Re: New ECPP interface

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

* Bill Allombert [2018-02-14 22:04]:
[...]
> primecert(N,1): return P-1 certificate (old isprime(N,1))

More precisely, old isprime(P,1) *without* allowing calls to APRCL,
which basically declared a "tough" integer to be prime without
providing a certificate. Now that we have ECPP and decent general purpose
primality certificates (which P-1 can't provide because it must
factor large integers), it no longer made sense.

As a result, both primecert(N,1) and new isprime(N,1) are likely to be
much slower than the old isprime(N,1) unless all primes p occurring in
the certificate are such that p-1 is easy to factor. On the other hand
it now always produces a full certificate (without declaring an integer
to be prime "because our APRCL implementation said so").

Cheers,

    K.B.

P.S. Of course, except for testing/pedagogical purposes, one should just
use the default primecert(N). Which is currently slow in the rare
cases where primecert(N,1) is fast because our ECPP doesn't support N-1
certificates yet, but this won't last.

--
Karim Belabas, IMB (UMR 5251)  Tel: (+33) (0)5 40 00 26 17
Universite de Bordeaux         Fax: (+33) (0)5 40 00 21 23
351, cours de la Liberation    http://www.math.u-bordeaux.fr/~kbelabas/
F-33405 Talence (France)       http://pari.math.u-bordeaux.fr/  [PARI/GP]
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