load algorithm2.sage
load Schirokauer.sage

def fast_is_p_rational(f,p):
    classOK = false
    unitOK = false
    epss = fast_units(f)
    for eps in epss:
        d = f.factor_mod(p)[0][0].degree()
        E = p^d - 1
        if Schirokauer(eps,p,E,p) != [0,0]:
            print f,eps
            unitOK = true
            break
    K.<a>=NumberField(f)
    if not K.class_number() % p == 0:
        classOK = true
    return (classOK and unitOK)