def main():
for i in range(100000,10000000):
startTime = time.time()
gcd.gcd(i,magNum)
stopTime = time.time()
if stopTime-startTime > 0.01:
print(i,' takes ',stopTime-startTime,'s')
def testPrimes(self):
for x in self.primes:
for y in self.primes:
if x != y:
self.assertEqual(gcd.gcd(x, y), 1)
else:
self.assertEqual(gcd.gcd(x, y), x)
def extended_euclidean(a, b):
if a < b:
tmp = a
a = b
b = tmp
r = [a, b]
s = [1, 0]
t = [0, 1]
q = [0, 0]
i = 2
while r[i - 1] > 0:
q.append(r[i - 2] // r[i - 1])
r.append(r[i - 2] - q[i] * r[i - 1])
s.append(s[i - 2] - q[i] * s[i - 1])
t.append(t[i - 2] - q[i] * t[i - 1])
#print i," : ",q[i],r[i],s[i],t[i]
i += 1
x = s[i - 2]
y = t[i - 2]
if x * a + b * y != gcd(a, b):
print "gcd ", gcd(a, b)
print "ans ", x * a + b * y
raise Exception("ans not accept")
return (x, y)
def findfactor(n): if n&1==0: return 2 y,c,m = random.randint(1,n-1),random.randint(1,n-1),random.randint(1,n-1) g,r,q=1,1,1 while g==1: x=y for i in xrange(r): y = ((y*y)%n+c)%n k=0 while (k<r and g==1): ys = y for i in xrange(min(m,r-k)): y = ((y*y)%n+c)%n q = q*(abs(x-y))%n g=gcd(q,n) k=k+m r<<=1 if g==n: while True: ys = ((ys*ys)%n+c)%n g = gcd(abs(x-ys),n) if g>1: break return g
def testBigNum(self):
#two big prime numbers
p = 100000000000657
q = 1000000000000783
self.assertEqual(gcd.gcd(p, q), 1)
a = p * q * 41 * 31
b = p * 1009 * 31
self.assertEqual(gcd.gcd(a, b), p * 31)
def factional_sequen(N,div):
while(N!=1):
N,div=N-1,div+1
if gcd.gcd(N,div)!=1:
tmp=gcd.gcd(N,div)
N,div=N/tmp,div/tmp
#factional_sequen(N,div)
N,div=N-1,div+1
return div
def test_gsd_in_param(self):
self.assertEqual(gcd.gcd(0, 7), 7)
self.assertEqual(gcd.gcd(7, 0), 7)
self.assertEqual(gcd.gcd(7, 7), 7)
self.assertEqual(gcd.gcd(1, 8), 1)
self.assertEqual(gcd.gcd(4, 6), 2)
self.assertEqual(gcd.gcd(10, 15), 5)
self.assertEqual(gcd.gcd(15, 10), 5)
self.assertEqual(gcd.gcd(5, 25), 5)
self.assertEqual(gcd.gcd(15, 45), 15)
def factor(n, x1):
x = x1
x0 = f(x) % n
p = gcd(abs(x - x0), n)
i = 1
while p == 1:
x = f(x) % n
x0 = f(x0) % n
x0 = f(x0) % n
p = gcd(abs(x - x0), n)
i += 1
if p == n:
return "failure"
return (p, i)
def __init__(self, n=1, d=1): #n:分子，d:分母
self.n = n
self.d = d
g = gcd.gcd(self.n,self.d)
if g != 1:
self.n = int(self.n/g)
self.d = int(self.d/g)
def decrypt(c: int, sk: Tuple[List[int], int, int]) -> BitString:
result = ''
w = sk[0]
q = sk[1]
r = sk[2]
if gcd.gcd(q, r) != 1:
raise ValueError("decrypt(): q and r not coprime")
c_real = (c * gcd.get_modular_inverse(r, q)) % q
for w_i in reversed(w):
if c_real >= w_i:
c_real -= w_i
result += '1'
else:
result += '0'
if c_real < 0:
raise ValueError("decrypt(): decrypt error")
if c_real != 0:
raise ValueError("decrypt(): decrypt error")
return BitString(result)
def test_out_int(self):
for n in range(20):
for m in range(20):
result = gcd.gcd(n, m)
if result!=0:
result = result/int(result)
self.assertEqual(result, 1)
def lcm(a, b):
'''
Computes LCM of two numbers
'''
g = gcd.gcd(a, b)
return (a / g) * b
def __public_key_generator(self):
""" Generate the public key. """
e = randint(1, self.totient)
while gcd(e, self.totient) != 1:
e = randint(1, self.totient)
