Re: [racket-dev] feature request: gcd, lcm for rationals
On 12/10/11 9:25 AM, David Van Horn wrote: On 12/9/11 3:31 PM, Daniel King wrote: On Fri, Dec 9, 2011 at 15:27, Carl Eastlund wrote: What does "divides" even mean in Q? I think we need David to explain what his extension of GCD and LCM means here, in that "divisors" and "multiples" are fairly trivial things in Q. I took "x divides y" to mean x/y is an integer. I meant: y/x is an integer. David _ For list-related administrative tasks: http://lists.racket-lang.org/listinfo/dev
Re: [racket-dev] feature request: gcd, lcm for rationals
On 12/9/11 3:31 PM, Daniel King wrote: On Fri, Dec 9, 2011 at 15:27, Carl Eastlund wrote: What does "divides" even mean in Q? I think we need David to explain what his extension of GCD and LCM means here, in that "divisors" and "multiples" are fairly trivial things in Q. I took "x divides y" to mean x/y is an integer. I don't suppose to understand all the math on this page, but I think it uses the same definition that dvh is using. http://mathworld.wolfram.com/GreatestCommonDivisor.html Yes, that's where I got the definition I suggested. As a concrete example of why I wanted gcd extended to rationals: I wrote a big-bang program that runs a set of big-bang programs, so it needs a tick-rate that is the gcd of all the tick-rates of the programs it runs, which may be rational. David _ For list-related administrative tasks: http://lists.racket-lang.org/listinfo/dev
Re: [racket-dev] feature request: gcd, lcm for rationals
2011/12/10 Stephen Bloch > > On Dec 9, 2011, at 3:31 PM, Daniel King wrote: > > > On Fri, Dec 9, 2011 at 15:27, Carl Eastlund wrote: > >> What does "divides" even mean in Q? I think we need David to explain > >> what his extension of GCD and LCM means here, in that "divisors" and > >> "multiples" are fairly trivial things in Q. > > > > I don't suppose to understand all the math on this page, but I think > > it uses the same definition that dvh is using. > > > > http://mathworld.wolfram.com/GreatestCommonDivisor.html > > Interesting: the Mathematica people have extended the gcd function from > the integers to the rationals, not by applying the usual definition of gcd > to Q (which would indeed be silly, as everything except 0 divides > everything else), but by coming up with a different definition which, when > restricted to integers, happens to coincide with the usual definition of > gcd. > If we for rational numbers x and y define "x divides y" to mean "y/x is an integer", then I believe the definition d is a gcd of x and y <=> i) d divides a and y ii) e divides x and y => d divides e coincides with the MathWorld definition. > I would wonder: is this the ONLY "reasonable" function on rationals which, > when restricted to integers, coincides with the usual definition of gcd? > Not sure, but this seems relevant. http://trac.sagemath.org/sage_trac/ticket/10771 -- Jens Axel Søgaard _ For list-related administrative tasks: http://lists.racket-lang.org/listinfo/dev
