Re: t_PADIC to t_INTMOD and use of chinese()

[Karim Belabas <Karim.Belabas@math.u-bordeaux.fr>]

* Karim Belabas [2025-02-14 15:31]:
> * Max Alekseyev [2025-02-14 15:09]:
> > dueHello,
> > 
> > I have a couple of requests:
> > 
> > 1) An easy way to convert t_PADIC to t_INTMOD, maybe extending Mod() to
> > support a single argument of type t_PADIC, e.g. Mod(1 + O(5^2)) would
> > produce Mod(1, 25).
> 
>   padic2mod(x) = Mod(x, x.p^padicprec(x, x.p));

Not sure about making this one built-in as Mod(x), but easy to do.

It could just as easily work recursively for polynomials, series, vectors,
matrices as well (we couldn't then extend to the comparatively less
useful Mod(x + O(x^2)) -> Mod(x, x^2))

But what would be the use cases ?

I would expect that the user would know the p-adic accuracy and just use
Mod(x, p^d) for the right d (which would also work recursively, compared
to my padic2mod which requires x to be a t_PADIC in order to determine a
proper d)

> > 2) Extend chinese() to support t_PADIC arguments (still producing t_INTMOD).
> 
>   padicchinese(v) = chinese(apply(padic2mod, v))
> 
>   ? padicchinese([1 + O(5^2), 3 + O(3^3)])
>   %3 = Mod(651, 675)

This one is now built-in in the 'master' branch: t_PADICs and t_INTMODs
can be used interchangeably.

    ? chinese(1 + O(5^2), 3 + O(3^3))
    %1 = Mod(651, 675)

    ? chinese((1+O(7)) * (x+1), Mod(x^2+1, 5))
    %2 = Mod(21, 35)*x^2 + Mod(15, 35)*x + Mod(1, 35)

    ? H = mathilbert(3); chinese(H * (1 + O(7^2)), Mod(H, 11))
    %3 = 
    [  Mod(1, 539) Mod(270, 539) Mod(180, 539)]

    [Mod(270, 539) Mod(180, 539) Mod(135, 539)]

    [Mod(180, 539) Mod(135, 539) Mod(108, 539)]

Cheers,

    K.B.
-- 
Pr. Karim Belabas, U. Bordeaux, Vice-président en charge du Numérique
Institut de Mathématiques de Bordeaux UMR 5251 - (+33) 05 40 00 29 77
http://www.math.u-bordeaux.fr/~kbelabas/