self.public_key = (e, self.n)
def naiveeulerphi(n):
count = 0
# n itself is excluded in this loop, since gcd(n,n) = n
for k in range(1,n):
if gcd(n,k) == 1:
count = count + 1
return count
def gsd_out_check_int(self):
for x in range(0, self.n_max_test):
for y in range(0, self.n_max_test):
result = gcd.gcd(x, y)
if result != 0:
result = result / int(result)
self.assertEqual(result, 1)
def generarE(fn): menor = 11 mayor = 99999 e = random.randrange(menor, mayor) #rango en el que quiero que este el valor de e while gcd(e, fn) != 1: #un do-while improvisado, parece que python no lo implementa por su cuenta e = random.randrange(menor, mayor) return e
def numbers_gcd(request, num1,num2):
num1 = int(num1)
num2 = int (num2)
flag = False
for tmp in Request.objects.all():
if (tmp.f == int(num1) and tmp.to == int(num2)):
flag = True
if (flag == False):
my_req = Request(f = num1 , to = num2)
my_req.save()
for i in xrange(int(num1),int(num2)+1):
for j in xrange(int(num1),int(num2)+1):
gcd_mod = GCD(
ch1 = i,
ch2 = j,
answ = gcd(i,j),
request = my_req
)
gcd_mod.save()
else:
my_req = Request.objects.filter(f=num1 ,to=num2 )
my_set = GCD.objects.filter(request = my_req)
print my_set
return render(request, 'GCD/index2.html', {"ans" : my_set} )
def __init__(self, n, d):
""" Construct a Frac from integers n and d.
Needs error message if d = 0!
"""
hcf = gcd.gcd(n, d)
self.num, self.den = n / hcf, d / hcf
def linear_congruence(a, b, n):
d = gcd(a, n)
if b % d != 0:
return []
if a < n:
s, r = extended_euclidean(a, n)
else:
r, s = extended_euclidean(a, n)
x0 = r * b / d
c = n / d
while x0 < 0:
x0 += c
if x0 >= n:
while x0 > 0:
x0 -= c
x0 += c
x = []
while x0 < n:
x.append(x0)
x0 += c
return x
def relative_prime(x):
e = 3
for i in range(e, x):
g = gcd(i, x)
if g == 1:
e = i
break
return e
def homogeneous(self):
A = self.A
B = self.B
C = self.C
D = self.D
E = self.E
F = self.F
eq = []
k = math.sqrt(B*B - 4*A*C)
if F ==0:
eq.append(parametric_eq([0],[0]))
if k == int(k):
eq.extend(diophantine_Eq([0,0,0,2*A,B+int(k),0]).solve())
eq.extend(diophantine_Eq([0,0,0,2*A,B-int(k),0]).solve())
else:
return eq
else:
if cond == int(cond):
fac = factoring(-4*A*F,True)
eq = []
for u in fac:
y = (u + (4*A*F)*(1.0)/u) / (2*k)
x = (u - (B+k)*y*(1.0)) / (2*A)
if int(x) == x and int(y)==y:
eq.append( parametric_eq([int(x)],[int(y)]) )
return eq
else:
g = gcd(gcd(A,B),C)
if F%g !=0:
return []
A = A/g
B = B/g
C = C/g
D = D/g
E = D/g
F = F/g
if 4*F*F < B*B - 4*A*C:
# convergents of the continued fraction of the roots of the equation At2 + Bt + C = 0
print "next"
else:
return eq
def phi(N):
"""docstring for phi"""
import gcd
count=0
for i in range(1,N):
if gcd.gcd(N,i)==1:
count+=1
return count
def optimize(self):
_gcd = gcd(self.a, self.divisor)
if _gcd > 1:
self.a //= _gcd
self.divisor //= _gcd
return _gcd
def shor(self, n):
if miller_robin.miller_robin(n):
return (1, n)
else:
tmp = power.power(n)
if tmp != -1:
return (tmp, n // tmp)
else:
if (n % 2 == 0):
return (2, n // 2)
while True:
# Parrel computing for some random x
xlist = random.sample(range(3, n - 1), self.Thread_Num)
g = [gcd.gcd(x, n) for x in xlist]
for idx, g in enumerate(g):
