Fix build and tests with pari 2.17

[antonio-rojas]

NEXT_PRIME_VIADIFF is removed in 2.17, port pari_prime_range to pari_PRIMES instead

Needs sagemath/cypari2#165 applied to cypari

[antonio-rojas]

Needs work because this is not compatible with 2.15. So either it needs to be merged with the pari upgrade or be made to work with older pari too (no idea how).

Running tests now.

[antonio-rojas]

Many test failures.

[jhpalmieri]

If the changes here eventually allow us to use a system Pari 2.17, then we should undo the change in #38772.

[antonio-rojas]

With this MR and the cypari fixes sagemath/cypari2#165 and sagemath/cypari2#166 all tests are passing with pari 2.17.

The changes are not compatible with 2.15 though, making them compatible requires more work. Also, some pari opeations (such as the number field prime ideals above a given prime) give random output with 2.17, which makes it harder to test. To solve both issues (and make tests more future proof), we should gradually move away from testing the exact output to just testing that the output is correct.

[tornaria]

There seems to be a major issue with pari 2.17: the computation of the units of a bnf is not deterministic:

? setrand(1) ; bnfinit(x^2-65).fu
%1 = [Mod(x - 8, x^2 - 65)]
? setrand(3) ; bnfinit(x^2-65).fu
%2 = [Mod(-x + 8, x^2 - 65)]

And also (related?) generators of ideals:

$ sage -c 'pari.setrand(1) ; K.<a> = QuadraticField(-6) ; L.<b> = K.extension(polygen(K)^4 + a) ; print(L.ideal(b).relative_norm())'
Fractional ideal (-a)
$ sage -c 'pari.setrand(3) ; K.<a> = QuadraticField(-6) ; L.<b> = K.extension(polygen(K)^4 + a) ; print(L.ideal(b).relative_norm())'
Fractional ideal (a)

and factorization are non-deterministic as well:

$ sage -c 'pari.setrand(1) ; R.<omega> = EisensteinIntegers() ; print(factor(3+omega))'
(omega) * (-3*omega - 2)
$ sage -c 'pari.setrand(2) ; R.<omega> = EisensteinIntegers() ; print(factor(3+omega))'
(omega + 1) * (-2*omega + 1)
$ sage -c 'pari.setrand(4) ; R.<omega> = EisensteinIntegers() ; print(factor(3+omega))'
omega + 3
$ sage -c 'pari.setrand(7) ; R.<omega> = EisensteinIntegers() ; print(factor(3+omega))'
(-omega) * (3*omega + 2)
$ sage -c 'pari.setrand(24) ; R.<omega> = EisensteinIntegers() ; print(factor(3+omega))'
(-1) * (-omega - 3)
$ sage -c 'pari.setrand(44) ; R.<omega> = EisensteinIntegers() ; print(factor(3+omega))'
(-omega - 1) * (2*omega - 1)

This is making tests a bit unstable, because running in --long or not reaches the examples with different pari random state...

[antonio-rojas]

There seems to be a major issue with pari 2.17: the computation of the units of a bnf is not deterministic:

Yes, see #38749 (comment). I have only tested with --long and still find failing tests from time to time due to this. The reasonable solution is to make all tests independent of the exact output, but that is a lot of work.

[antonio-rojas]

I am also seeing one test failure with a specific random seed:

sage -t --long --warn-long 30.0 --random-seed=164564093241797715927265696104150551458 /usr/lib/python3.12/site-packages/sage/rings/integer.pyx
**********************************************************************
File "/usr/lib/python3.12/site-packages/sage/rings/integer.pyx", line 3074, in sage.rings.integer.Integer.divisors
Failed example:
    for i in range(20):           # long time                             # needs sage.libs.pari
        try:
            alarm(RDF.random_element(1e-3, 0.5))
            _ = n.divisors()
            cancel_alarm()  # we never get here
        except AlarmInterrupt:
            pass
Exception raised:
    Traceback (most recent call last):
      File "<doctest sage.rings.integer.Integer.divisors[20]>", line 4, in <module>
        _ = n.divisors()
            ^^^^^^^^^^^^
      File "sage/rings/integer.pyx", line 3160, in sage.rings.integer.Integer.divisors (build/cythonized/sage/rings/integer.c:31916)
        for p, e in f:
      File "/usr/lib/python3.12/site-packages/sage/structure/factorization.py", line 327, in __getitem__
        def __getitem__(self, i):
        
