Mapytex/mapytex/calculus/core/arithmetic.py

85 lines
1.5 KiB
Python

#!/usr/bin/env python
# encoding: utf-8
__all__ = ["gcd"]
def gcd(a, b):
"""Compute gcd(a,b)
:param a: first number (need to support abs, comparison, * and %)
:param b: second number (need to support abs, comparison, * and %)
:returns: the gcd
>>> gcd(3, 15)
3
>>> gcd(15, 3)
3
>>> gcd(-3, -15)
-3
>>> gcd(5, 12)
1
>>> gcd(4, 14)
2
"""
try:
pos_a, _a = (a >= 0), abs(a)
pos_b, _b = (b >= 0), abs(b)
gcd_sgn = -1 + 2 * (pos_a or pos_b)
except TypeError:
_a = a
_b = b
gcd_sgn = 1
if _a > _b:
c = _a % _b
else:
c = _b % _a
if c == 0:
return gcd_sgn * min(_a, _b)
elif _a == 1:
return gcd_sgn * _b
elif _b == 1:
return gcd_sgn * _a
else:
return gcd_sgn * gcd(min(_a, _b), c)
def lcm(a, b):
"""Compute lcm(a,b)
:param a: first number (need to support abs, comparison, *, % and //)
:param b: second number (need to support abs, comparison, *, % and //)
:returns: the lcm
>>> lcm(3, 15)
15
>>> lcm(15, 3)
15
>>> lcm(-3, -15)
-15
>>> lcm(5, 12)
60
>>> lcm(4, 14)
28
"""
return (a * b) // gcd(a, b)
if __name__ == "__main__":
print(gcd(3, 15))
print(gcd(3, 15))
print(gcd(-15, -3))
print(gcd(-3, -12))
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