if (g != 1):
# ======= For debug ===========
# while gcd.gcd(xlist[idx], n) != 1:
# newx = random.randint(3, n - 1)
# xlist[idx] = newx
# ======= In Real Quantum Computer =========
return (g, n // g)
print("======== Order Finding Started ========")
threadPool = ThreadPool(processes=self.Thread_Num)
results = []
for x in xlist:
results.append(
threadPool.apply_async(self.order_finding,
args=(x, n)))
threadPool.close()
threadPool.join()
results = [r.get() for r in results]
for r in results:
if r == -1:
continue
if (r % 2 == 0):
s = fastPow.fastPow(x, r // 2, n)
if (s != 1 and s != n - 1):
g1 = gcd.gcd(s + 1, n)
g2 = gcd.gcd(s - 1, n)
if (g1 != 1):
return (g1, n // g1)
elif (g2 != 1):
return (g2, n // g2)
def relative_prime(x):
e = 3
for i in range(e, x):
g = gcd(i, x)
if g == 1:
e = i
break
return e
def main():
''' main '''
parser = argparse.ArgumentParser(description='calculate Greatest Common Divisor')
parser.add_argument("n1", type=int, nargs='?', default=1024)
parser.add_argument("n2", type=int, nargs='?', default=768)
args = parser.parse_args()
r = gcd(args.n1, args.n2)
print(f'gcd({args.n1}, {args.n2}) = {r}')
def __init__(self, numerator=0, denominator=1):
if denominator == 0: # fraction is undefined
self._numer = 0
self._denom = 0
else:
factor = gcd( abs(numerator), abs(denominator) )
if denominator < 0: # want to divide through by negated factor
factor = -factor
self._numer = numerator // factor
self._denom = denominator // factor
def triples( max ) :
"""Generate a list of all prime pythagorean triples in range.
MAX is the largest value of the hypotenuse to allow.
"""
for i in range( 1, max ) :
for j in range ( i+1, max ) :
k = hypot( i, j )
if k < max and k == int( k ) and 1 == gcd( i, j ):
yield ( i, j, int(k) )
def mulr(self, a, b): #掛け算
x = Rational()
x.n = a.n*b.n
x.d = a.d*b.d
g = gcd.gcd(x.n, x.d)
if g != 1:
x.n = int(x.n/g)
x.d = int(x.d/g)
return x
def test_zero(self):
a = 0
b = random.randint(1, 100)
ans = _(
"Test zero - The greatest common divisor between {} and {} is {} and you returned {}."
)
stu_ans = gcd.gcd(a, b)
corr_ans = corr.gcd(a, b)
self.assertEqual(corr_ans, stu_ans, ans.format(a, b, corr_ans,
stu_ans))
def __init__(self, numerator=0, denominator=1):
if denominator == 0: # fraction is undefined
self._numer = 0
self._denom = 0
else:
factor = gcd(abs(numerator), abs(denominator))
if denominator < 0: # want to divide through by negated factor
factor = -factor
self._numer = numerator // factor
self._denom = denominator // factor
def get_public_exponent(m):
n = m-1
while n > 0:
if gcd(n, m) == 1 and is_prime(n):
return n
n -= 1
return -1
def subr(self, a, b): #引き算
x = Rational()
x.n = a.n*b.d - b.n*a.d
x.d = a.d*b.d
g = gcd.gcd(x.n,x.d)
if g != 1:
x.n = int(x.n/g)
x.d = int(x.d/g)
return x
def divr(self, a, b): #割り算
x = Rational()
x.n = a.n*b.d
x.d = a.d*b.n
g = gcd.gcd(x.n,x.d)
if g != 1:
x.n = int(x.n/g)
x.d = int(x.d/g)
return x
def addr(self, a, b): #足し算
x = Rational()
x.n = a.n*b.d + b.n*a.d
x.d = a.d*b.d
g = gcd.gcd(x.n,x.d)
if g != 1:
x.n = int(x.n/g)
x.d = int(x.d/g)
return x
def triples(max):
"""Generate a list of all prime pythagorean triples in range.
