Hello,

My GSoC project is to implement Gabidulin codes which require the Skew 
Polynomial ticket #13215. While, a lot of the errors have been eliminated, 
we are stuck with a couple of nasty ones that are hampering the progress on 
the project. I'm attaching a file that has the tracebacks for them. Can 
someone please explain what is going wrong and help arrive at a way to 
resolve these?

Thanks in advance.

Sincerely,
Arpit.

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too few successful tests, not using stored timings
Running doctests with ID 2016-06-20-00-59-25-8e75afbe.
Git branch: apply_skew_polynomials_patch
Using --optional=mpir,python2,sage
Doctesting 1 file.
sage -t src/sage/rings/polynomial/skew_polynomial_ring.py
**********************************************************************
File "src/sage/rings/polynomial/skew_polynomial_ring.py", line 589, in 
sage.rings.polynomial.skew_polynomial_ring.SkewPolynomialRing_general.twist_map
Failed example:
    S.twist_map(-1)
Expected:
    Traceback (most recent call last):
    ...
    NotImplementedError
Got:
    <BLANKLINE>
    Traceback (most recent call last):
      File 
"/home/arpit/Documents/GSOC_16/sage-7.2/local/lib/python2.7/site-packages/sage/doctest/forker.py",
 line 496, in _run
        self.compile_and_execute(example, compiler, test.globs)
      File 
"/home/arpit/Documents/GSOC_16/sage-7.2/local/lib/python2.7/site-packages/sage/doctest/forker.py",
 line 858, in compile_and_execute
        exec(compiled, globs)
      File "<doctest 
sage.rings.polynomial.skew_polynomial_ring.SkewPolynomialRing_general.twist_map[6]>",
 line 1, in <module>
        S.twist_map(-Integer(1))
      File 
"/home/arpit/Documents/GSOC_16/sage-7.2/local/lib/python2.7/site-packages/sage/rings/polynomial/skew_polynomial_ring.py",
 line 605, in twist_map
        map = self._map**n
      File "sage/categories/map.pyx", line 1264, in 
sage.categories.map.Map.__pow__ 
(/home/arpit/Documents/GSOC_16/sage-7.2/src/build/cythonized/sage/categories/map.c:8985)
        return generic_power(self, n)
      File "sage/structure/element.pyx", line 3671, in 
sage.structure.element.generic_power 
(/home/arpit/Documents/GSOC_16/sage-7.2/src/build/cythonized/sage/structure/element.c:28593)
        return generic_power_c(a,n,one)
      File "sage/structure/element.pyx", line 3704, in 
sage.structure.element.generic_power_c 
(/home/arpit/Documents/GSOC_16/sage-7.2/src/build/cythonized/sage/structure/element.c:29266)
        a = ~a
    TypeError: bad operand type for unary ~: 
'sage.rings.morphism.RingHomomorphism_im_gens'
**********************************************************************
**********************************************************************
File "src/sage/rings/polynomial/skew_polynomial_finite_field.pyx", line 2419, 
in sage.rings.polynomial.skew_polynomial_finite_field.factorizations
Failed example:
    a = x^3 + (t^2 + 1)*x^2 + (2*t + 3)*x + t^2 + t + 2
Exception raised:
    Traceback (most recent call last):
      File 
"/home/arpit/Documents/GSOC_16/sage-7.2/local/lib/python2.7/site-packages/sage/doctest/forker.py",
 line 496, in _run
        self.compile_and_execute(example, compiler, test.globs)
      File 
"/home/arpit/Documents/GSOC_16/sage-7.2/local/lib/python2.7/site-packages/sage/doctest/forker.py",
 line 858, in compile_and_execute
        exec(compiled, globs)
      File "<doctest 
sage.rings.polynomial.skew_polynomial_finite_field.factorizations[3]>", line 1, 
in <module>
        a = x**Integer(3) + (t**Integer(2) + Integer(1))*x**Integer(2) + 
(Integer(2)*t + Integer(3))*x + t**Integer(2) + t + Integer(2)
      File "sage/structure/element.pyx", line 1798, in 
sage.structure.element.RingElement.__mul__ 
(/home/arpit/Documents/GSOC_16/sage-7.2/src/build/cythonized/sage/structure/element.c:16351)
        return coercion_model.bin_op(left, right, mul)
      File "sage/structure/coerce.pyx", line 1020, in 
sage.structure.coerce.CoercionModel_cache_maps.bin_op 
(/home/arpit/Documents/GSOC_16/sage-7.2/src/build/cythonized/sage/structure/coerce.c:8743)
        action = self.get_action(xp, yp, op, x, y)
      File "sage/structure/coerce.pyx", line 1557, in 
sage.structure.coerce.CoercionModel_cache_maps.get_action 
