Failed example:: Got: Traceback (most recent call last): File "/sage/src/sage/doctest/forker.py", line 712, in _run self.compile_and_execute(example, compiler, test.globs) File "/sage/src/sage/doctest/forker.py", line 1147, in compile_and_execute exec(compiled, globs) File "<doctest sage.modules.free_module.?[39]>", line 1, in <module> FreeModule(ZZ, rank=Integer(3), basis_keys=['c','d']) File "/sage/src/sage/modules/free_module.py", line 554, in FreeModule raise ValueError(f'inconsistent basis_keys: should be of cardinality {rank}, ' ValueError: inconsistent basis_keys: should be of cardinality 3, got ['c', 'd']

Failed example:: Exception raised: Traceback (most recent call last): File "sage/matrix/matrix2.pyx", line 7658, in sage.matrix.matrix2.Matrix._echelonize_ring a, d, p = self._echelon_form_PID() File "sage/matrix/matrix2.pyx", line 16381, in sage.matrix.matrix2.Matrix._echelon_form_PID left_mat = s.new_matrix(1, 1, [1]).block_sum(s) * left_mat File "sage/matrix/matrix1.pyx", line 2775, in sage.matrix.matrix1.Matrix.new_matrix return self._parent(entries, coerce=coerce, copy=copy) File "sage/structure/parent.pyx", line 903, in sage.structure.parent.Parent.__call__ return mor._call_with_args(x, args, kwds) File "sage/structure/coerce_maps.pyx", line 182, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_with_args raise File "sage/structure/coerce_maps.pyx", line 172, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_with_args return C._element_constructor(x, **kwds) File "/sage/src/sage/matrix/matrix_space.py", line 1019, in _element_constructor_ return self.element_class(self, entries, **kwds) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ File "sage/matrix/matrix_generic_dense.pyx", line 82, in sage.matrix.matrix_generic_dense.Matrix_generic_dense.__init__ self._entries = ma.list(coerce) File "sage/matrix/args.pyx", line 814, in sage.matrix.args.MatrixArgs.list L = list(self.iter(convert)) File "sage/matrix/args.pyx", line 574, in iter row = sized_iter(next(row_iter), self.ncols) File "sage/misc/misc_c.pyx", line 677, in sage.misc.misc_c.sized_iter.__init__ self.iterator = iter(iterable) TypeError: 'int' object is not iterable During handling of the above exception, another exception occurred: Traceback (most recent call last): File "/sage/src/sage/doctest/forker.py", line 712, in _run self.compile_and_execute(example, compiler, test.globs) File "/sage/src/sage/doctest/forker.py", line 1147, in compile_and_execute exec(compiled, globs) File "<doctest sage.modules.free_module.span[6]>", line 1, in <module> M= span( [[x, x**Integer(2)+Integer(1)], [Integer(1)/x, x**Integer(3)]], R); M ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ File "/sage/src/sage/modules/free_module.py", line 784, in span return M.span(gens=gens, base_ring=base_ring, check=check, ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ File "/sage/src/sage/modules/free_module.py", line 1695, in span return M.span(gens) ^^^^^^^^^^^^ File "/sage/src/sage/modules/free_module.py", line 1686, in span return self._submodule_class(self.ambient_module(), gens, check=check, already_echelonized=already_echelonized) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ File "/sage/src/sage/modules/free_module.py", line 7616, in __init__ FreeModule_submodule_with_basis_pid.__init__(self, ambient, basis=gens, File "/sage/src/sage/modules/free_module.py", line 6557, in __init__ basis = self._echelonized_basis(ambient, basis) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ File "/sage/src/sage/modules/free_module.py", line 6747, in _echelonized_basis E = A.echelon_form() ^^^^^^^^^^^^^^^^ File "sage/matrix/matrix2.pyx", line 7957, in sage.matrix.matrix2.Matrix.echelon_form v = E.echelonize(cutoff=cutoff, **kwds) File "sage/matrix/matrix2.pyx", line 7862, in sage.matrix.matrix2.Matrix.echelonize return self._echelonize_ring(**kwds) File "sage/matrix/matrix2.pyx", line 7660, in sage.matrix.matrix2.Matrix._echelonize_ring raise NotImplementedError("%s\nechelon form over %s not yet implemented"%(msg, self.base_ring())) NotImplementedError: 'int' object is not iterable echelon form over Univariate Polynomial Ring in x over Rational Field not yet implemented

