pari/NTL conversions

[videlec]

We implement C conversions between pari and NTL for

• integers
• finite fields
• univariate polynomials over the above

One of the goal is to make faster the coercion from the base ring with polynomials with coefficients in GF(p^e)

sage: p = random_prime(2**256)
sage: F.<i> = GF(p^2)
sage: R.<x> = PolynomialRing(F)
sage: a = F.random_element()
sage: %timeit R(a)
14.7 μs ± 727 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)

📝 Checklist

• I have linked a relevant issue or discussion.
• I have updated the documentation and checked the documentation preview.

[github-actions]

Documentation preview for this PR (built with commit 6c6f5ab; changes) is ready! 🎉
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[user202729]

You should run tools/update-meson.py. Running it results in the following patch:

diff --git a/src/sage/data_structures/meson.build b/src/sage/data_structures/meson.build
index 8c100328378..3cc243fe62a 100644
--- a/src/sage/data_structures/meson.build
+++ b/src/sage/data_structures/meson.build
@@ -42,9 +42,7 @@ foreach name, pyx : extension_data
   )
 endforeach
 
-extension_data_cpp = {
-  'pairing_heap' : files('pairing_heap.pyx'),
-}
+extension_data_cpp = {'pairing_heap' : files('pairing_heap.pyx')}
 
 foreach name, pyx : extension_data_cpp
   py.extension_module(
diff --git a/src/sage/libs/pari/meson.build b/src/sage/libs/pari/meson.build
index 5952060267c..a7bf079ffbe 100644
--- a/src/sage/libs/pari/meson.build
+++ b/src/sage/libs/pari/meson.build
@@ -3,6 +3,7 @@ py.install_sources(
   'all.py',
   'convert_flint.pxd',
   'convert_gmp.pxd',
+  'convert_ntl.pxd',
   'convert_sage.pxd',
   'convert_sage_complex_double.pxd',
   'convert_sage_real_double.pxd',
@@ -21,6 +22,7 @@ extension_data = {
   'convert_sage_real_double' : files('convert_sage_real_double.pyx'),
   'convert_sage_real_mpfr' : files('convert_sage_real_mpfr.pyx'),
   'misc' : files('misc.pyx'),
+  'convert_ntl' : files('convert_ntl.pyx'),
 }
 
 foreach name, pyx : extension_data

---

also,

• is this sufficiently faster than round-tripping to SageMath's ZZ (which it uses mpz under the hood anyway?)
• where is the sig_off()?

[videlec]

Thanks for your comments. I did update the meson configuration files.

Concerning conversion via ZZ the aim is precisely to avoid the creation of any Python objects. Note that the current branch is just experimental. One should not go via gmp at all when converting from pari to NTL.

Concerning sig_off it is in the new_gen function in cypari2 (stack.pyx)

cdef Gen new_gen(GEN x):
    """
    Create a new ``Gen`` from a ``GEN``. Except if `x` is ``gnil``, then
    return ``None`` instead.

    Also call ``sig_off``() and clear the PARI stack.
    """
    sig_off()
    if x is gnil:
        reset_avma()
        return None
    return new_gen_noclear(x)