(/home/arpit/Documents/GSOC_16/sage-7.2/src/build/cythonized/sage/structure/coerce.c:15560)
        action = self.discover_action(R, S, op, r, s)
      File "sage/structure/coerce.pyx", line 1697, in 
sage.structure.coerce.CoercionModel_cache_maps.discover_action 
(/home/arpit/Documents/GSOC_16/sage-7.2/src/build/cythonized/sage/structure/coerce.c:17010)
        action = (<Parent>R).get_action(S, op, True, r, s)
      File "sage/structure/parent.pyx", line 2742, in 
sage.structure.parent.Parent.get_action 
(/home/arpit/Documents/GSOC_16/sage-7.2/src/build/cythonized/sage/structure/parent.c:21612)
        action = self.discover_action(S, op, self_on_left, self_el, S_el)
      File "sage/structure/parent.pyx", line 2818, in 
sage.structure.parent.Parent.discover_action 
(/home/arpit/Documents/GSOC_16/sage-7.2/src/build/cythonized/sage/structure/parent.c:22849)
        action = detect_element_action(self, S, self_on_left, self_el, S_el)
      File "sage/structure/coerce_actions.pyx", line 230, in 
sage.structure.coerce_actions.detect_element_action 
(/home/arpit/Documents/GSOC_16/sage-7.2/src/build/cythonized/sage/structure/coerce_actions.c:5232)
        return (RightModuleAction if X_on_left else LeftModuleAction)(Y, X, y, 
x)
      File "sage/structure/coerce_actions.pyx", line 339, in 
sage.structure.coerce_actions.ModuleAction.__init__ 
(/home/arpit/Documents/GSOC_16/sage-7.2/src/build/cythonized/sage/structure/coerce_actions.c:6087)
        self.extended_base = pushout(G, S)
      File 
"/home/arpit/Documents/GSOC_16/sage-7.2/local/lib/python2.7/site-packages/sage/categories/pushout.py",
 line 3667, in pushout
        while len(Ss) > 0 and Rs[-1].has_coerce_map_from(Ss[-1]):
      File "sage/structure/parent.pyx", line 2238, in 
sage.structure.parent.Parent.has_coerce_map_from 
(/home/arpit/Documents/GSOC_16/sage-7.2/src/build/cythonized/sage/structure/parent.c:17921)
        cpdef bint has_coerce_map_from(self, S) except -2:
      File "sage/structure/parent.pyx", line 2260, in 
sage.structure.parent.Parent.has_coerce_map_from 
(/home/arpit/Documents/GSOC_16/sage-7.2/src/build/cythonized/sage/structure/parent.c:17871)
        return self._internal_coerce_map_from(S) is not None
      File "sage/structure/parent.pyx", line 2400, in 
sage.structure.parent.Parent._internal_coerce_map_from 
(/home/arpit/Documents/GSOC_16/sage-7.2/src/build/cythonized/sage/structure/parent.c:18788)
        mor = self.discover_coerce_map_from(S)
      File "sage/structure/parent.pyx", line 2591, in 
sage.structure.parent.Parent.discover_coerce_map_from 
(/home/arpit/Documents/GSOC_16/sage-7.2/src/build/cythonized/sage/structure/parent.c:19948)
        mor = mor * connecting
      File "sage/categories/map.pyx", line 906, in 
sage.categories.map.Map.__mul__ 
(/home/arpit/Documents/GSOC_16/sage-7.2/src/build/cythonized/sage/categories/map.c:7354)
        return self._composition(right)
      File "sage/categories/map.pyx", line 947, in 
sage.categories.map.Map._composition 
(/home/arpit/Documents/GSOC_16/sage-7.2/src/build/cythonized/sage/categories/map.c:7606)
        return self._composition_(right, H)
      File "sage/rings/morphism.pyx", line 786, in 
sage.rings.morphism.RingHomomorphism._composition_ 
(/home/arpit/Documents/GSOC_16/sage-7.2/src/build/cythonized/sage/rings/morphism.c:5895)
        return homset([self(g) for g in right.im_gens()], False)
      File 
"/home/arpit/Documents/GSOC_16/sage-7.2/local/lib/python2.7/site-packages/sage/rings/homset.py",
 line 263, in __call__
        return morphism.RingHomomorphism_from_quotient(self, phi)
      File "sage/rings/morphism.pyx", line 1749, in 
sage.rings.morphism.RingHomomorphism_from_quotient.__init__ 
(/home/arpit/Documents/GSOC_16/sage-7.2/src/build/cythonized/sage/rings/morphism.c:12771)
        if phi(x) != 0:
      File "sage/rings/polynomial/skew_polynomial_element.pyx", line 279, in 
sage.rings.polynomial.skew_polynomial_element.SkewPolynomial.__richcmp__ 
(/home/arpit/Documents/GSOC_16/sage-7.2/src/build/cythonized/sage/rings/polynomial/skew_polynomial_element.c:4897)
        return (<Element>left)._richcmp_(right, op)
    TypeError: Cannot convert int to sage.structure.element.Element
************************************************************************

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