Failed example:: Exception raised: Traceback (most recent call last): File "/sage/src/sage/doctest/forker.py", line 712, in _run self.compile_and_execute(example, compiler, test.globs) File "/sage/src/sage/doctest/forker.py", line 1147, in compile_and_execute exec(compiled, globs) File "<doctest sage.modules.free_module.span[7]>", line 1, in <module> M.basis()[Integer(0)][Integer(0)].parent() ^ NameError: name 'M' is not defined

Failed example:: Exception raised: Traceback (most recent call last): File "sage/matrix/matrix2.pyx", line 7658, in sage.matrix.matrix2.Matrix._echelonize_ring a, d, p = self._echelon_form_PID() File "sage/matrix/matrix2.pyx", line 16381, in sage.matrix.matrix2.Matrix._echelon_form_PID left_mat = s.new_matrix(1, 1, [1]).block_sum(s) * left_mat File "sage/matrix/matrix1.pyx", line 2775, in sage.matrix.matrix1.Matrix.new_matrix return self._parent(entries, coerce=coerce, copy=copy) File "sage/structure/parent.pyx", line 903, in sage.structure.parent.Parent.__call__ return mor._call_with_args(x, args, kwds) File "sage/structure/coerce_maps.pyx", line 182, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_with_args raise File "sage/structure/coerce_maps.pyx", line 172, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_with_args return C._element_constructor(x, **kwds) File "/sage/src/sage/matrix/matrix_space.py", line 1019, in _element_constructor_ return self.element_class(self, entries, **kwds) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ File "sage/matrix/matrix_generic_dense.pyx", line 82, in sage.matrix.matrix_generic_dense.Matrix_generic_dense.__init__ self._entries = ma.list(coerce) File "sage/matrix/args.pyx", line 814, in sage.matrix.args.MatrixArgs.list L = list(self.iter(convert)) File "sage/matrix/args.pyx", line 574, in iter row = sized_iter(next(row_iter), self.ncols) File "sage/misc/misc_c.pyx", line 677, in sage.misc.misc_c.sized_iter.__init__ self.iterator = iter(iterable) TypeError: 'int' object is not iterable During handling of the above exception, another exception occurred: Traceback (most recent call last): File "/sage/src/sage/doctest/forker.py", line 712, in _run self.compile_and_execute(example, compiler, test.globs) File "/sage/src/sage/doctest/forker.py", line 1147, in compile_and_execute exec(compiled, globs) File "<doctest sage.modules.free_module.Module_free_ambient.__richcmp__[27]>", line 1, in <module> W3 = F3.span([[Integer(1),Integer(1),Integer(0)], [Integer(0),Integer(4),Integer(0)]]) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ File "/sage/src/sage/modules/free_module.py", line 1686, in span return self._submodule_class(self.ambient_module(), gens, check=check, already_echelonized=already_echelonized) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ File "/sage/src/sage/modules/free_module.py", line 7616, in __init__ FreeModule_submodule_with_basis_pid.__init__(self, ambient, basis=gens, File "/sage/src/sage/modules/free_module.py", line 6557, in __init__ basis = self._echelonized_basis(ambient, basis) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ File "/sage/src/sage/modules/free_module.py", line 6747, in _echelonized_basis E = A.echelon_form() ^^^^^^^^^^^^^^^^ File "sage/matrix/matrix2.pyx", line 7957, in sage.matrix.matrix2.Matrix.echelon_form v = E.echelonize(cutoff=cutoff, **kwds) File "sage/matrix/matrix2.pyx", line 7862, in sage.matrix.matrix2.Matrix.echelonize return self._echelonize_ring(**kwds) File "sage/matrix/matrix2.pyx", line 7660, in sage.matrix.matrix2.Matrix._echelonize_ring raise NotImplementedError("%s\nechelon form over %s not yet implemented"%(msg, self.base_ring())) NotImplementedError: 'int' object is not iterable echelon form over Univariate Polynomial Ring in x over Finite Field of size 5 not yet implemented