MAX is the largest value of the hypotenuse to allow.
"""
for i in range(1, max):
for j in range(i + 1, max):
k = hypot(i, j)
if k < max and k == int(k) and 1 == gcd(i, j):
yield (i, j, int(k))
def triples( max ) :
"""Generate a list of all prime pythagorean triples in range.
MAX is the largest value of the hypotenuse to allow.
"""
for k in range( 1, 1+max ) :
imax = int( floor( sqrt( k*k/2.0 ) ) )
for i in range( 1, 1+imax ) :
j = sqrt( k*k - i*i )
if abs( floor( j ) - j ) < 0.000001 and 1 == gcd( i, int( j ) ) :
yield ( i, int( j ), k )
def __init__(self, num, denom = 1):
if not isinstance(num,Rat) and not isinstance(denom,Rat):
num, denom = int(num),int(denom)
d = gcd.gcd(abs(num), abs(denom))
# The sign is always in the numerator
self.num = sign(num*denom)*abs(num)//d
self.denom = abs(denom)//d
else:
fraction = num/denom
self.num = fraction.num
self.denom = fraction.denom
def test_gcd(self):
a = [random.randint(1, 100) for _ in range(5)]
b = [random.randint(1, 100) for _ in range(5)]
ans = _(
"The greatest common divisor between {} and {} is {} and you returned {}."
)
for i in range(len(a)):
stu_ans = gcd.gcd(a[i], b[i])
corr_ans = corr.gcd(a[i], b[i])
self.assertEqual(corr_ans, stu_ans,
ans.format(a[i], b[i], corr_ans, stu_ans))
def pollard_rho(n):
x, y, d = 2, 2, 1
g = lambda i: (i**2 + 1)%n
while d == 1:
x = g(x)
y = g(g(y))
d = gcd(abs(x-y), n)
if d == n: return 0
else: return d
def triples(max):
"""Generate a list of all prime pythagorean triples in range.
MAX is the largest value of the hypotenuse to allow.
"""
for k in range(1, 1 + max):
imax = int(floor(sqrt(k * k / 2.0)))
for i in range(1, 1 + imax):
j = sqrt(k * k - i * i)
if abs(floor(j) - j) < 0.000001 and 1 == gcd(i, int(j)):
yield (i, int(j), k)
def __init__(self, num, denom=1):
if not isinstance(num, Rat) and not isinstance(denom, Rat):
num, denom = int(num), int(denom)
d = gcd.gcd(abs(num), abs(denom))
# The sign is always in the numerator
self.num = sign(num * denom) * abs(num) // d
self.denom = abs(denom) // d
else:
fraction = num / denom
self.num = fraction.num
self.denom = fraction.denom
def generarN(): #generar n y fn, regresa una tupla de ambos p = generarprimo() q = 1 gcd_bool = True while (p is not q) and gcd_bool: q = generarprimo() auxiliar = gcd(p - 1, q - 1) if auxiliar < 10: gcd_bool = False n = p * q fn = (p - 1) * (q - 1) nfn = (n, fn) return nfn
def inverse_modulo(x, n):
a, b = x, n
if n > x:
a, b = b, a
result = gcd(a, b)
if result != 1:
# print ("As gcd(%d, %d) != 1, the inverse does not exists" % (x, n))
return None
ans = extended_euclid(x, n)
if ans[0] > 0:
return ans[0]
else:
return (ans[0] + n)
def add(x, y):
xtp, xnum, xdenom = x
ytp, ynum, ydenom = y
ndenom = xdenom * ydenom
nnum = xnum * ydenom + xdenom * ynum
if xtp == 'basic':
return 'basic', nnum, ndenom
elif xtp == 'auto_simpl':
cur_gcd = gcd(nnum, ndenom)
return ('auto_simpl',
nnum / cur_gcd,
ndenom / cur_gcd)
assert False, "Unsupported rational type" + \
" for add" + xtp
def pythagoreanIterator(limit) : sq_limit = int((limit + 1) ** 0.5) for i in range(1, sq_limit) : print >> sys.stderr, i, "\r", for j in range(i+1, sq_limit) : i_sq, j_sq = i**2, j**2 a = j_sq - i_sq b = 2*i*j c = i_sq + j_sq p = a+b+c if p > limit : break if not triangleTest(a,b,c) : break if (i&1 == 0 or j&1 == 0) and gcd.gcd(i,j) == 1 : yield sorted( (a,b,c) ) return
def __init__(self, top, bottom):
