pari(n).isprime(1) does not give the primality certificate to the user

[zimmerma]

The Pari isprime function is able to return a primality certificate:

gp: isprime(2^31-1,1)

[2 3 1]

[3 5 1]

[7 3 1]

[11 3 1]

[31 2 1]

[151 3 1]

[331 3 1]

However when calling this function from Sage, the certificate is lost:

sage: pari(2^31-1).isprime(1)
True

[mjo]

sage: pari(3).isprime()
True
sage: pari(3).isprime(1)
False
sage: pari(3).isprime(2)
True

...what?

[zimmerma]

apparently something changed (in worse) since I reported this, since indeed we now get:

sage: pari(2^31-1).isprime(1)
False

I change the priority to "major".

Paul

[zimmerma]

by the way I notice there is no indication on how to access or change the "arithmetic proof flag" mentioned in the documentation of n.is_prime.

And the documentation of get_flag is ill-formed in the terminal version.

Paul

[zimmerma]

for the ill-formed documentation of get_flag, see #15096.

[zimmerma]

the attached patch does several things:

1) it fixes two typos in gen.pyx

2) it corrects the behaviour of pari(n).isprime(1) which incorrectly was returning False for prime n

3) for prime n, now pari(n).isprime(1) returns a tuple (True, cert) where cert is the primality certificate (currently as Pari object, I didn't figure out how to convert it to a Python object)

Comments are welcome.

Paul

[pbruin]

In principle OK, but needs to be rebased on #15124.

Also, it would be much cleaner to call new_gen() instead of initialising the gen and resetting the stack by hand:

cdef GEN x
pari_catch_sig_on()
x = gisprime(self.g, flag)
if typ(x) != t_INT:
    # case flag=1 with prime input: x is the certificate
    return True, P.new_gen(x)
else:
    pari_catch_sig_off()
    return bool(signe(x))

[rws]

Rebased on 6.2.base2, applied comment:7 by pbruin

---

New commits:

​9d8a0eb	skeleton interface
​70a29e1	core functionality
​6df1fc6	guess(), random_element(), some refactoring
​9095be0	ref doc completed; coefficients(), slicing added
​f73e11e	handle ogf > 1
​e7958b0	Merge branch 'ticket/15714' into develop
​597b22e	Trac #9401: pari(n).isprime(1) does not give the primality certificate to the user
​0974f9d	Trac #9401: use pari_catch_sig* and new_gen (pbruin's code in comment:7)

[rws]

Only the last two commits apply. If I create a new branch without the first stray commits, will trac handle this?

[pbruin]

Yes, this is no problem. I did this (using git rebase -i) in the branch I just pushed, and made one trivial additional change (in Cython, s != 0 turns out to be faster than bool(s)). You can set this to positive_review if you are happy with this branch.