William (stein), You mentioned in the thread below on the speeds of the other packages for poly mult that you use number fields of high degree when computing modular forms. Are these number fields as such, or local fields?
If they are number fields, then what degree fields do you compute in. I've timed MAGMA and Pari at this and MAGMA seems hopelessly slow for fields of degree say 15 or higher. Pari occasionally manages a degree 17 and I imagine on a fast machine might do slightly better. The limitation in Pari appears to be factoring the discriminant, which for a degree 24 field might have a 5000 bit discriminant. After that I believe the matrix algebra would eventually finish, even though it takes quite some time. But Obviously a 5000 bit integer will never factor unless it has many small factors (in which case the elliptic curve method ala GMP-ECM would benefit it greatly, since Pari's own ECM is a bit outdated). But it is not clear to me that for a generic number field, you actually can expect the discriminant to have many small factors. At any rate, how are you working with number fields of "large degree". Are they abelian, Probably that helps. I don't know what the situation is for those. Also, you didn't mention how fast polynomial multiplication helps. Do you mean just in multiplying elements of the number field expressed as polynomials in powers of the generator together. Bill. P.S: Check out my timings for FLINT's Karatsuba in the thread below where you posted your timings. :-) --~--~---------~--~----~------------~-------~--~----~ 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/ -~----------~----~----~----~------~----~------~--~---
