address Travis' comments

Author: xcaruso

src/sage/rings/polynomial/skew_polynomial_element.pxd

@@ -8,23 +8,27 @@ cdef class SkewPolynomial(AlgebraElement):
     cdef _is_gen
 
     cdef long _hash_c(self)
-    cdef SkewPolynomial _new_c(self,list coeffs,Parent P,char check=*)
-    cpdef SkewPolynomial _new_constant_poly(self,RingElement a,Parent P,char check=*)
+    cdef SkewPolynomial _new_c(self, list coeffs, Parent P, char check=*)
+    cpdef SkewPolynomial _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)
-
+ 
     cpdef operator_eval(self, eval_pt)
 
+    cdef SkewPolynomial _left_lcm_cofactor(self, SkewPolynomial other)
+    cdef SkewPolynomial _right_lcm_cofactor(self, SkewPolynomial other)
+
     # Abstract methods
     cdef void _inplace_rmul(self, SkewPolynomial_generic_dense right)
     cdef void _inplace_pow(self, Py_ssize_t n)
     cpdef int degree(self)
     cpdef list coefficients(self, sparse=*)
 
+
 cdef class SkewPolynomial_generic_dense(SkewPolynomial):
     cdef list _coeffs
 
@@ -38,7 +42,7 @@ cdef class SkewPolynomial_generic_dense(SkewPolynomial):
     cpdef right_power_mod(self, exp, modulus)
     cpdef left_power_mod(self, exp, modulus)
 
+
 cdef class SkewPolynomialBaseringInjection(Morphism):
     cdef RingElement _an_element
     cdef object _new_constant_poly_
-

src/sage/rings/polynomial/skew_polynomial_element.pyx

@@ -1381,7 +1381,7 @@ cdef class SkewPolynomial(AlgebraElement):
             A = A.left_monic()
         return A
 
-    def _left_lcm_cofactor(self, other):
+    cdef SkewPolynomial _left_lcm_cofactor(self, SkewPolynomial other):
         r"""
         Return a skew polynomial `U` such that `U P = c L`
         where `P` is this skew polynomial (``self``), `L`
@@ -1390,6 +1390,12 @@ cdef class SkewPolynomial(AlgebraElement):
 
         TESTS::
 
+            sage: cython('''
+            ....: from sage.rings.polynomial.skew_polynomial_element cimport SkewPolynomial
+            ....: def left_lcm_cofactor(SkewPolynomial P, SkewPolynomial Q):
+            ....:     return P._left_lcm_cofactor(Q)
+            ....: ''')
+
             sage: k.<a> = GF(7^5)
             sage: Frob = k.frobenius_endomorphism(3)
             sage: S.<x> = k['x', Frob]
@@ -1398,23 +1404,21 @@ cdef class SkewPolynomial(AlgebraElement):
             sage: P = S.random_element() * D
             sage: Q = S.random_element() * D
             sage: L = P.left_lcm(Q)
-            sage: U = P._left_lcm_cofactor(Q)
+            sage: U = left_lcm_cofactor(P, Q)
             sage: (U*P).right_monic() == L
             True
         """
-        R = self._parent
-        U = R.one()
-        G = self
-        V1 = R.zero()
-        V3 = other
-        while not V3.is_zero():
-            Q, R = G.right_quo_rem(V3)
-            T = U - Q*V1
-            U = V1
-            G = V3
-            V1 = T
-            V3 = R
-        return V1
+        cdef SkewPolynomial Q, R, T
+        cdef SkewPolynomial U = <SkewPolynomial>self._parent.one()
+        cdef SkewPolynomial V = <SkewPolynomial>self._parent.zero()
+        while other:
+            Q, R = self.right_quo_rem(other)
+            T = U - Q*V
+            U = V
+            V = T
+            self = other
+            other = R
+        return V
 
     @coerce_binop
     def left_xlcm(self, other, monic=True):
@@ -1454,14 +1458,20 @@ cdef class SkewPolynomial(AlgebraElement):
             V1 = s * V1
         return L, V1, L // other
 
-    def _right_lcm_cofactor(self, other):
+    cdef SkewPolynomial _right_lcm_cofactor(self, SkewPolynomial other):
         r"""
         Return a skew polynomial `U` such that `P U = L c`
         where `P` is this skew polynomial (``self``), `L`
         is the right lcm of `P` and ``other`` and `c` is a
         constant
 
-        EXAMPLES::
+        TESTS::
+
+            sage: cython('''
+            ....: from sage.rings.polynomial.skew_polynomial_element cimport SkewPolynomial
+            ....: def right_lcm_cofactor(SkewPolynomial P, SkewPolynomial Q):
+            ....:     return P._right_lcm_cofactor(Q)
+            ....: ''')
 
             sage: k.<a> = GF(7^5)
             sage: Frob = k.frobenius_endomorphism(3)
@@ -1471,23 +1481,21 @@ cdef class SkewPolynomial(AlgebraElement):
             sage: P = D * S.random_element()
             sage: Q = D * S.random_element()
             sage: L = P.right_lcm(Q)
-            sage: U = P._right_lcm_cofactor(Q)
+            sage: U = right_lcm_cofactor(P, Q)
             sage: (P*U).left_monic() == L
             True
         """
-        R = self._parent
-        U = R.one()
-        G = self
-        V1 = R.zero()
-        V3 = other
-        while not V3.is_zero():
-            Q, R = G.left_quo_rem(V3)
-            T = U - V1*Q
-            U = V1
-            G = V3
-            V1 = T
-            V3 = R
-        return V1
+        cdef SkewPolynomial Q, R, T
+        cdef SkewPolynomial U = <SkewPolynomial>self._parent.one()
+        cdef SkewPolynomial V = <SkewPolynomial>self._parent.zero()
+        while other:
+            Q, R = self.left_quo_rem(other)
+            T = U - V*Q
+            U = V
+            V = T
+            self = other
+            other = R
+        return V
 
     @coerce_binop
     def right_xlcm(self, other, monic=True):

src/sage/rings/polynomial/skew_polynomial_finite_field.pxd

@@ -1,12 +1,12 @@
 from sage.rings.polynomial.skew_polynomial_finite_order cimport SkewPolynomial_finite_order_dense
-from sage.matrix.matrix_dense cimport Matrix_dense
 
 cdef class SkewPolynomial_finite_field_dense (SkewPolynomial_finite_order_dense):
     cdef _norm_factor
-    cdef dict _rdivisors
     cdef dict _types
     cdef _factorization
 
+    cdef inline _reduced_norm_factored(self)
+
     # Finding divisors
     cdef SkewPolynomial_finite_field_dense _rdivisor_c(P, N)