NZMATH  1.2.0
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nzmath.gcd Namespace Reference

Functions

def gcd (a, b)
 
def binarygcd (a, b)
 
def extgcd (x, y)
 
def gcd_of_list (integers)
 
def lcm (a, b)
 
def coprime (a, b)
 
def pairwise_coprime (int_list)
 

Detailed Description

funtions related to the greatest common divisor of integers.

Function Documentation

◆ binarygcd()

def nzmath.gcd.binarygcd (   a,
  b 
)
Return the greatest common divisor of 2 integers a and b
by binary gcd algorithm.

Definition at line 16 of file gcd.py.

◆ coprime()

def nzmath.gcd.coprime (   a,
  b 
)
Return True if a and b are coprime, False otherwise.

For Example:
>>> coprime(8, 5)
True
>>> coprime(-15, -27)
False
>>>

Definition at line 68 of file gcd.py.

References nzmath.gcd.gcd().

Referenced by nzmath.gcd.pairwise_coprime().

◆ extgcd()

def nzmath.gcd.extgcd (   x,
  y 
)
Return a tuple (u, v, d); they are the greatest common divisor d
of two integers x and y and u, v such that d = x * u + y * v.

Definition at line 25 of file gcd.py.

Referenced by nzmath.gcd.gcd_of_list(), and nzmath.finitefield.ExtendedFieldElement.inverse().

◆ gcd()

def nzmath.gcd.gcd (   a,
  b 
)

◆ gcd_of_list()

def nzmath.gcd.gcd_of_list (   integers)
Return a list [d, [c1, ..., cn]] for a list of integers [x1, ..., xn]
such that d = c1 * x1 + ... + cn * xn.

Definition at line 40 of file gcd.py.

References nzmath.gcd.extgcd(), and nzmath.bigrange.range().

◆ lcm()

def nzmath.gcd.lcm (   a,
  b 
)
Return the least common multiple of given 2 integers.
If both are zero, it raises an exception.

Definition at line 61 of file gcd.py.

References nzmath.gcd.gcd().

◆ pairwise_coprime()

def nzmath.gcd.pairwise_coprime (   int_list)
Return True if all integers in int_list are pairwise coprime,
False otherwise.

For example:
>>> pairwise_coprime([1, 2, 3])
True
>>> pairwise_coprime([1, 2, 3, 4])
False
>>>

Definition at line 81 of file gcd.py.

References nzmath.gcd.coprime().