Karim Belabas on Fri, 14 Nov 2014 21:03:39 +0100 |
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Re: Thue equations |
* 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) 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. 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] `