Working implementation of Ore polynomials

src/module_list.py

@@ -1525,6 +1525,9 @@ def uname_specific(name, value, alternative):
     Extension('sage.rings.polynomial.symmetric_reduction',
               sources = ['sage/rings/polynomial/symmetric_reduction.pyx']),
 
+    Extension('sage.rings.polynomial.ore_polynomial_element',
+              sources = ['sage/rings/polynomial/ore_polynomial_element.pyx']),
+
     Extension('sage.rings.polynomial.skew_polynomial_element',
               sources = ['sage/rings/polynomial/skew_polynomial_element.pyx']),
 

src/sage/categories/rings.py

@@ -1069,9 +1069,10 @@ def normalize_arg(arg):
 
             if isinstance(arg, tuple):
                 from sage.categories.morphism import Morphism
-                if len(arg) == 2 and isinstance(arg[1], Morphism):
-                   from sage.rings.polynomial.skew_polynomial_ring import SkewPolynomialRing
-                   return SkewPolynomialRing(self, arg[1], names=arg[0])
+                from sage.rings.derivation import RingDerivation
+                if len(arg) == 2 and isinstance(arg[1], (Morphism, RingDerivation)):
+                   from sage.rings.polynomial.ore_polynomial_ring import OrePolynomialRing
+                   return OrePolynomialRing(self, arg[1], names=arg[0])
 
             # 2. Otherwise, if all specified elements are algebraic, try to
             #    return an algebraic extension

src/sage/rings/derivation.py

@@ -203,7 +203,7 @@
 from sage.categories.lie_algebras import LieAlgebras
 
 from sage.categories.map import Map
-from sage.categories.all import Rings
+from sage.categories.rings import Rings
 
 
 class RingDerivationModule(Module, UniqueRepresentation):

src/sage/rings/polynomial/all.py

@@ -45,7 +45,8 @@
 # Infinite Polynomial Rings
 from sage.rings.polynomial.infinite_polynomial_ring import InfinitePolynomialRing
 
-# Skew Polynomial Rings
+# Ore Polynomial Rings
+from sage.rings.polynomial.ore_polynomial_ring import OrePolynomialRing
 from sage.rings.polynomial.skew_polynomial_ring import SkewPolynomialRing
 
 # Evaluation of cyclotomic polynomials

src/sage/rings/polynomial/ore_polynomial_element.pxd

@@ -0,0 +1,46 @@
+from sage.structure.element cimport AlgebraElement
+from sage.structure.parent cimport Parent
+from sage.rings.morphism cimport Morphism
+from sage.structure.element cimport RingElement
+from sage.rings.polynomial.polynomial_element cimport Polynomial_generic_dense
+
+cdef class OrePolynomial(AlgebraElement):
+    cdef _is_gen
+
+    cdef long _hash_c(self)
+    cdef OrePolynomial _new_c(self, list coeffs, Parent P, char check=*)
+    cpdef OrePolynomial _new_constant_poly(self, RingElement a, Parent P, char check=*)
+    cpdef _neg_(self)
+    cpdef _floordiv_(self, right)
+    cpdef _mod_(self, right)
+
+    cpdef bint is_zero(self)
+    cpdef bint is_one(self)
+
+    cdef _left_quo_rem(self, OrePolynomial other)
+    cdef _right_quo_rem(self, OrePolynomial other)
+    cdef OrePolynomial _left_lcm_cofactor(self, OrePolynomial other)
+    cdef OrePolynomial _right_lcm_cofactor(self, OrePolynomial other)
+
+    # Abstract methods
+    cpdef int degree(self)
+    cpdef list coefficients(self, sparse=*)
+
+
+cdef void lmul_gen(list A, Morphism m, d)
+
+cdef class OrePolynomial_generic_dense(OrePolynomial):
+    cdef list _coeffs
+
+    cdef void __normalize(self)
+    cpdef _add_(self, other)
+    cdef list _mul_list(self, list A)
+    cpdef _mul_(self, other)
+
+    cpdef dict dict(self)
+    cpdef list list(self, bint copy=*)
+
+
+cdef class OrePolynomialBaseringInjection(Morphism):
+    cdef RingElement _an_element
+    cdef object _new_constant_poly_