def test_triples(self):
def key(x):
return (x[2], x[1])
for t in itertools2.take(10000,
itertools2.ensure_sorted(triples(), key)):
assert_true(is_pythagorean_triple(*t))
def primes(n):
"""memoized list of n first primes
:warning: do not call with large n, use prime_gen instead
"""
m=n-len(_primes)
if m>0:
more=list(itertools2.take(m,primes_gen(_primes[-1]+1)))
_primes.extend(more)
_primes_set.union(set(more))
return _primes[:n]
def primes(n):
"""memoized list of n first primes
:warning: do not call with large n, use prime_gen instead
"""
m = n - len(_primes)
if m > 0:
more = list(itertools2.take(m, primes_gen(_primes[-1] + 1)))
_primes.extend(more)
_primes_set.union(set(more))
return _primes[:n]
def test_fibonacci(self):
# checks that fibonacci and fibonacci_gen give the same results
f = [fibonacci(i) for i in range(10)]
assert_equal(f, [0, 1, 1, 2, 3, 5, 8, 13, 21, 34])
assert_equal(f, itertools2.take(10, fibonacci_gen()))
# http://controlfd.com/2016/07/05/using-floats-in-python.html
assert_equal(fibonacci(78), 8944394323791464)
f50 = fibonacci(50)
f51 = fibonacci(51)
phi = (1 + sqrt(5)) / 2
assert_equal(f51 / f50, phi)
# mod 1000000007 has the effect of using int32 only
assert_equal(fibonacci(int(1E19), 1000000007), 647754067)
assert_equal(fibonacci(int(1E19), 10), 5)
def test_fibonacci(self):
# checks that fibonacci and fibonacci_gen give the same results
f=[fibonacci(i) for i in range(10)]
assert_equal(f,[0,1,1,2,3,5,8,13,21,34])
assert_equal(f,itertools2.take(10,fibonacci_gen()))
#http://controlfd.com/2016/07/05/using-floats-in-python.html
assert_equal(fibonacci(78),8944394323791464)
f50=fibonacci(50)
f51=fibonacci(51)
phi=(1+sqrt(5))/2
assert_equal(f51/f50,phi)
#mod 1000000007 has the effect of using int32 only
assert_equal(fibonacci(int(1E19),1000000007),647754067)
assert_equal(fibonacci(int(1E19),10),5)
def test_repeat(self):
#check that we can iterate twice in the same Sequence
l1 = list(itertools2.take(20, A000040))
l2 = list(itertools2.take(20, A000040))
assert_equal(l1, l2)
def test_repeat(self):
# check that we can iterate twice in the same Sequence
l1 = list(itertools2.take(20, A000040))
l2 = list(itertools2.take(20, A000040))
assert_equal(l1, l2)
def test_triples(self):
key=lambda x:(x[2],x[1])
for t in take(10000,itertools2.ensure_sorted(triples(),key)):
assert_true(is_pythagorean_triple(*t))
def test_triples(self):
key=lambda x:(x[2],x[1])
for t in take(10000,itertools2.ensure_sorted(triples(),key)):
assert_true(is_pythagorean_triple(*t))
def test_repunit_gen(self):
assert_equal(itertools2.take(5, repunit_gen(digit=1)),
[0, 1, 11, 111, 1111])
assert_equal(itertools2.take(5, repunit_gen(digit=9)),
[0, 9, 99, 999, 9999])
desc="Smallest member 'a' of the primitive Pythagorean triples (a,b,c) ordered by increasing c, then b"
A046086=Sequence(math2.primitive_triples,desc=desc).apply(lambda x:x[0])
# .sort(key=lambda x:x[2]) \ #not needed anymore
# .apply(lambda x:x[0])
""" found a bug in OEIS ! 20th term of the serie is 145, not 142 !
desc="Hypotenuse of primitive Pythagorean triangles sorted on area (A024406), then on hypotenuse"
A121727=Sequence(math2.primitive_triples,desc=desc) \
.sort(lambda x:(x[0]*x[1],x[2])) \
.apply(lambda x:x[2])
"""
# Build oeis dict by module introspection : Simple and WOW !
seqs=globals().copy()
oeis={}
for id in seqs:
if id[0]=='A' and len(id)==7:
seqs[id].name=id
oeis[id]=seqs[id]
if __name__ == "__main__":
"""local tests"""
it=itertools2.sorted_iterable(math2.primitive_triples(),(lambda x:(x[0]*x[1],x[2])))
for p in itertools2.take(30,it):
print(p,p[0]*p[1]/2)
def test_repunit_gen(self):
assert_equal(itertools2.take(5,repunit_gen(digit=1)),[0,1,11,111,1111])
assert_equal(itertools2.take(5,repunit_gen(digit=9)),[0,9,99,999,9999])