Use PARI implementation of Frobenius morphism

[remyoudompheng]

📚 Description

This pull request uses PARI fffrobenius and ffmap to implement the p-th power map for Finite fields using the PARI implementation (issue #4625).

It does not seem necessary to implement a similar thing for the Givaro implementation (where exponentiation is very fast) or the NTL implementation (only for characteristic 2).

📝 Checklist

• I have made sure that the title is self-explanatory and the description concisely explains the PR.
• I have linked an issue or discussion.
• I have created tests covering the changes.
• I have updated the documentation accordingly.

[remyoudompheng]

As opposed to suggestions in the linked issue, it does not use a matrix method, although this could be implemented concisely using this snippet:

# Cache these elements
ap = (K.gen().frobenius()).powers(degree)
# Compute
def frobenius(x): sum(z * a for z, a in zip(x.list(), ap))

The linear method needs to cache O(d) field elements, whereas PARI field morphism are defined by the image of the single generator, using less memory. For practical field sizes, the difference remains small and both methods are vastly more efficient than exponentiation, except for extremely small characteristics or very large extension degrees.

Performance numbers are as follows: for a 16-bit prime, the simple exponentiation is faster than PARI field morphisms only for degrees > 128.

p size = 128 bits, degree=2
old 625 loops, best of 3: 205 μs per loop
new 625 loops, best of 3: 3.69 μs per loop

p size = 128 bits, degree=64
old 25 loops, best of 3: 21.1 ms per loop
new 125 loops, best of 3: 2.44 ms per loop

p size = 1024 bits, degree=2
old  125 loops, best of 3: 4.07 ms per loop
new 625 loops, best of 3: 5.06 μs per loop

p size = 1024 bits, degree=128
old 5 loops, best of 3: 3.23 s per loop
new 5 loops, best of 3: 65.5 ms per loop

[remyoudompheng]

Updated with review comments and updated commit message (Brent-Kung complexity is sqrt(degree))

[github-actions]

Documentation preview for this PR is ready! 🎉
Built with commit: bd225fd

[tscrim]

Thank you. LGTM.