Re: cubic equation - is it really solvable?

Jean-Claude Arbaut wrote:
> On 20/06/2005 05:37, Gerry Myerson wrote:
>
> > In article <42B2FF7C.B0D82182@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
> > Jim Spriggs <jim.sprigs@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote:
> >

> >> If all the solutions are rational then the cubic can be factored. There
> >> are trial and error methods where the number of trials is happily
> >> finite.
> >
> > Of course, if the coefficients are 200-digit numbers,
> > you may face some practical difficulties.
>
> Would you prefer to simplify the radicals or the trig ?
> BTW, the number of digits is not the problem, the integer factorization is.
> If the first and last coefficients are easily factored, then it's ok.
> Since it depends on your problem and we had no information on that, it was
> worth noting the method I think.

Factoring is not necessarily required.
Perform the substitution x=y/a[3].
Multiply through by a[3]**2.
Solve numerically for integer solutions for y.

.

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