def fundamental_solution(N):
context = Context(prec=1000)
val = Decimal(context.sqrt(N))
rep = [floor(val)]
val = Decimal(
context.divide(1, (context.subtract(val, Decimal(floor(val))))))
rep.append(floor(val))
ctr = 1
h_base = [0, 1]
k_base = [1, 0]
h_1 = rep[0] * h_base[-1] + h_base[-2]
k_1 = rep[0] * k_base[-1] + k_base[-2]
if check_sol(h_1, k_1, N):
return h_1, k_1
h_2 = rep[1] * h_1 + h_base[-1]
k_2 = rep[1] * k_1 + k_base[-1]
if check_sol(h_2, k_2, N):
return h_2, k_2
H = [h_1, h_2]
K = [k_1, k_2]
h = h_2
k = k_2
ind = 3
frac = Fraction(int(h), int(k))
while not (check_sol(frac.numerator, frac.denominator, N)):
val = Decimal(
context.divide(1, (context.subtract(val, Decimal(floor(val))))))
rep.append(floor(val))
#val = rep[ind-1]
h = long(long(floor(val)) * H[-1] + H[-2])
k = long(long(floor(val)) * K[-1] + K[-2])
frac = Fraction(long(h), long(k))
H.append(frac.numerator)
K.append(frac.denominator)
ind += 1
return h, k
def cont_frac(N):
context = Context(prec=1000)
val = Decimal(context.sqrt(N))
rep = [floor(val)]
ctr = 1
while ctr <= 1000:
val = Decimal(
context.divide(1, (context.subtract(val, Decimal(floor(val))))))
rep.append(floor(val))
ctr += 1
return rep
def cont_frac(N):
context = Context(prec=1000)
val = Decimal(context.sqrt(N))
init_val = floor(val)
rep = [init_val]
ctr = 1
while floor(val) != 2 * init_val:
val = Decimal(
context.divide(1, (context.subtract(val, Decimal(floor(val))))))
rep.append(floor(val))
ctr += 1
return rep
