Normalize interface for finite field construction

This will likely break callers in other places. However, this is not a public
interface so it should be fine to just fix those.

src/sage/rings/finite_rings/finite_field_ntl_gf2e.py

@@ -69,7 +69,7 @@ class FiniteField_ntl_gf2e(FiniteField):
 
     - ``q`` -- `2^n` (must be 2 power)
 
-    - ``names`` -- variable used for poly_repr (default: ``'a'``)
+    - ``name`` -- variable used for poly_repr (default: ``'a'``)
 
     - ``modulus`` -- A minimal polynomial to use for reduction.
 
@@ -107,7 +107,7 @@ class FiniteField_ntl_gf2e(FiniteField):
         True
     """
 
-    def __init__(self, q, names="a", modulus=None, repr="poly"):
+    def __init__(self, q, name="a", modulus=None, repr="poly"):
         """
         Initialize ``self``.
 
@@ -145,7 +145,7 @@ def __init__(self, q, names="a", modulus=None, repr="poly"):
         k = q.exact_log(2)
         if q != 1 << k:
             raise ValueError("q must be a 2-power")
-        FiniteField.__init__(self, GF2, names, normalize=True)
+        FiniteField.__init__(self, GF2, name, normalize=True)
 
         self._kwargs = {'repr':repr}
 

src/sage/rings/finite_rings/finite_field_pari_ffelt.py

@@ -98,11 +98,10 @@ class FiniteField_pari_ffelt(FiniteField):
         sage: loads(K.dumps()) == K
         True
     """
-    def __init__(self, p, modulus, name=None):
+    def __init__(self, q, modulus, name=None):
         """
-        Create a finite field of characteristic `p` defined by the
-        polynomial ``modulus``, with distinguished generator called
-        ``name``.
+        Create a finite field of ``q`` elements defined by the polynomial
+        ``modulus``, with distinguished generator called ``name``.
 
         EXAMPLE::
 
@@ -115,6 +114,7 @@ def __init__(self, p, modulus, name=None):
         if n < 2:
             raise ValueError("the degree must be at least 2")
 
+        p, n = q.is_prime_power(get_data=True)
         FiniteField.__init__(self, base=GF(p), names=name, normalize=True)
 
         self._modulus = modulus

src/sage/rings/finite_rings/residue_field.pyx

@@ -486,11 +486,11 @@ class ResidueField_generic(Field):
         """
         self.p = ideal
         FFclass = self._finite_field_class()
-        if modulus is None:
+        if k == 1:
             # prime field
-            FFclass.__init__(self, p, name)
+            FFclass.__init__(self, p=p, modulus=modulus)
         else:
-            FFclass.__init__(self, p**k, name, modulus)
+            FFclass.__init__(self, q=p**k, name=name, modulus=modulus)
 
     def _repr_(self):
         """