# #5 solution for exercise 5 from 1.7 module - chap-1
if not isinstance(top, int):
valErr = ValueError("{} is not integer".format(top))
raise valErr
if not isinstance(bottom, int):
valErr = ValueError("{} is not integer".format(bottom))
raise valErr
# #6 solution for exercise 6 from 1.7 module - chap-1
if top < 0 and bottom < 0:
top = abs(top)
bottom = abs(bottom)
elif bottom < 0:
top = -top
bottom = abs(bottom)
common = gcd(abs(top), abs(bottom))
self.num = top // common
self.den = bottom // common
def primitive_triples(limit):
"""Return a list of pythagorean primitive triples.
Returns all primitive pythagorean primitive triples
(a,b,c) where c^2 <= limit. The results are unsorted,
a is always odd, and b is always even.
The pythagorean triples are integers (a,b,c) such that
a*a + b*b = c*c. Primitive triples are triples such that
a, b, and c are relatively prime.
To generate the triples, we look at all positive integers
m and n, with n < m. If m and n are coprime, and m-n is odd,
then we can calculate a, b, and c as follows:
a = m^2 - n^2, b = 2mn, c = m^2 + n^2
http://en.wikipedia.org/wiki/Pythagorean_triple
"""
result = []
m, m2 = 1, 1
while m2 <= limit:
# Check each n less than m. We only need to check the odd
# n if m is even and vice versa. Also, we can stop checking
# if we get to a case where c is greater than limit. Inside
# this loop, c is always increasing.
for n in xrange((m % 2) + 1, m, 2):
n2 = n*n
c = n2 + m2
# stop if c is too big for this n.
if c > limit:
break
if gcd.gcd(n,m) == 1:
# m and n are coprime. found a result!
result.append((m2-n2, 2*m*n, m2+n2))
m = m + 1
m2 = m * m
return result
def returnList():
# incorporate x, y, z symmetries
indices = []
sizes = []
for h in range(1,40):
for k in range(0,40):
for l in range(0,40):
if (abs(gcd(gcd(h,k),gcd(k,l)))==1) or (abs(gcd(gcd(h,k),gcd(k,l)))==0) and not h+k+l==0:
new_index = [h,k,l]
indices.append(new_index)
surf=makeSurface('Pt','fcc', new_index,size=(1,1,5))
volume = abs(np.dot(np.cross(surf.get_cell()[0],surf.get_cell()[1]),surf.get_cell()[2]))
sizes.append(volume)
else:
break
return indices, sizes
def __truediv__(self, other):
num = self.num * other.den
den = self.den * other.num
common = gcd(abs(num), abs(den))
return Fraction(num // common, den // common)
def __init__(self, numerator, denominator=1): """ create a fraction from a numerator and denominator """ g = gcd(numerator, denominator) self.numerator = numerator / g self.denominator = denominator / g
def solution(N, M):
d = gcd(N, M)
return N / d
def __sub__(self, other):
num = (self.num * other.den) - (self.den * other.num)
den = self.den * other.den
common = gcd(abs(num), abs(den))
return Fraction(num // common, den // common)
def test_gcd(self):
for case in self.test_cases:
a = case[0]
b = case[1]
g = case[2]
self.assertEqual(gcd.gcd(a, b), g)
def __euler_loop(n):
coprimes = [1]
for i in xrange(2, n):
if gcd(i, n) == 1:
coprimes.append(i)
return len(coprimes)
def simplify(self):
"""Simplifies a rational number"""
common = gcd.gcd(self.numerator, self.denominator)
self.numerator = self.numerator / common
self.denominator = self.denominator / common
def lcm(a,b):
return a * b / gcd(a,b)
from gcd import gcd
from gcd_fast import gcd as gcd_fast
for i in range(1, 100):
for j in range(1, 100):
print('testing for ', i, j)
assert (gcd(i, j) == gcd_fast(i, j))
def problem005(argument = range(1, 21)):
"""Return the lcm of 1 through 20."""
