def run(c, sq):
run_time = timer()
if c is None:
return
cc = sq[c]
for b in range(ceil(sqrt(cc / 2)), c + 1):
if not c & 1 and not b & 1:
continue
bb = sq[b]
gbc = gcd(b, c)
for a in range(int(sqrt(cc - bb)) + 1, b + 1):
if (a & 1) + (b & 1) + (c & 1) != 2 or gcd(a, gbc) != 1:
continue
aa = sq[a]
area2 = (aa + bb + cc) * (aa + bb - cc) * (aa - bb +
cc) * (-aa + bb + cc)
if is_square(area2):
area = int(sqrt(area2)) // 4
print(
f'\r{datetime.now().strftime("%Y-%m-%d %H:%M:%S")} - (a={a}², b={b}², c={c}², area={area}) - '
f'Heron Triangle with Square Sides!')
with open('sheron.out', 'a') as f:
f.write(f'\ra={a}^2, b={b}^2, c={c}^2, area={area}')
run_duration = datetime.utcfromtimestamp(timer() - run_time)
print(
f'\r{datetime.now().strftime("%Y-%m-%d %H:%M:%S")} - c={c}² - '
f'Cycle: {run_duration.strftime("%H:%M:%S.%f")[:-3]}',
end='')
def minX(D):
if is_square(D):
return 0
for frac in sqrtconvergents(D):
x = frac.numerator
y = frac.denominator
if x*x - D*y*y == 1:
return x
def primegenerating(n):
if is_square(n):
return 0
for div in divisors(
n
): #unfortunately a generator does not work, as it does not order the divisors, and we would break out of the loop too soon.
if div * div > n:
break
if not isprime(div + (n // div)):
return 0
return n
def sqrtperiod(n):
if is_square(n) and int(sqrt(n))==sqrt(n):
return (int(sqrt(n)),[])
a0 = floor(sqrt(n))
a = [a0]
r = (1,a0)
for period in count(1):
denom = n-r[1]*r[1]
a.append(floor(r[0]*(sqrt(n)+r[1])/denom))
r = (denom//r[0], (a[-1]*denom-r[0]*r[1])//r[0])
if periodic(a):
return (a[0],a[1:])
def sqrtperiod(n):
if is_square(n):
return 0
a0 = floor(sqrt(n))
a = [a0]
r = (1,a0)
for period in count(1):
denom = n-r[1]*r[1]
a.append(floor(r[0]*(sqrt(n)+r[1])/denom))
r = (denom//r[0], (a[-1]*denom-r[0]*r[1])//r[0])
if periodic(a):
#print(f"p({n}) = {period}")
return period
def test_is_square():
assert [i for i in range(25) if is_square(i)] == [0, 1, 4, 9, 16]
# issue #17044
assert not is_square(60**3)
assert not is_square(60**5)
assert not is_square(84**7)
assert not is_square(105**9)
assert not is_square(120**3)
def fermats_factor(n):
from sympy import integer_nthroot
from sympy.ntheory.primetest import is_square
tmp = integer_nthroot(n, 2)
a = tmp[0]
b = pow(a, 2) - n
k = 0
bool = tmp[1]
while not is_square(b):
a += 1
b = pow(a, 2) - n
k += 1
p = a + integer_nthroot(b, 2)[0]
q = a - integer_nthroot(b, 2)[0]
return (p, q)
def test_is_square():
assert [i for i in range(25) if is_square(i)] == [0, 1, 4, 9, 16]
def is_triangle(n):
return is_square(8 * n + 1)
def test_is_square():
assert [i for i in range(25) if is_square(i)] == [0, 1, 4, 9, 16]