On Sunday, 9 October 2016 18:08:29 UTC+2, Dima Pasechnik wrote: > > > > On Sunday, October 9, 2016 at 3:35:57 PM UTC, Bill Hart wrote: >> >> By default, Singular uses 16 bit exponents. But it is perfectly capable >> of working with exponents up to 64 bits. That will be slower of course. >> >> why? I presume arithmetic on 16-bit integers is not faster than on > 32-bit, or even 64-bit. >
It's the exponent arithmetic, not the coefficients we are talking about. The exponents are packed, with four 16 bit field in a 64 bit word. This is *much* faster. I use the same trick, as does just about every decent computer algebra system out there. Interestingly, Magma only allows exponents up to about 30 bits, but it takes a few minutes to compute x^(2^30 - 1). > > > >> I guess it isn't easy for Sage to change the relevant ring upon overflow >> to one using 64 bit exponents. >> >> I can't say whether it would be easy or hard for Singular to >> automatically change the exponent size for you. For basic arithmetic, I >> have implemented precisely this in the code I've been writing. But Singular >> is almost infinitely more complex than the very simple cases I've been >> dealing with in my own code. At this stage I couldn't even hazard a guess. >> >> I'll ask Hans if I remember. But either way, I believe this would be an >> *extremely* time consuming thing to fix. How important is it? >> >> Bill. >> >> On Wednesday, 5 October 2016 01:10:31 UTC+2, Jakob Kroeker wrote: >>> >>> >>> https://trac.sagemath.org/ticket/6472 >>> >>> even for recent singular upgrade >>> >>> https://trac.sagemath.org/ticket/17254 >>> >>> and it was not(?) reported to upstream... >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.