      File "src/cysignals/signals.pyx", line 341, in cysignals.signals.python_check_interrupt
    cysignals.signals.AlarmInterrupt

    During handling of the above exception, another exception occurred:

    Traceback (most recent call last):
      File "/usr/lib/python3.12/site-packages/sage/doctest/forker.py", line 715, in _run
        self.compile_and_execute(example, compiler, test.globs)
      File "/usr/lib/python3.12/site-packages/sage/doctest/forker.py", line 1136, in compile_and_execute
        exec(compiled, globs)
      File "<doctest sage.rings.integer.Integer.divisors[20]>", line 6, in <module>
        except AlarmInterrupt:
               ^^^^^^^^^^^^^^
      File "/usr/lib/python3.12/site-packages/sage/doctest/util.py", line 497, in __getitem__
        def __getitem__(self, name):
        
      File "src/cysignals/signals.pyx", line 341, in cysignals.signals.python_check_interrupt
    cysignals.signals.AlarmInterrupt
**********************************************************************

This is not reproducible with pari 2.15, but I don't know if it's because of some pari change or because the pari upgrade influences the choice of random timeouts. The obvious fix (adding from cysignals import AlarmInterrupt as in line 7119) doesn't help.

[tornaria]

@antonio-rojas I can reproduce it deterministically with pari 2.15 and 2.17 with this change:

--- a/src/sage/rings/integer.pyx	2024-08-23 10:46:19.000000000 -0300
+++ b/src/sage/rings/integer.pyx	2024-11-06 11:23:36.666702122 -0300
@@ -3075,9 +3075,9 @@
         so a memory leak will not go unnoticed)::
 
             sage: n = prod(primes_first_n(25))                                          # needs sage.libs.pari
-            sage: for i in range(20):           # long time                             # needs sage.libs.pari
+            sage: for t in [0.5, 0.003]:
             ....:     try:
-            ....:         alarm(RDF.random_element(1e-3, 0.5))
+            ....:         alarm(t)
             ....:         _ = n.divisors()
             ....:         cancel_alarm()  # we never get here
             ....:     except AlarmInterrupt:

I couldn't reproduce this outside doctesting this file.

EDIT: the point is that with this change, the failure happens every time, regardless of seed, and regardless of --long. The randomness is just hitting a sequence of timeouts where this triggers (i.e. a very small timeout after a largish timeout as I did up there).

[tornaria]

There seems to be a major issue with pari 2.17: the computation of the units of a bnf is not deterministic:

Yes, see #38749 (comment). I have only tested with --long and still find failing tests from time to time due to this. The reasonable solution is to make all tests independent of the exact output, but that is a lot of work.

Sure, but there is still something weird with this. Some of the E.isogeny_class() computations take a very long time (randomly) and I'm wondering if this is the cause.

I found other issues with reduced_basis() which I tracked back to the new LLL being quite unstable (numerically) and in that case I solved by reverting to the old LLL. Now I am wondering if all this unstability in units, factoring, generators, may be due to the same LLL unstability.

In principle, this new FLATTER version of LLL is better (faster) but...

[tornaria]

BTW: I'm preparing a patch for 32-bit. Besides all the unstability, pari 2.17 changed the default real precision to be 128 bits for both 64-bit and 32-bit arches (previously it was 128 bits = 38 digits for 64-bit arch and 96 bit = 28 digits for 32-bit arch).

[tornaria]

More updates in antonio-rojas#4

[tornaria]

See: sagemath/cypari2#165 (comment)