Karim Belabas on Tue, 30 Sep 2014 21:11:08 +0200

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 Re: thue question

```* Ariel Martin Pacetti [2014-09-30 20:45]:
> ? S=thueinit(2*x^3 + 2*x^2 + 11*x - 114);
> ? thue(S,200)
> %2 = []
>
> The values (1,0) and (0,-1) give: 2, 114, so shouldn't they be solutions to
> the equation?

Not sure I understand this one: thue(S,200) looks for solutions of

2*x^3 + 2*x^2*y + 11*x*y^2 - 114*y^3 = 200

which doesn't seem related to the special values you give.  As
expected, OTOH, you find

(21:04) gp > thue(S,2)
%1 = [[1, 0]]
(21:04) gp > thue(S,114)
%2 = [[0, -1]]

> BTW, it I want to solve "many" thue equations, is there a way to get "all
> the solutions up to a" (which are probably tested in the search).

What do you mean by "solutions up to a" ? Such that max(|x|,|y|) <= a ?

If so, either loop over pairs (x,y) [ a^2 trials, optimal for small a ]
or only over x and for each such use nfrootsQ() [ better for large a ]

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]
`

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