quadratic_solver.py

'''@package quadratic_solver
This package contains a quadratic solver'''
import math

def quadratic_solver(a, b, c, complex_allowed=False):
    '''A solver for quadratic equations in the form ax^2+bx+c=0
    Will return any roots of the equation in a list
    If complex roots are allowed, the returned values may be complex
    If complex roots are not allowed and there are no non-complex roots then a ValueError will be returned
    If both the quadratic and linear coefficients are zero then a ValueError will be returned
    @param a (numeric) The quadratic coefficient
    @param b (numeric) The linear coefficient
    @param c (numeric) The constant
    @param complex_allowed (optional) (bool) If True, complex roots will be returned (if appropriate). If False, a ValueError will be returned if the discriminant is negative'''
    if a == 0:
        if b == 0:
            ##If the quadratic and linear coefficients are both zero, raise a ValueError
            raise ValueError("Both 'a' and 'b' were zero, meaning there was no defined value for 'x'")
        else:
            ##If the quadratic coefficient is zero, return the constant divided by the linear coefficient
            return([-c/b])

    ##@var discriminant (float) The discriminant of the equation
    discriminant = b ** 2 - 4 * a * c

    if discriminant < 0:
        if complex_allowed:
            ##If the discriminant is negative and complex roots are allowed, return two complex roots
           return([(b - 1j*math.sqrt( - discriminant))/(2 * a), (b + 1j * math.sqrt(-discriminant))/(2 * a)])
        else:
            ##If the discriminant is negative and complex roots are not allowed, raise a ValueError
            raise ValueError("The discriminant was negative and complex results were not allowed")
    elif discriminant == 0:
        ##If the discriminant is zero, return one real root
        return([b / (2 * a)])
    else:
        ##If the discriminant is positive, return two real roots
        return([(b-math.sqrt(discriminant))/(2*a), (b+math.sqrt(discriminant))/(2*a)])