Look at the docstrings in GcdDomain. I think, we can do better.
gcd : (%, %) -> %
++ gcd(x, y) returns the greatest common divisor of x and y.
lcm : (%, %) -> %
++ lcm(x, y) returns the least common multiple of x and y.
In particular, it is not clearly specified what gcd(0,0) will return.
Currently gcd(0,0) in Fraction(Integer) gives 1. Why?
Because there is a default definition in Field
gcd(x, y) == 1
In Integer, we have gcd(0,0)=0.
Mathematica, Maple, and Sage all yield 0 as a result of gcd(0,0).
I'm not saying that is the best, but 1 is also not really nice, since then
\exists a,b : gcd(x,y) = a*x + b*y
would not hold for x=y=0.
It all depends on what the definition of "greatest common divisor" in
the docstring of gcd (see above) actually is.
Opinions?
Ralf
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