return reduce(lambda a, b: a * b / gcd(a, b), argument)
def makeSurface(symbol,structure,indices,size=(1,1,1),tol=1e-10,lattice_const=None):
"""
this function makes the surface and also identical bulk structure with atoms
symbol: what type of atom, in a string
structure: currently supported fcc, bcc, hcp, diamond
indices: miller index of the surface
size: tuple of (s_x,s_y,s_z) to use for the box
the lattice constant in ASE database may not be accurate, make your own...
"""
#if isinstance(structure, str):
#lattice = bulk(structure, cubic=True)
# first decide which function we want to use to build the structure
if structure=='fcc':
atoms_fn = getattr(ase.lattice.cubic,'FaceCenteredCubic')
elif structure=='bcc':
atoms_fn = getattr(ase.lattice.cubic,'BodyCenteredCubic')
elif structure=='hcp':
atoms_fn = getattr(ase.lattice.hexagonal, 'HexagonalClosedPacked')
elif structure=='diamond':
atoms_fn = getattr(ase.lattice.cubic,'Diamond')
elif structure=='sc':
atoms_fn = getattr(ase.lattice.cubic, 'SimpleCubic')
else:
print "structure defined not supported"
raise Exception
h , k , l = indices
miller = [None,None,[h,k,l]] # put in this argument as internal check
lattice = atoms_fn(symbol)
if lattice_const:
lattice = atoms_fn(symbol,latticeconstant = lattice_const)
# problem, should specify miller at the same time as directions
# now calculate the vectors to put along x,y,z directions
a1, a2, a3 = lattice.cell
h0, k0, l0 = (h == 0,k==0,l==0)
if h0 and k0 or h0 and l0 or k0 and l0: # if two indices are zero
if not h0:
c1, c2, c3 = [(0, 1, 0), (0, 0, 1), (1, 0, 0)]
if not k0:
c1, c2, c3 = [(1, 0, 0), (0, 0, 1), (0, 1, 0)]
if not l0:
c1, c2, c3 = [(1, 0, 0), (0, 1, 0), (0, 0, 1)]
else:
p, q = ext_gcd(k, l)
a1, a2, a3 = lattice.cell # this is the lattice constants
# constants describing the dot product of basis c1 and c2:
# dot(c1,c2) = k1+i*k2, i in Z
k1 = np.dot(p * (k * a1 - h * a2) + q * (l * a1 - h * a3), l * a2 - k * a3)
k2 = np.dot(l * (k * a1 - h * a2) - k * (l * a1 - h * a3), l * a2 - k * a3)
if abs(k2) > tol:
i = -int(round(k1 / k2)) # i corresponding to the optimal basis
p, q = p + i * l, q - i * k
a, b = ext_gcd(p * k + q * l, h)
c1 = (p * k + q * l, -p * h, -q * h)
c2 = np.array((0, l, -k)) // abs(gcd(l, k))
c3 = (b, a * p, a * q)
# layers wanted in surface direction
# along each surface direction, the number of atoms are different
# have to first determine that
layers=size[2]
d_v3 = max(int(1.0*layers/(np.dot(np.array(c3),indices/norm(indices)))),1)
#print d_v3
size_to_build = (size[0],size[1],d_v3)
#size_to_build = (size[0],size[1],size[2])
surface = build(lattice, np.array([c1,c2,c3]),size_to_build,tol)
return surface