Perhaps a trivial contribution, but I would like to give primes ideals "human-readable" names such as P2a,P2b,.. for primes above 2, etc; so then when I print a factorizaed idea I see something like P2a^3*P2b*P17.
I suppose this idea would apply to other complicated structures too. John 2008/9/4 Robert Bradshaw <[EMAIL PROTECTED]>: > > On Sep 3, 2008, at 5:25 PM, Nick Alexander wrote: > >> Hi sage-devel, >> >> At this time, Sage prints number field ideals in two-generator form. >> There are good reasons for this, perhaps most notably that this is a >> normal form best suited for visual inspection. >> >> For most of the things I do, I don't care exactly what ideal I have: I >> would be perfectly happy to know I had just some ideal I of norm N of >> a number field K. In particular, I want to calculate in the residue >> field K/I; the actual ideal counts very little; the norm N and the map >> from K -> K/I count a lot. >> >> This would all be fine, except... number field ideals hash to the hash >> of their string representation. And the string representation >> computes a two-generator form, and computing two-generator forms is >> slow. *Excruciatingly slow*. So just to construct K/I, which hashes >> the ideal I into its unique key, takes me minutes if not hours. >> >> So I'd like opinions on two things: >> 1) changing the printing of number field ideals, and > > I think this is a good idea, I've avoided printing out number field > ideals for this exact reason. > >> 2) changing the hash key of a residue field K/I to not reference I >> directly, but instead the map K -> K/I. > > +1 For sure. As long as hashing respects equality, lets make it as > fast as we can. > >> I haven't thought about this for a long time, but it basically works: >> I have a hacked version of a few functions that tries to avoid hashing >> and changes the relevant __repr__s, and so far it works. This is the >> difference between not being able to reduce curves defined over number >> fields of degree 40 to easily reducing at dozens of primes. Thoughts, >> please? > > Also, I wonder how much of the number field arithmetic can be sped up > using Sage's much faster HNF rather than pari's. > > - Robert > > > > > --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
