human
I wrote the below code

    coeff = S.One
    try:
        (_, poly) = poly.clear_denoms(convert=True)
    except DomainError:
        return (coeff, poly)
    poly = poly.primitive()[1]
    poly = poly.retract()
    if (poly.get_domain().is_Poly and all((c.is_term for c in poly.rep.coeffs()))):
        poly = poly.inject()
        strips = list(zip(*poly.monoms()))
        gens = list(poly.gens[1:])
        (base, strips) = (strips[0], strips[1:])
        for (gen, strip) in zip(list(gens), strips):
            reverse = False
            if (strip[0] < strip[(-1)]):
                strip = reversed(strip)
                reverse = True
            ratio = None
            for (a, b) in zip(base, strip):
                if ((not a) and (not b)):
                    continue
                elif ((not a) or (not b)):
                    break
                elif ((b % a) != 0):
                    break
                else:
                    _ratio = (b // a)
                    if (ratio is None):
                        ratio = _ratio
                    elif (ratio != _ratio):
                        break
            else:
                if reverse:
                    ratio = (- ratio)
                poly = poly.eval(gen, 1)
                coeff *= (gen ** (- ratio))
                gens.remove(gen)
        if gens:
            poly = poly.eject(*gens)
    if (poly.is_univariate and poly.get_domain().is_ZZ):
        basis = _integer_basis(poly)
        if (basis is not None):
            n = poly.degree()
            def func(k, coeff):
                return (coeff // (basis ** (n - k[0])))
            poly = poly.termwise(func)
            coeff *= basis
    return (coeff, poly)

What's a good function header?
 Here's a good function header?
assistant
#Here's a good function header.

def preprocess_roots(poly):