def find_root(self, *, guess=None):
if self.num_roots():
if guess is None:
return ln(-self.c / self.a) / ln(self.b)
return super(Exponent, self).find_root(guess=guess)
else:
return None
def prime(n):
# f = 2
# n2 = 0
try:
return _p.prime(n)
except (ValueError, TypeError, AttributeError):
pass
if n <= 0:
raise ValueError("n must be greater than 0")
elif n < len(known_primes):
return known_primes[n - 1]
# while n2 != n:
# test = primeQ(f)
# if test:
# n2 += 1
# if n2 == n:
# break
# f += 1
# return f
# a = 2
# b = int(n * (log(n, e) + log(log(n, e), e)))
#
# while a < b:
# mid = (a + b) >> 1
# if li(mid) > n:
# b = mid
# else:
# a = mid + 1
# n_primes = primepi(a - 1)
# while n_primes < n:
# if primeQ(a):
# n_primes += 1
# a += 1
# return a - 1
lower = int(n * ln(n) + n * (ln(ln(n)) - 1))
if lower % 2 == 0:
lower += 1
upper = int(n * ln(n) + n * ln(ln(n)))
print(lower, upper)
for i in range(lower, upper, 2):
if not primeQ(i):
continue
if primepi(i) == n:
return i
def get_root_bounds(self):
return ln(-self.c / self.a) / ln(self.b), ln(-self.c / self.a) / ln(self.b)
def integrate(self, a=None, b=None):
integ = Exponent(self.a / ln(self.b), self.b) + Polynomial([self.c, 0])
if a is not None:
return integ(b) - integ(a)
return integ
def derivative(self, value=None):
der = Exponent(self.a * ln(self.b), self.b)
if value is not None:
return der(value)
return der