619.sagews

def bisection_find_root(f, a, b, num_iterations=10, full_output=True):
    """
    Use Bisection method to numerically find a root of ``f`` on the closed interval `[a,b]`
    (or `[b,a]`) if possible, where ``f`` is a function in the one variable.
    """  

    #convert to floats
    a = float(a); b = float(b)
    if a > b:
        a, b = b, a
    
    for i in range (num_iterations):
        c = (a + b)/2
        if f(a)*f(c) < 0:
            b=c
        else:
            a=c
        if full_output == True:
            print float(c)
    
    return c

f(x) = x^2 - 2
bisection_find_root(f, 1, 2,20)

1.5 1.25 1.375 1.4375 1.40625 1.421875 1.4140625 1.41796875 1.416015625 1.4150390625 1.41455078125 1.41430664062 1.41418457031 1.41424560547 1.41421508789 1.4141998291 1.4142074585 1.41421127319 1.41421318054 1.41421413422 1.4142141342163086