I just ran across a MathOverflow thread<http://mathoverflow.net/questions/55674/greatest-common-divisor-of-algebraic-integers>discussing gcds of algebraic integers living in rings with class number bigger than 1. We may not have the tools in Sage to implement it yet, but if someone's interested in working on gcd and lcm in number fields, you should take a look. David
On Mon, Feb 14, 2011 at 06:59, Simon King <simon.k...@uni-jena.de> wrote: > On 14 Feb., 12:40, Simon King <simon.k...@uni-jena.de> wrote: > > Question: Shall I remove the custom gcd/lcm for QQ and replace it by > > something that restricts to the usual gcd/lcm on ZZ? Or is that likely > > to break stuff? I could imagine that number theory people have a > > certain preference for a particular choice of a gcd in QQ. So, I am > > cross-posting to sage-nt. > > Oops, I have to slightly correct myself: > > * The rationale was given for lcm, not for gcd. > > * Fortunately, the current lcm does exactly what we want for the > fraction field of a PID: > sage: lcm(1/3,1/6) > 1/3 > So, there is no need to change lcm for the rationals. > > * The gcd of the rationals should be changed: Currently, it returns > either 1 or 0, which is not interesting. > > So, my patch for #10771 will provide lcm and gcd for fraction fields > of PID (so that it works, e.g., in Frac(QQ['x'])), will remove or > rename the current rational gcd (it shall in future be inherited from > the category), and will preserve the current rational lcm (for > efficiency). > > Moreover, since in future lcm and gcd for fraction fields behave > nicely wrt. the base ring, there shall be coercion before computing > gcd/lcd. > > Best regards, > Simon > > -- > You received this message because you are subscribed to the Google Groups > "sage-nt" group. > To post to this group, send an email to sage...@googlegroups.com. > To unsubscribe from this group, send email to > sage-nt+unsubscr...@googlegroups.com. > For more options, visit this group at > http://groups.google.com/group/sage-nt?hl=en-GB. > > -- 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
