use RingExtensionWithBasis for general p-adic extensions

src/sage/rings/padics/extension_element.py

@@ -1,18 +1,29 @@
+# -*- coding: utf-8 -*-
 """
 Elements of general extensions of p-adic rings and fields; the base ring may also be an extension.
 
 These are implemented as proxy elements, backed by an absolute extension.
 """
+#*****************************************************************************
+#       Copyright (C) 2019 David Roe <roed.math@gmail.com>
+#                          Julian Rüth <julian.rueth@fsfe.org>
+#
+#  Distributed under the terms of the GNU General Public License (GPL)
+#  as published by the Free Software Foundation; either version 2 of
+#  the License, or (at your option) any later version.
+#
+#                  http://www.gnu.org/licenses/
+#*****************************************************************************
 
 from copy import deepcopy
 from sage.rings.infinity import infinity
 from sage.rings.integer import Integer
 from sage.rings.rational import Rational
 from sage.rings.morphism import RingHomomorphism
-from sage.structure.element import AlgebraFMElement
+from sage.rings.ring_extension_element import RingExtensionElement
 from .padic_generic_element import pAdicGenericElement
 
-class pAdicGeneralExtensionElement(AlgebraFMElement, pAdicGenericElement):
+class pAdicGeneralExtensionElement(RingExtensionElement, pAdicGenericElement):
     # We start with the interesting functions; need to port these to two step extensions
     def polynomial(self, var='x'):
         raise NotImplementedError

src/sage/rings/padics/extension_parent.py

@@ -1,3 +1,4 @@
+# -*- coding: utf-8 -*-
 r"""
 General extensions of p-adic rings and fields; the base ring may also be an
 extension.
@@ -16,17 +17,18 @@
 #*****************************************************************************
 
 from sage.misc.cachefunc import cached_method
-from .extension_element import pAdicGenericExtensionElement
+from .extension_element import pAdicGeneralExtensionElement
 from .padic_extension_generic import pAdicExtensionGeneric
+from sage.rings.ring_extension import RingExtensionWithBasis
 
 # NotImplementedError: AlgebraFromMorphism shouldn't inherit from UniqueRepresentation
-class pAdicGeneralExtension(AlgebraFromMorphism, pAdicExtensionGeneric):
+class pAdicGeneralExtension(RingExtensionWithBasis, pAdicExtensionGeneric):
     def __init__(self, exact_modulus, poly, prec, print_mode, shift_seed, names, implementation='FLINT'):
         self._exact_modulus = exact_modulus
         self._shift_seed = shift_seed
         self._implementation = 'proxy'
         defining_morphism = None # NotImplementedError
-        AlgebraFromMorphism.__init__(self, defining_morphism, False)
+        RingExtensionWithBasis.__init__(self, defining_morphism, False)
         pAdicGeneric.__init__(self, poly, prec, print_mode, names, pAdicGenericExtensionElement)
         # Fix the following
         self._gen = None

src/sage/rings/padics/factory.py

@@ -1,3 +1,4 @@
+# -*- coding: utf-8 -*-
 r"""
 Factory
 
@@ -20,6 +21,7 @@
 #*****************************************************************************
 #       Copyright (C) 2007-2013 David Roe <roed.math@gmail.com>
 #                               William Stein <wstein@gmail.com>
+#                          2019 Julian Rüth <julian.rueth@fsfe.org>
 #
 #  Distributed under the terms of the GNU General Public License (GPL)
 #  as published by the Free Software Foundation; either version 2 of
@@ -57,6 +59,7 @@
 
 from .padic_extension_leaves import *
 from .relative_extension_leaves import *
+from .extension_parent import pAdicGeneralExtension
 from functools import reduce
 #This imports all of the classes used in the ext_table below.
 
@@ -67,10 +70,10 @@
 ext_table['e', pAdicRingFixedMod] = EisensteinExtensionRingFixedMod
 #ext_table['e', pAdicRingFloatingPoint] = EisensteinExtensionRingFloatingPoint
 #ext_table['e', pAdicFieldFloatingPoint] = EisensteinExtensionFieldFloatingPoint
-#ext_table['p', pAdicFieldCappedRelative] = pAdicGeneralExtensionFieldCappedRelative
-#ext_table['p', pAdicRingCappedAbsolute] = pAdicGeneralExtensionRingCappedAbsolute
-#ext_table['p', pAdicRingCappedRelative] = pAdicGeneralExtensionRingCappedRelative
-#ext_table['p', pAdicRingFixedMod] = pAdicGeneralExtensionRingFixedMod
+ext_table['p', pAdicFieldCappedRelative] = pAdicGeneralExtension
+ext_table['p', pAdicRingCappedAbsolute] = pAdicGeneralExtension
+ext_table['p', pAdicRingCappedRelative] = pAdicGeneralExtension
+ext_table['p', pAdicRingFixedMod] = pAdicGeneralExtension
 ext_table['u', pAdicFieldCappedRelative] = UnramifiedExtensionFieldCappedRelative
 ext_table['u', pAdicRingCappedAbsolute] = UnramifiedExtensionRingCappedAbsolute
 ext_table['u', pAdicRingCappedRelative] = UnramifiedExtensionRingCappedRelative