Re: Is it possible to have several solutions in this way to this equation using Pari/ɢᴘ ?

[Laël Cellier <lael.cellier@laposte.net>]

Not exactly as there’s no second equation mais un polynome…

Currently the script for solving this is :

beta=-(V\W);
alpha=W*(V+W*beta);
xx=alpha^2*x^2+(2*alpha*beta-f*b)*x+(beta^2-c);
nfr=nfroots(,xx);

So given v,w,b,c I want to find integers alpha and beta such I can find at least 2 different but valid values of nfr. I think this means modifying the part of script for finding alpha and beta. This might not even be mathematically possible at all…
Cordialement,

Le 19/01/2025 à 15:07, Bill Allombert a écrit :
> On Sun, Jan 19, 2025 at 11:58:47AM +0100, Laël Cellier wrote:
> > Bonjour,
> >
> > I’ve the following equation where the aim is to find /alpha/ and /beta/ as
> > integers given /w/ and /v/ as integers
> >
> > alpha == w (v + w beta)
> > Of course finding several solution for the equation above is possible, but
> > then I want /nfroots()/ to return a second set of possible results given /c/
> > and /b/ and where /x/ is an unknow
> >
> > xx=alpha^2*x^2+(2*alpha*beta-abs(b))*x+(beta^2-c);
> > nfroots(,xx);
> So given v,w,b,c you want to find integers alpha, beta and rational x such that
>
> alpha = w *(v + w * beta)
> alpha^2*x^2+(2*alpha*beta-abs(b))*x+(beta^2-c) = 0
>
> Is it correct ?
>
> Cheers,
> Bill.