Question

From Python ProblemSet I would like to test the following functions but it seems that mult and coprime could not be defined. I tried importing math but that did not help. Any recommendations?

>>> import itertools
>>> def prime_factors(value):
    if value > 3:
        for this in itertools.chain(iter([2]), xrange(3,int(value ** 0.5)+1, 2)):
            if this*this > value:  break
            while not (value % this):
                if value == this: break
                value /=  this
                yield this
    yield value
>>> prime_factors(315)
generator object prime_factors at 0x01182468>
>>> def prime_factors_mult(n):
    res = list(prime_factors(n))
    return sorted([fact, res.count(fact)] for fact in set(res))
>>> prime_factors_mult(315)
[[3, 2], [5, 1], [7, 1]]
>>> def totient(n):
    from operator import mul
    if n == 1: return 1
    return reduce(mul, [(p-1) * p**(m-1) for p,m in prime_factors_mult(n)])

>>> totient(315)
144

Answer 1

If you check the documentation for the operator module, you’ll find that the multiplication operator is mul.

Also, I believe the definition of coprime relies on definitions from previous problems.