exception ftplib.error_perm Exception raised when an error code signifying a permanent error (response codes in the range 500–599) is received.

ftplib.all_errors The set of all exceptions (as a tuple) that methods of FTP instances may raise as a result of problems with the FTP connection (as opposed to programming errors made by the caller). This set includes the four exceptions listed above as well as OSError.

class frozenset([iterable]) Return a new frozenset object, optionally with elements taken from iterable. frozenset is a built-in class. See frozenset and Set Types — set, frozenset for documentation about this class. For other containers see the built-in set, list, tuple, and dict classes, as well as the collections module.

class frozenset([iterable]) Return a new set or frozenset object whose elements are taken from iterable. The elements of a set must be hashable. To represent sets of sets, the inner sets must be frozenset objects. If iterable is not specified, a new empty set is returned. Instances of set and frozenset provide the following operations: len(s) Return the number of elements in set s (cardinality of s). x in s Test x for membership in s. x not in s Test x for non-membership in s.

fractions.gcd(a, b) Return the greatest common divisor of the integers a and b. If either a or b is nonzero, then the absolute value of gcd(a, b) is the largest integer that divides both a and b. gcd(a,b) has the same sign as b if b is nonzero; otherwise it takes the sign of a. gcd(0, 0) returns 0. Deprecated since version 3.5: Use math.gcd() instead.

__round__() __round__(ndigits) The first version returns the nearest int to self, rounding half to even. The second version rounds self to the nearest multiple of Fraction(1, 10**ndigits) (logically, if ndigits is negative), again rounding half toward even. This method can also be accessed through the round() function.

__floor__() Returns the greatest int <= self. This method can also be accessed through the math.floor() function: >>> from math import floor >>> floor(Fraction(355, 113)) 3

__ceil__() Returns the least int >= self. This method can also be accessed through the math.ceil() function.

numerator Numerator of the Fraction in lowest term.

limit_denominator(max_denominator=1000000) Finds and returns the closest Fraction to self that has denominator at most max_denominator. This method is useful for finding rational approximations to a given floating-point number: >>> from fractions import Fraction >>> Fraction('3.1415926535897932').limit_denominator(1000) Fraction(355, 113) or for recovering a rational number that’s represented as a float: >>> from math import pi, cos >>> Fraction(cos(pi/3)