Polynomials.hs

Upon receiving a challenge to make a program which parses and solves a polynomial to an arbitrary power, I made this.

Solution approximation uses Durand-Kerner, solutions are in the Cartesian form of complex numbers.

[Currently] Number of iterations of Durand-Kerner is hardcoded in src/Solve.hs

Building

$ git clone https://github.com/ofthegoats/polynomials.hs.git
$ cd polynomials.hs
$ stack build

Usage

$ stack run

Program takes input as a polynomial.

Terms in the polynomial are separate by a +/-/=.

There can only be one instance of =.

Example

$ stack run
x^3 + 2xx + 9 = -11
1.0x^3.0 + 2.0x^2.0 + 20.0 = 0
x_1 ≈ 0.7848018266102612 - 2.23314778453945i
x_2 ≈ 0.7848018266102613 + 2.23314778453945i
x_3 ≈ -3.5696036532205233 + 1.3602980171576907e-16i

Note that as the method used is an approximation, complex solutions whose imaginary component is very small (e.g. x_3 in above example) may not actually have any imaginary component.

As it is technically possible for a solution to just have a very small imaginary component, I do not intend to change this, though I may implement some other check at another time.

For now, just observe is there is any other solution which is the complex conjugate of the suspicious solution. If there is not, it must be a real solution (for any polynomial there is an even number of solutions with a nonzero imaginary component).

License

Licensed under the BSD 3 clause license.

Contributing

Format with Ormolu, avoid long lines, separate components into modules under src/ as reasonable.

TODO

• implement tests
  • parsing
  • solving (within a reasonable margin of error)