On Wed, 2011-02-09 at 22:18 -0800, rjf wrote: > 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. >
It is a question of domains. In Axiom you can specify the domains. 2/1 is a Fraction(Integer) aka rational 4 is an Integer (2/1)::Integer => 2 where 2 is an Integer. 4::Fraction(Integer) is a Fraction(Integer) So there are several cases: gcd((2/1),4::Fraction(Integer)) => 1 of type Fraction(Integer) gcd((2/1)::Integer,4)) => 2 of type PositiveInteger gcd(2/1,4) => 1 of type Fraction(Integer) gcd(2,4) => 2 of type PositiveInteger gcd(2,4::Fraction(Integer)) => 1 of type Fraction(Integer) Tim Daly -- 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
