blindanagram wrote: > What is the rationale for gcd(x, y) in Fractions returning a negative > value when y is negtive?
Good question. Normally, gcd is only defined for non-negative integers. Wolfram Mathworld, for example, doesn't mention negative values at all (as far as I can see): http://mathworld.wolfram.com/GreatestCommonDivisor.html although buried deep in the documentation for Mathematica's GCD function is hidden the fact that it treats GCD(-a, -b) the same as GCD(a, b): http://functions.wolfram.com/IntegerFunctions/GCD/04/02/01/ and sure enough Wolfram Alpha tells me that the GCD of *all* of: (100, 20) (-100, 20) (100, -20) (-100, -20) are equal to +20. On the other hand, Excel and LibreOffice both give an error for the GCD of a negative value, and I've seen versions of gcd() which do the same as fractions.gcd. So I think there is not one single standard way to extend GCD to negative numbers. > For example gcd(3, -7) returns -1, which means that a co-prime test that > would work in many other languages 'if gcd(x, y) == 1' will fail in > Python for negative y. True, but either of: abs(gcd(x, y)) == 1 gcd(x, y) in (1, -1) will work. > And, of course, since -|x| is less than |x|, returning -|x| rather than > |x| is not returning the greatest common divisor of x and y when y is > negative. That's a good argument for gcd if it were in a general maths module, but since it is specifically used for generating fractions, I guess that the developers won't be very convinced by that. -- Steven -- https://mail.python.org/mailman/listinfo/python-list
