On May 28, 2007, at 4:36 AM, Michel wrote:
>> Does this idea >> only make sense over division rings? Because it is sometimes nice to >> do integer arithmetic and have everything factored, as well. > > The factor cache works of course for non-fields. There is not much > point > taking the fraction field of a field, is there:-) Naturally you can > use it for integers but it would > probably be very slow since integer arithmetic is already extremely > fast. > It is really meant for rings for which no specialized arithmetic is > available. Actually the gcd code in the most recent release of GMP is O(N^2). (This is supposed to be fixed in the upcoming GMP 5, but it may not be for several years). So for example: sage: a = ZZ.random_element(2**1000000) sage: b = ZZ.random_element(2**1000000) sage: c = ZZ.random_element(2**1000000) sage: time x = a*b CPU times: user 0.02 s, sys: 0.00 s, total: 0.02 s Wall time: 0.02 sage: time x = 1/(a*b) + 1/(a*c) CPU times: user 9.58 s, sys: 0.01 s, total: 9.59 s Wall time: 9.59 Presumably if this was done in the factor cache fraction field it would be much faster. I think the general case of a factor cache for rings could be useful in some situations, but I admit I'm at a loss to name any specific examples. I think I would generally support including the code you are proposing, assuming a referee is happy with the code. (I insist however on the spelling "caching" rather than "cacheing" :-)) Qualification: obviously, if this ever gets integrated with the FractionField constructor, it should be only *optional*... I would expect there would be many applications where the caching would actually slow things down. What do you think about this? 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://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
