jsclary / quartic

Solve Quartic equations. Implementations in C, Haskell, and Python

Quartic

Solve Quartic equations (4th degree polynomials) in C, Haskell, and Python.

License: BSD.

(Also solves cubic, quadratic, and linear equations)

The implementations are very close in their structure/design. Naturally, the Haskell and Python implementations are much shorter than the C implementation.

C implementation

There's one implementation for complex numbers, and another for real numbers (double), which only finds real roots.

Haskell implementation

This implementation is generic and should work for finite fields too (I think).

Note about Cubic equations

The solving of cubic equations only finds one root. Finding all three roots for Complex Doubles isn't hard but I wanted to keep the code generic.

For that a type-class providing primitive roots of unity would be required. The class providing the primitive square root of unity, (-1), exists in Haskell and it is Floating, but here we would need a primitive cubic root of unity..

Python implementation

Numpy already has a built-in roots function, so this implementation isn't necessary. It was only made for comparison with the others. Also consider https://github.com/NKrvavica/fqs if you require a faster implementation than numpy.