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

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)