Failed example:: Exception raised: Traceback (most recent call last): File "/sage/src/sage/doctest/forker.py", line 712, in _run self.compile_and_execute(example, compiler, test.globs) File "/sage/src/sage/doctest/forker.py", line 1147, in compile_and_execute exec(compiled, globs) File "<doctest sage.modules.free_module.Module_free_ambient.__richcmp__[28]>", line 1, in <module> V3 <= W3 ^^ NameError: name 'W3' is not defined

Failed example:: Exception raised: Traceback (most recent call last): File "/sage/src/sage/doctest/forker.py", line 712, in _run self.compile_and_execute(example, compiler, test.globs) File "/sage/src/sage/doctest/forker.py", line 1147, in compile_and_execute exec(compiled, globs) File "<doctest sage.modules.free_module.Module_free_ambient.__richcmp__[29]>", line 1, in <module> W3 <= V3 ^^ NameError: name 'W3' is not defined

Failed example:: Exception raised: Traceback (most recent call last): File "sage/matrix/matrix0.pyx", line 1672, in sage.matrix.matrix0.Matrix.change_ring return self._change_ring(ring) File "sage/matrix/matrix_integer_dense.pyx", line 5668, in sage.matrix.matrix_integer_dense.Matrix_integer_dense._change_ring raise NotImplementedError NotImplementedError During handling of the above exception, another exception occurred: Traceback (most recent call last): File "/sage/src/sage/modules/free_module.py", line 1695, in span return M.span(gens) ^^^^^^^^^^^^ File "/sage/src/sage/modules/free_module.py", line 1686, in span return self._submodule_class(self.ambient_module(), gens, check=check, already_echelonized=already_echelonized) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ File "/sage/src/sage/modules/free_module.py", line 7616, in __init__ FreeModule_submodule_with_basis_pid.__init__(self, ambient, basis=gens, File "/sage/src/sage/modules/free_module.py", line 6557, in __init__ basis = self._echelonized_basis(ambient, basis) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ File "/sage/src/sage/modules/free_module.py", line 6749, in _echelonized_basis E = E.matrix_over_field()*(~d) # divide out denominator ^^^^^^^^^^^^^^^^^^^^^ File "sage/matrix/matrix1.pyx", line 760, in sage.matrix.matrix1.Matrix.matrix_over_field return self.change_ring(self.base_ring().fraction_field()) File "sage/matrix/matrix0.pyx", line 1675, in sage.matrix.matrix0.Matrix.change_ring mat = M(self.list(), coerce=True, copy=False) File "sage/structure/parent.pyx", line 903, in sage.structure.parent.Parent.__call__ return mor._call_with_args(x, args, kwds) File "sage/structure/coerce_maps.pyx", line 182, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_with_args raise File "sage/structure/coerce_maps.pyx", line 172, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_with_args return C._element_constructor(x, **kwds) File "/sage/src/sage/matrix/matrix_space.py", line 1019, in _element_constructor_ return self.element_class(self, entries, **kwds) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ File "sage/matrix/matrix_rational_dense.pyx", line 189, in sage.matrix.matrix_rational_dense.Matrix_rational_dense.__init__ for t in ma.iter(coerce, True): File "sage/matrix/args.pyx", line 574, in iter row = sized_iter(next(row_iter), self.ncols) File "sage/misc/misc_c.pyx", line 677, in sage.misc.misc_c.sized_iter.__init__ self.iterator = iter(iterable) TypeError: 'sage.rings.integer.Integer' object is not iterable During handling of the above exception, another exception occurred: Traceback (most recent call last): File "/sage/src/sage/doctest/forker.py", line 712, in _run self.compile_and_execute(example, compiler, test.globs) File "/sage/src/sage/doctest/forker.py", line 1147, in compile_and_execute exec(compiled, globs) File "<doctest sage.modules.free_module.Module_free_ambient.__richcmp__[34]>", line 1, in <module> A = (QQ**Integer(1)).span([[Integer(1)/Integer(3)]],ZZ); B = (QQ**Integer(1)).span([[Integer(1)]],ZZ) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ File "/sage/src/sage/modules/free_module.py", line 1697, in span raise ValueError("argument gens (= %s) is not compatible " % gens + ValueError: argument gens (= [[1/3]]) is not compatible with base_ring (= Integer Ring)

