Re: What’s the equivalent of Mathematica’s Solve[] Function in Pari/Gp ?

[hermann@stamm-wilbrandt.de]

On 2025-01-12 22:07, Thomas D. Dean wrote:
> On 1/12/25 03:14, Bill Allombert wrote:
> > On Sun, Jan 12, 2025 at 11:46:43AM +0100, Laël Cellier wrote:
> > > No,
> > >
> > > it stops after finding the first solution instead of returning every
> > > possible values and that’s what I’m needing.
> >
> > Given the size of the solution it cannot just try all integers until 
> > finding
> > one that works, it must do something smarter.
> >
> > > And even if gcdext was the
> > > solution, how would I be able to use it since the equation contains a 
> > > ==
> > > sign ?
> >
> > Every equation contains a equal sign by definition.
> >
> > Set
> > RSA260=22112825529529666435281085255026230927612089502470015394413748319128822941402001986512729726569746599085900330031400051170742204560859276357953757185954298838958709229238491006703034124620545784566413664540684214361293017694020846391065875914794251435144458199
> >
> > F=(sqrtint(RSA260)+1)^2
> >
> > You want to solve
> >
> > ((25)^2 + x RSA260)/(y) == F
> >
> > after multiplying by y one get:
> >
> > x*RSA260 -F*y == -(25^2)
> >
> > Compute
> > [X,Y,d]=gcdext(RSA260,F)
> > we find d=1 so
> > X*RSA260 + Y*F == 1
> > So you just need to multiply by -(25^2)
> > -(25^2)*X*RSA260 -(25^2)*Y*F == -(25^2)
> > hence the solution is
> >
> > x = -(25^2)*X
> > y = (25^2)*Y
>
> Mathematica indicates there are an infinite number of solutions in the
> integers by including the constant C[1] in the solution. Maple uses
> _Z1.
>
> Tom Dean
I did show complete output with C[1] in previous posting:

https://pari.math.u-bordeaux.fr/archives/pari-users-2501/msg00002.html

Mathematica is not good in simplifying the condition:

(C[1] ∈ Integers && C[1] >= 0) || (C[1] ∈ Integers && C[1] <= -1)

is equivalent to

(C[1] ∈ Integers)