Trac 16855: make finite fields satisfy comparison by identity
Trac 16855: correct option implemention -> impl
Refactor some methods for finite fields elements.
Cleanup unused code and move doctests for finite field elements.
Typo in moved doctest.
Merge back changes from ticket 16930.
New code produce different square root choices for FF elements.
Use new style Python error formatting.
Typo in error text... and update three other errors syntax.
Merge branch 'develop' into ticket/16855-FiniteField_comparison

Conflicts:
	src/sage/rings/finite_rings/finite_field_base.pyx
	src/sage/rings/finite_rings/finite_field_ext_pari.py
	src/sage/rings/finite_rings/finite_field_givaro.py
	src/sage/rings/finite_rings/finite_field_prime_modn.py
Merge commit 'dad808d6234b0b4152c17a793af41e294652883b'; commit '8d9f33c40df9d5b7bd89833a3b761c80553e152d' into ticket/17297
Deprecate FiniteField_ext_pari
Change module title
Trac #16855: Make finite fields satisfy comparison by identity

For efficiency and simplicity, finite fields should compare equal if and
only if they are identical.  Ideally this would be accomplished by
inheriting from `WithEqualityById`.  Since `FiniteField` is a Cython
class and Cython does not support multiple inheritance, we implement
this by copying the `__hash__()` and `__richcmp__()` methods from
`WithEqualityById`.

URL: http://trac.sagemath.org/16855
Reported by: pbruin
Ticket author(s): Peter Bruin
Reviewer(s): Jean-Pierre Flori
Trac #17165: Refactor some generic finite field code

There are some generic methods defined in `element_ext_pari` files.
There is no reason why they shouldn't be in `element_base` files.

URL: http://trac.sagemath.org/17165
Reported by: jpflori
Ticket author(s): Jean-Pierre Flori
Reviewer(s): Jeroen Demeyer
Trac #17297: Deprecate FiniteField_ext_pari

Many newer PARI functions are not supported for this old PARI finite
field implementation and it's slower.

Removing this will be harder since we need to find a solution for older
pickles.

URL: http://trac.sagemath.org/17297
Reported by: jdemeyer
Ticket author(s): Jeroen Demeyer
Reviewer(s): Peter Bruin