Hello,
there was recently a letter on the subject like
" gcd(0,0) should be 0 ".
Unfortunately, I had lost it and cannot citate.
Here are simple considerations to prevent the confusion.
(1)
gcd(0,0) = 0 is all right.
But setting this would hardly improve anything. For in mathematics,
they write gcd(a,b) (think, say, of a/gcd(a,b) )
only after the case a=b=0 is considered separately or excluded
by default.
In other words, this would be is like setting 0/0 = 0.
(2)
The letter contained some discource on the subject.
Everything on gcd was explained by the classics:
" gcd(a,b) is the greatest by inclusion ideal (d) among the
ones with the property of
(d) = {x*d | x <- R} to be contained inside
(a)+(b) = {x*a + y*b | x,y <- R}
"
This was formutated so in order to fit not only the Integers.
Now (1) follows trivially from this definition as well as
(3)
(the author mentions the case of the rational numbers)
Here we keep in mind that for the Rationals and "the like domains",
gcd is trivial:
if a /= 0 then gcd(a,b) = 1.
Sergey Mechveliani
[EMAIL PROTECTED]
