Ticket #14832: trac_14832-PolynomialRing_dense_finite_field.patch

sage/rings/polynomial/polynomial_ring.py

@@ -1404 +1404 @@
                            PolynomialRing_singular_repr,
                            principal_ideal_domain.PrincipalIdealDomain,
                            ):
-    def __init__(self, base_ring, name="x", sparse=False, element_class=None, implementation=None):
+    def __init__(self, base_ring, name="x", sparse=False, element_class=None):
         """
         TESTS:
             sage: from sage.rings.polynomial.polynomial_ring import PolynomialRing_field as PRing
@@ -1426 +1426 @@
             sage: x^(10^20) # this should be fast
             x^100000000000000000000
         """
-        from sage.rings.finite_rings.finite_field_base import is_FiniteField
-        from sage.rings.rational_field import QQ
         from sage.rings.polynomial.polynomial_singular_interface import can_convert_to_singular
-        if implementation is None:
-            implementation = "NTL"
-
-        if implementation == "NTL" and is_FiniteField(base_ring) and not(sparse):
-            from sage.libs.ntl.ntl_ZZ_pEContext import ntl_ZZ_pEContext
-            from sage.libs.ntl.ntl_ZZ_pX import ntl_ZZ_pX
-            from sage.rings.polynomial.polynomial_zz_pex import Polynomial_ZZ_pEX
-
-            p=base_ring.characteristic()
-            self._modulus = ntl_ZZ_pEContext(ntl_ZZ_pX(list(base_ring.polynomial()), p))
-            element_class = Polynomial_ZZ_pEX
 
         if not element_class:
             if sparse:
@@ -1798 +1785 @@
                 self._fraction_field = FractionField_1poly_field(self)
             return self._fraction_field
 
+class PolynomialRing_dense_finite_field(PolynomialRing_field):
+    """
+    Univariate polynomial ring over a finite field.
+
+    EXAMPLE::
+
+        sage: R = PolynomialRing(GF(27, 'a'), 'x')
+        sage: type(R)
+        <class 'sage.rings.polynomial.polynomial_ring.PolynomialRing_dense_finite_field_with_category'>
+    """
+    def __init__(self, base_ring, name="x", element_class=None, implementation=None):
+        if implementation is None:
+            implementation = "NTL"
+
+        if implementation == "NTL":
+            from sage.libs.ntl.ntl_ZZ_pEContext import ntl_ZZ_pEContext
+            from sage.libs.ntl.ntl_ZZ_pX import ntl_ZZ_pX
+            from sage.rings.polynomial.polynomial_zz_pex import Polynomial_ZZ_pEX
+
+            p=base_ring.characteristic()
+            self._modulus = ntl_ZZ_pEContext(ntl_ZZ_pX(list(base_ring.polynomial()), p))
+            element_class = Polynomial_ZZ_pEX
+
+        PolynomialRing_field.__init__(self, base_ring, sparse=False, name=name,
+                                      element_class=element_class)
+
 class PolynomialRing_dense_padic_ring_generic(PolynomialRing_integral_domain):
     pass
 
@@ -1995 +2008 @@
         return s + self._implementation_repr
 
 
-class PolynomialRing_dense_mod_p(PolynomialRing_field,
+class PolynomialRing_dense_mod_p(PolynomialRing_dense_finite_field,
                                  PolynomialRing_dense_mod_n,
                                  PolynomialRing_singular_repr):
     def __init__(self, base_ring, name="x", implementation=None):

sage/rings/polynomial/polynomial_ring_constructor.py

@@ -40 +40 @@
 import sage.rings.padics.padic_base_leaves as padic_base_leaves
 
 from sage.rings.integer import Integer
+from sage.rings.finite_rings.constructor import is_FiniteField
 from sage.rings.finite_rings.integer_mod_ring import is_IntegerModRing
 
 from sage.misc.cachefunc import weak_cached_function
@@ -533 +534 @@
             else:  # n == 1!
                 R = m.PolynomialRing_integral_domain(base_ring, name)   # specialized code breaks in this case.
 
+        elif is_FiniteField(base_ring) and not sparse:
+            R = m.PolynomialRing_dense_finite_field(base_ring, name, implementation=implementation)
+
         elif isinstance(base_ring, padic_base_leaves.pAdicFieldCappedRelative):
             R = m.PolynomialRing_dense_padic_field_capped_relative(base_ring, name)
 
@@ -546 +550 @@
             R = m.PolynomialRing_dense_padic_ring_fixed_mod(base_ring, name)
 
         elif base_ring.is_field(proof = False):
-            R = m.PolynomialRing_field(base_ring, name, sparse, implementation=implementation)
+            R = m.PolynomialRing_field(base_ring, name, sparse)
 
         elif base_ring.is_integral_domain(proof = False):
             R = m.PolynomialRing_integral_domain(base_ring, name, sparse, implementation)