gh-41062: remove deprecations in finite_rings
    
after

File: src/sage/rings/finite_rings/element_base.pyx ; PR: #32664 ; Closed
Date: 2023-03-19
File: src/sage/rings/finite_rings/finite_field_constructor.py ; PR:
#32664 ; Closed Date: 2023-03-19
File: src/sage/rings/finite_rings/finite_field_base.pyx ; PR: #32664 ;
Closed Date: 2023-03-19

### 📝 Checklist

- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
- [x] I have linked a relevant issue or discussion.
    
URL: #41062
Reported by: Frédéric Chapoton
Reviewer(s):

Author: Release Manager

src/sage/rings/finite_rings/element_base.pyx

@@ -24,30 +24,6 @@ from sage.rings.integer_ring import ZZ
 from sage.rings.integer import Integer
 
 
-def is_FiniteFieldElement(x):
-    """
-    Return ``True`` if ``x`` is a finite field element.
-
-    This function is deprecated.
-
-    EXAMPLES::
-
-        sage: from sage.rings.finite_rings.element_base import is_FiniteFieldElement
-        sage: is_FiniteFieldElement(1)
-        doctest:...: DeprecationWarning: the function is_FiniteFieldElement is deprecated; use isinstance(x, sage.structure.element.FieldElement) and x.parent().is_finite() instead
-        See https://github.com/sagemath/sage/issues/32664 for details.
-        False
-        sage: is_FiniteFieldElement(IntegerRing())
-        False
-        sage: is_FiniteFieldElement(GF(5)(2))
-        True
-    """
-    from sage.misc.superseded import deprecation
-    deprecation(32664, "the function is_FiniteFieldElement is deprecated; use isinstance(x, sage.structure.element.FieldElement) and x.parent().is_finite() instead")
-
-    from sage.rings.finite_rings.finite_field_base import FiniteField
-    return isinstance(x, Element) and isinstance(x.parent(), FiniteField)
-
 
 cdef class FiniteRingElement(CommutativeRingElement):
     def _nth_root_common(self, n, all, algorithm, cunningham):

src/sage/rings/finite_rings/finite_field_base.pyx

@@ -2239,30 +2239,3 @@ def unpickle_FiniteField_prm(_type, order, variable_name, kwargs):
 
 register_unpickle_override(
     'sage.rings.ring', 'unpickle_FiniteField_prm', unpickle_FiniteField_prm)
-
-
-def is_FiniteField(R):
-    r"""
-    Return whether the implementation of ``R`` has the interface provided by
-    the standard finite field implementation.
-
-    This function is deprecated.
-
-    EXAMPLES::
-
-        sage: from sage.rings.finite_rings.finite_field_base import is_FiniteField
-        sage: is_FiniteField(GF(9,'a'))
-        doctest:...: DeprecationWarning: the function is_FiniteField is deprecated; use isinstance(x, sage.rings.finite_rings.finite_field_base.FiniteField) instead
-        See https://github.com/sagemath/sage/issues/32664 for details.
-        True
-        sage: is_FiniteField(GF(next_prime(10^10)))
-        True
-
-    Note that the integers modulo n are not backed by the finite field type::
-
-        sage: is_FiniteField(Integers(7))
-        False
-    """
-    from sage.misc.superseded import deprecation
-    deprecation(32664, "the function is_FiniteField is deprecated; use isinstance(x, sage.rings.finite_rings.finite_field_base.FiniteField) instead")
-    return isinstance(R, FiniteField)

src/sage/rings/finite_rings/finite_field_constructor.py

@@ -178,10 +178,6 @@
 from sage.rings.polynomial.polynomial_element import Polynomial
 from sage.rings.integer import Integer
 
-# the import below is just a redirection
-from sage.rings.finite_rings.finite_field_base import is_FiniteField
-assert is_FiniteField  # just to silent pyflakes
-
 try:
     # We don't late import this because this means trouble with the Givaro library
     # On a Macbook Pro OSX 10.5.8, this manifests as a Bus Error on exiting Sage.
@@ -868,34 +864,4 @@ def create_object(self, version, key, **kwds):
 GF = FiniteField = FiniteFieldFactory("FiniteField")
 
 
-def is_PrimeFiniteField(x):
-    """
-    Return ``True`` if ``x`` is a prime finite field.
-
-    This function is deprecated.
-
-    EXAMPLES::
-
-        sage: from sage.rings.finite_rings.finite_field_constructor import is_PrimeFiniteField
-        sage: is_PrimeFiniteField(QQ)
-        doctest:...: DeprecationWarning: the function is_PrimeFiniteField is deprecated; use isinstance(x, sage.rings.finite_rings.finite_field_base.FiniteField) and x.is_prime_field() instead
-        See https://github.com/sagemath/sage/issues/32664 for details.
-        False
-        sage: is_PrimeFiniteField(GF(7))
-        True
-        sage: is_PrimeFiniteField(GF(7^2, 'a'))
-        False
-        sage: is_PrimeFiniteField(GF(next_prime(10^90, proof=False)))
-        True
-    """
-    from sage.misc.superseded import deprecation
-    deprecation(32664, "the function is_PrimeFiniteField is deprecated; use isinstance(x, sage.rings.finite_rings.finite_field_base.FiniteField) and x.is_prime_field() instead")
-
-    from .finite_field_prime_modn import FiniteField_prime_modn
-    from sage.rings.finite_rings.finite_field_base import FiniteField as FiniteField_generic
-
-    return isinstance(x, FiniteField_prime_modn) or \
-           (isinstance(x, FiniteField_generic) and x.degree() == 1)
-
-
 zech_log_bound = 2**16