I started writing `gcd()`

for whatever reason and then compared with `math.gcd()`

and it’s surprising that `math.gcd(-1,0)`

says that 1 is a common denominator between -1 and 0.

```
def gcd(a : int, b : int) -> int:
if a == 0 or b == 0:
return 0
if a == 1 or b == 1:
return 1
_a, _b = (a,b) if a > b else (b,a)
for n in (_b, math.floor(_b/2) if not _b % 2 else _b, *range(math.floor(_b/2), 1, -1)):
if not _a % n and not _b % n:
return abs(n) # this appears to match math.gcd()
# return n # this has undefined behavior with negative-valued inputs
return 1
assert gcd(10, 20) == 10 == math.gcd(10,20)
assert gcd(20, 10) == 10 == math.gcd(20,10)
assert gcd(60, 20) == 2*2*5
assert gcd(20, 60) == 2*2*5
assert gcd(3, 11) == 1 == math.gcd(3, 11)
assert gcd(3, 3) == 3
assert gcd(3, 1) == 1 == math.gcd(3,1)
assert gcd(11, 3) == 1
assert gcd(512, 32) == 32 == math.gcd(512, 32)
assert gcd(512, 64) == 64
assert gcd(2,4) == 2
assert gcd(4,2) == 2
assert gcd(0,0) == 0 == math.gcd(0,0)
assert gcd(-1, 0) == 0
assert gcd(0, -1) == 0
assert gcd(-10,20) == 10 == math.gcd(-10, 20)
assert gcd(37, 71) == 1 == math.gcd(37,71), gcd(37, 71)
for ab in (*itertools.combinations(range(1, 1000), r=2), (0,-1), (1,0) ):
#display(dict(ab=ab))
assert gcd(*ab) == math.gcd(*ab), (dict(ab=ab, gcd=gcd(*ab), mathgcd=math.gcd(*ab)))
```

```
AssertionError: {'ab': (0, -1), 'gcd': 0, 'mathgcd': 1}
```

So, (1) is this the case with all versions of python?; (2) should it be; does the math definition of gcd() say that 0 is ever a common denominator?; (3) and can or should `math.gcd()`

be changed?

```
import math
assert math.gcd(0,-1) == 1
assert math.gcd(1, 0) == 1
assert math.gcd(0, 0) == 0
assert math.gcd(0, 1) == 1
assert math.gcd(-1, 0) == 1
# also fwiw:
assert math.gcd(-1, 1) == 1
assert math.gcd(1, -1) == 1
```