Re: helping nfinit
John Cremona <[email protected]> Thu, 14 May 2026 14:04:17 +0100
| Newsgroups | gmane.comp.mathematics.pari.user |
|---|---|
| Message-ID | <CAD0p0K582YsobPhuwKhrRSMAVSd8xy-o7hhTt-bnNXPV+HB=uQ@mail.gmail.com> |
--0000000000007153740651c6bd52 Content-Type: text/plain; charset="UTF-8" On Thu, 14 May 2026 at 11:57, Bill Allombert <[email protected]> wrote: > > On Thu, May 14, 2026 at 11:03:31AM +0100, John Cremona wrote: > > In gp, ?nfinit says that the first parameter must be a polynomial. > > The longer documentation in ??nfinit says that the first parameter can > > be a pair or triple [pol,B], [pol,B,P] or [pol,listP] where B is a > > lift of an integral basis, P and listP are lists of primes. But the > > example given if nfinit([pol,10^3]) which shows that the second > > parameter can be a bound on the primes and not just a list of primes. > > Perhaps this should be corrected (if I am right)? > > See ??nfbasis. OK -- I was misled by calling the parameter Plist and did not see the significance of the wording that Plist "specifies" a list of primes, not "is" a list of primes. In fact, I see that for my current purposes, nfbasis() does what I need so I will use that instead of nfinit0(). > > > Also, the situation I am in is that as well as a polynomial pol (monic > > irreducible and integral) defining the field, I have a collection of > > known algebraic integers a2=Mod(g2,pol), a3=Mod(g3,pol), .... It > > seems that knowing these should help nfinit but I don't see an easy > > way of doing so. In one example, the degree is 45, the minpolys of > > a2 and a3 (both of full degree) have discriminants which are too large > > to factor but the gcd of their discriminants -- which is the field > > discriminant times a much smaller square -- can be factored. In my > > example that gcd is 2^10 times an integer with 117 digits which can be > > factored in reasonable time (under a minute on my 10-year-old laptop) > > as the product of 709, 11652785276119009306943, > > 33453572138997299442641, > > 3430518186990900226076508080139548308272997052056646116033470256885927. > > If I do nfinit([pol,plist]) where plist contains 2 and these primes > > then I can see that the field discriminant is just their product (with > > no factor of 2 and all is well). So this is an example where knowing > > just pol=minpoly(a2) it is impossible (in practice) to get an integral > > basis, but knowing minpoly(a3) also makes it possible. > > Mind sending us your actual data ? See the attached file! Thanks, John > > Cheers, > Bill. --0000000000007153740651c6bd52 Content-Type: text/plain; charset="US-ASCII"; name="719c.txt" Content-Disposition: attachment; filename="719c.txt" Content-Transfer-Encoding: base64 Content-ID: <f_mp5i2fzn0> X-Attachment-Id: f_mp5i2fzn0 UShjKSA9IFFbWF0vKFheNDUtMypYXjQ0LTcwKlheNDMrMjEzKlheNDIrMjI2MipYXjQxLTY5OTQq WF40MC00NDc3NipYXjM5KzE0MDk5MCpYXjM4KzYwNzUzMCpYXjM3LTE5NTM0NjQqWF4zNi01OTg5 ODQzKlheMzUrMTk3MzU1MDkqWF4zNCs0NDM4MjUyNipYXjMzLTE1MDUyMTMzMSpYXjMyLTI1MjA1 OTQwNipYXjMxKzg4NTI5NjUwNypYXjMwKzExMDg0NzUzMTEqWF4yOS00MDY2Njg3OTA5KlheMjgt Mzc4NDA0MDYzNSpYXjI3KzE0Njg2NDA3MjkxKlheMjYrOTk3MjAxMDgwOSpYXjI1LTQxNzY3MjM0 NTg5KlheMjQtMTk5NTQzNDEyNzEqWF4yMys5MzI3OTk1NTEyNypYXjIyKzI5MjIyMzc0MzIxKlhe MjEtMTYyNDAwMjk0OTk3KlheMjAtMjg1Nzk0MTQxMzUqWF4xOSsyMTc2NjUxNjYxMjMqWF4xOCsx Mjc5NjQ3MzIyNSpYXjE3LTIyMDMzNTg1OTg4OSpYXjE2Kzk2MjI2MjM0MDUqWF4xNSsxNjM3MzM2 NDI2MTQqWF4xNC0yMjE5NzY2ODUyMCpYXjEzLTg1NTc3MTk0MTU3KlheMTIrMTg4NDcyNDg0NzAq 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