You say, > gcd(2/1,4) returns 1 "for simplicity" (!), because 2/1 is a rational. > This is shockingly silly.
I don't know exactly how this came up, but if 2/1 is in a different domain (rational) from 2, (integer), then gcd should probably be 1, since any non- zero rational number divides any other, and one commonly uses the positive "unit" 1 for such a case. You could argue that since you can coerce 2/1, you should. That's sometimes OK, but not always. Really, the issue is much broader. for example, do you also want to treat the complex number 1+0*i the same as 1? do you want to treat the floating point number 1.0 the same as 1? What about 1X1 matrices? Is 1^0 the same as 1^0.0 or 1.0^0 or 1.0^0.0? Do you perhaps wish to consider/dismiss the existence of number systems with signed zeros (IEEE floating-point standard) on the grounds that -0 = +0, [true, for numerical comparison] and therefore there should be only a single zero? While I don't know the exact formulation of this GCD problem, the issue of implicit coercion is one of the troubling sore spots in a system design, and should not be decided by counting up casual +1 votes. I think the Axiom people might have thought more about it than others. -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
