John Cremona on Fri, 14 Nov 2014 22:28:43 +0100 |
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Re: Thue equations |
On 14 November 2014 20:03, Karim Belabas <Karim.Belabas@math.u-bordeaux.fr> wrote: > * John Cremona [2014-11-14 20:34]: >> Thanks for the replies, especially from Guillaume! (G, I remember you >> giving talks about your work on this many years ago, possibly when you >> were still a student). >> >> Charles misunderstood the question slightly, I was wondering whether >> the method used was the one which uses S-units (and this might have >> depended on the degree; currently I am only interested in solving >> degree 3 ones). > > Ariel Pacetti recently made the interesting remark that replacing the > (arbitrary) model input by the user by a "reduced" one could have a > dramatic effect. E.g. > > ? thue(-1744357*x^3 - 9313887*x^2 - 16576896*x - 9834496, 1) > time = 8,264 ms. > %1 = [] > > \\ reduced form associated to the same cubic order > ? thue(196*x^3 - 468*x^2 - 207*x + 228, 1) > time = 32 ms. > %2 = [] > > (Ariel's original example) > Ariel and I are working on a joint project -- this reduction of cubics with negative discriminant is done using a gp script I wrote last week implementing "juila reduction" -- which we all know is better than "Matthewws reduction" in this case ;) > I don't think this would affect your computations (I'd expect you > to use reduced models, esp. in the cubic case :-), but I didn't have > time to incorporate that trick yet. I'm not sure what you thought "my computations" are then! John > > Cheers, > > K.B. > -- > Karim Belabas, IMB (UMR 5251) Tel: (+33) (0)5 40 00 26 17 > Universite de Bordeaux Fax: (+33) (0)5 40 00 69 50 > 351, cours de la Liberation http://www.math.u-bordeaux1.fr/~kbelabas/ > F-33405 Talence (France) http://pari.math.u-bordeaux1.fr/ [PARI/GP] > ` >