Re: is there a way to globally rely on ispseudoprime() for primality testing?

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Thu, Oct 03, 2024 at 02:08:33PM -0400, Max Alekseyev wrote:
> Thank you for the pointer to ispseudoprimepower. I was not able to locate
> it with ???
> 
> ? ???isprimepower
> isprimepower
> 
> As for the global option, I do not have a particular instance to share. My
> question is motivated by the *set-and-forget* approach - I do not want to
> analyze for each function whether it uses isprime() is ispseudoprime(), but
> just to specify my preference once and be sure that every function follows
> it. It will allow, say, to run some preliminary code backboned
> by ispseudoprime(), but then use the same code backboned by isprime() when
> the primality certainty is important.
> 
> For example, as far as I remember, nextprime() and prevprime() rely on

> ispseudoprime(). However, following the logic with isprimepower()
> / ispseudoprimepower() there should have been function nextpseudoprime()
> and prevpseudoprime().

The function is called precprime() but your (an Ilya) point stands,
it should have been named nextpseudoprime/precpseudoprime
(and why not forprime/forpseudoprime).

Before 2002, PARI has both functions isprime and ispseudoprime, but
isprime did not actually do a proven primality test, just a stronger
pseudoprimality test.
Then Henri implemented the APR-CL primality proof, and 
we decided to have ispseudoprime use the stronger pseudoprimality
test and isprime to use a proven test, which we hoped to be more in accordance
with users expectationa.
Unfortunately that slowed down a number of scripts that expected isprime to be
fast. 

At this time, changing nextprime/precprime can cause more problems that it solves.

Note that there is a default 'factor_proven' to have factor use isprime instead
of ispseudoprime to validate factors. Maybe we could extend its effect.

Cheers,
Bill.