'''
This file assumes that the conjecturing spkg is installed and that 'conjecturing.py' is loaded.
'''
def digits10(n):
return len(n.digits(10))
def digits2(n):
return len(n.digits(2))
def count_divisors(n):
return len(divisors(n))
def count_prime_divisors(n):
return len(factor(n))
def count_quadratic_residues(n):
return len(quadratic_residues(n))
def number(n):
return n
def automatedSearch(objects, invariants, universe, upperBound=True, steps=10, mainInvariant=0):
for _ in range(steps):
l = conjecture(objects, invariants, mainInvariant, upperBound=upperBound)
noCounterExample = True
for i in universe:
if any([not c.evaluate(Integer(i)) for c in l]):
print "Adding {}".format(i)
objects.append(i)
universe.remove(i)
noCounterExample = False
break
if noCounterExample:
print "No counterexample found"
break
return l
invariants = [('prime_pi',prime_pi), ('euler_phi', euler_phi), number, digits10, digits2, ('sigma', sigma), count_divisors, next_prime, previous_prime, count_quadratic_residues]
objects = [Integer(n) for n in [5, 12, 30, 50]]
universe = [Integer(n) for n in range(3, 1000001)]
for n in objects:
universe.remove(n)
conjectures = automatedSearch(objects, invariants, universe, steps=210)
print("The conjectures are stored in the variable conjectures.")
