Use of variables in SAGE procedure

Question

I am learning how to write SAGE procedures and I am looking at various examples. Here is one for the Method of Bisection (to find a zero of a function:

def method_of_bisection(a, b, n, f, x=x):
    c, d = a, b
    f(x) = f
    for i in range(n):
        # compute midpoint, then compare
        e = (c + d)/2
        if (f(c) > 0 and f(e) > 0) or (f(c) < 0 and f(e) < 0):
            c=e
        elif f(e) == 0:
            c=d=e
            break
        else:
            d=e 
    return (c, d)

My question is: why do we need to rename a,b to c,d? What is wrong with using instead:

def method_of_bisection(a, b, n, f, x=x):
    f(x) = f
    for i in range(n):
        # compute midpoint, then compare
        e = (a+b)/2
        if (f(a) > 0 and f(e) > 0) or (f(a) < 0 and f(e) < 0):
            a=e
        elif f(e) == 0:
            a=b=e
            break
        else:
            b=e 
    return (a,b)

This initial renaming of variables is done in all the examples of SAGE procedures I am looking at, and I am sure there must be a basic "good programming" practice behind it, but I don't know what it is.

Answer 1

You are correct, you don't need to rename a and b to c and d, respectively. The variables a and b are local variables - local copies inside the scope of f, and modifying them would not affect any global variables.