THere's a ticket somewhere asking for the implementation of sensible coercion between finite fields. Obviously only F_q -> F_q' where q' ia a power of q. But I have no idea how to do this in a way which is canonical -- so at the very least is transitive so that q -> q' -> q" is the same as q->q". If anyone out there has an idea here it would be good to hear it.
Is the following a sensible strategy: For each prime p maintain a list of fields of p-power order which have been created so far, with maps between them, always normalised to that if n is the largest degree of a field in the list (i.e. p^n is the largest power of p) then all the others are divisors of n. Now, on the creation of a new field of size p^m, if n|m then (do something fairly simple), or if gcd(n,m)=1 then (do something else fairly simple, else (do something more complicated). Does anyone know how Magma handles this? John 2008/4/14 David Harvey <[EMAIL PROTECTED]>: > > > On Apr 13, 2008, at 12:50 PM, Kiran Kedlaya wrote: > > > Any opinions about what > > > > sage: F9.<a> = GF(9); F81.<b> = GF(81); F81(a) > > > > should return? There is no canonical answer, so it may be better to > > throw an exception rather than pick one of the two correct answers. > > But any of these would be better than the current behavior, which is > > to return 0. > > Interesting.... that's not what happens in my install of sage 2.11. I > get: > > > sage: F9.<a> = GF(9) > sage: F81.<b> = GF(81) > sage: F81(a) > [.....] > <type 'exceptions.IndexError'>: n=17606600 must be < self.order() > > david > > > > > > > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
