On Sep 3, 5:25 pm, Nick Alexander <[EMAIL PROTECTED]> wrote: > Hi sage-devel, > > So I'd like opinions on two things: > 1) changing the printing of number field ideals, and > 2) changing the hash key of a residue field K/I to not reference I > directly, but instead the map K -> K/I.
I assume that you mean R/I where R subset K is the order with respect to which I is an ideal? Since the same code is probably going to be used for fractional ideals as well, you probably need to put the denominator in there too, i.e., hash ( d, R->R/(d*I) ), where d is the minimal positive integer such that d*I subset R. What is the hash of R->R/(d*I) ? Is it the hash of the HNF of the Z- basis of d*I, expressed relative to the basis of R? Are there cases where computing that hash is expensive? I imagine it could be for, say, principal ideals. One can give a very compact representation in that case (the generator), but the HNF can be quite nasty. In extremely big cases, one may have to settle for an LLL-reduced basis instead. Is it acceptable that asking for the hash of such an ideal might cause sage to explode? Still, I imagine that the worst case of that is not nearly as bad as computing the standard 2-generator form of an ideal. Can orders change their basis? Are isomorphic orders with different bases considered equal? Are isomorphic ideals in such orders considered equal? How does that interact with hashes? OK, it's not really an opinion. My opinion is that hash should be cheap whenever possible and your proposal seems to go that way, so that's great! I just recall that the choice of hash function has been problematic before, so I thought I'd give some feedback on of possible problems that sprang to mind. --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] 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 -~----------~----~----~----~------~----~------~--~---
