Are there open-source implementations of this available? the only (somewhat) fast library I know is Singular's factory (https://github.com/Singular/Sources/blob/spielwiese/factory/README) used both in Singular and in Macaulay2...
Also, if you need to output factors, which might exist only over proper extensions, you would have to build these extensions, no? On Thursday, November 3, 2016 at 7:37:58 PM UTC, Nils Bruin wrote: > > On Thursday, November 3, 2016 at 1:37:25 PM UTC-4, Dima Pasechnik wrote: >> >> >> >> On Thursday, November 3, 2016 at 1:06:05 PM UTC, Bill Hart wrote: >>> >>> >>> >>> On Friday, 28 October 2016 18:44:09 UTC+2, Dima Pasechnik wrote: >>>> >>>> 5 variables and degree 100 is really, really huge. Especially over QQ, >>>> the coefficients of >>>> polynomials will just totally blow. >>>> In fact, 5 variables and degree 10 might still be quite hard, in >>>> particular over QQ or other char. 0 fields. >>>> >>> >>> I disagree with all of the above, especially when the polynomials are >>> randomly generated. >>> >> >> Huh? Algebraic geometers are mostly not interested in random data. >> With probability 1, your random data will define something irreducible. >> While if your data is reducible, you might need to build algebraic >> extensions >> of high degree to factor. I don't see how you can handle extensions of >> degrees that might pop >> out of the data of this format... >> > > It should be easy for exactly the same reason why factoring over ZZ[x] is > fast: you reduce to factoring over GF(p)[x] and if you end up with a > square-free factorization, you lift p-adically. There's a (theoretical?) > issue of factor combination that is solved (theoretically as well as > practically) by LLL > > This works for multivariate factorization just as well: you specialize > variables and lift (repeatedly); you don't eliminate variables. No need to > build algebraic extensions. There are still details you need to check for > and you need to show you have a reasonable chance of not making unfortunate > choices, but polynomial factorization in general show be pretty efficient. > > -- 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.
