Fixups

src/sage/modules/free_module.py

@@ -183,7 +183,6 @@
 import sage.misc.latex as latex
 
 from sage.modules.module import Module
-import sage.rings.finite_rings.finite_field_constructor as finite_field
 import sage.rings.ring as ring
 import sage.rings.abc
 import sage.rings.integer_ring
@@ -195,6 +194,7 @@
 from sage.categories.infinite_enumerated_sets import InfiniteEnumeratedSets
 from sage.misc.lazy_attribute import lazy_attribute
 from sage.misc.randstate import current_randstate
+from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.structure.factory import UniqueFactory
 from sage.structure.sequence import Sequence
 from sage.structure.richcmp import (richcmp_method, rich_to_bool, richcmp,
@@ -6348,7 +6348,7 @@ def _element_constructor_(self, e, *args, **kwds):
         """
         try:
             k = e.parent()
-            if finite_field.isinstance(k, FiniteField) and k.base_ring() == self.base_ring() and k.degree() == self.degree():
+            if isinstance(k, FiniteField) and k.base_ring() == self.base_ring() and k.degree() == self.degree():
                 return self(e._vector_())
         except AttributeError:
             pass

src/sage/rings/finite_rings/element_base.pyx

@@ -34,6 +34,7 @@ def is_FiniteFieldElement(x):
         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://trac.sagemath.org/32664 for details.
         False
         sage: is_FiniteFieldElement(IntegerRing())
         False

src/sage/rings/finite_rings/finite_field_base.pyx

@@ -2122,6 +2122,7 @@ def is_FiniteField(R):
         sage: from sage.rings.finite_rings.finite_field_base import 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://trac.sagemath.org/32664 for details.
         True
         sage: is_FiniteField(GF(next_prime(10^10)))
         True

src/sage/rings/finite_rings/finite_field_constructor.py

@@ -797,8 +797,10 @@ def is_PrimeFiniteField(x):
 
     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://trac.sagemath.org/32664 for details.
         False
         sage: is_PrimeFiniteField(GF(7))
         True

src/sage/schemes/hyperelliptic_curves/constructor.py

@@ -249,7 +249,11 @@ def HyperellipticCurve(f, h=0, names=None, PP=None, check_squarefree=True):
 
     genus_classes = {2: HyperellipticCurve_g2}
 
-    is_pAdicField = lambda x: isinstance(x, sage.rings.abc.pAdicField)
+    def is_FiniteField(x):
+        return isinstance(x, FiniteField)
+
+    def is_pAdicField(x):
+        return isinstance(x, sage.rings.abc.pAdicField)
 
     fields = [
         ("FiniteField", is_FiniteField, HyperellipticCurve_finite_field),