by hand) ...

Testing

There are a number of sub-package modules, and some algex command tests. You can run them with ./test.sh in the top level directory.

Features planned

• Rational polynomial factorization isn’t yet implemented. Currently, we only cancel common simple numerical factors of the denominator and the numerator, and whole copies the numerator and denominator. Example:

$ ./algex
> (x+y)*(x-y)/(x+y)
 x-y
> (x+y)/(x^2-y^2)
 1/(x-y)
> 2*(x+y)*(x-y)/(x^2-y^2)
 2
> (x+y)*(x-y)/(x+y)^2
 (x^2-y^2)/(2*x*y+x^2+y^2)
> tex (x+y)*(x-y)/(x+y)^2
 \frac{x^{2} - y^{2}}{2 x y +x^{2} +y^{2}}
> exit
exiting

This last tex output formats inline as \( \frac{x^{2} - y^{2}}{2 x y +x^{2} +y^{2}} \). Or as a stand alone formula like this (which I want to simplify to the RHS):

\[ \frac{x^{2} - y^{2}}{2 x y +x^{2} +y^{2}} \rightarrow \frac{x-y}{x+y}. \]

License info

The algex package is distributed with the same BSD 3-clause license as that used by golang itself.

Reporting bugs

Use the github algex bug tracker.