Failed example:: Exception raised: Traceback (most recent call last): File "/sage/src/sage/doctest/forker.py", line 712, in _run self.compile_and_execute(example, compiler, test.globs) File "/sage/src/sage/doctest/forker.py", line 1147, in compile_and_execute exec(compiled, globs) File "<doctest sage.modules.free_module.Module_free_ambient.__richcmp__[35]>", line 1, in <module> A.intersection(B) ^ NameError: name 'B' is not defined

Failed example:: Got: False

Failed example:: Exception raised: Traceback (most recent call last): File "sage/structure/category_object.pyx", line 850, in sage.structure.category_object.CategoryObject.getattr_from_category return self._cached_methods[name] KeyError: '_FreeModule_submodule_with_basis_pid__rref_to_echelon_matrix' During handling of the above exception, another exception occurred: Traceback (most recent call last): File "/sage/src/sage/modules/free_module.py", line 7281, in _rref_to_echelon_matrix return self.__rref_to_echelon_matrix ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ File "sage/structure/category_object.pyx", line 844, in sage.structure.category_object.CategoryObject.__getattr__ return self.getattr_from_category(name) File "sage/structure/category_object.pyx", line 859, in sage.structure.category_object.CategoryObject.getattr_from_category attr = getattr_from_other_class(self, cls, name) File "sage/cpython/getattr.pyx", line 357, in sage.cpython.getattr.getattr_from_other_class raise AttributeError(dummy_error_message) AttributeError: 'sage.rings.integer_ring.IntegerRing_class' object has no attribute '_SageObject__custom_name' During handling of the above exception, another exception occurred: Traceback (most recent call last): File "sage/structure/coerce.pyx", line 1219, in sage.structure.coerce.CoercionModel.bin_op action = self._action_maps.get(xp, yp, op) File "sage/structure/coerce_dict.pyx", line 1326, in sage.structure.coerce_dict.TripleDict.get raise KeyError((k1, k2, k3)) KeyError: (Full MatrixSpace of 1 by 1 dense matrices over Integer Ring, Integer Ring, <built-in function truediv>) During handling of the above exception, another exception occurred: Traceback (most recent call last): File "/sage/src/sage/doctest/forker.py", line 712, in _run self.compile_and_execute(example, compiler, test.globs) File "/sage/src/sage/doctest/forker.py", line 1147, in compile_and_execute exec(compiled, globs) File "<doctest sage.modules.free_module.Module_free_ambient.__richcmp__[44]>", line 1, in <module> V.coordinates(w) File "/sage/src/sage/modules/free_module.py", line 2748, in coordinates return self.coordinate_vector(v, check=check).list() ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ File "/sage/src/sage/modules/free_module.py", line 7678, in coordinate_vector return self.echelon_coordinate_vector(v, check=check) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ File "/sage/src/sage/modules/free_module.py", line 7529, in echelon_coordinate_vector return FreeModule(self.base_ring().fraction_field(), self.rank())(self.echelon_coordinates(v, check=check)) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ File "/sage/src/sage/modules/free_module.py", line 7058, in echelon_coordinates T = self._rref_to_echelon_matrix() ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ File "/sage/src/sage/modules/free_module.py", line 7283, in _rref_to_echelon_matrix self.__rref_to_echelon_matrix = ~self._echelon_to_rref_matrix() ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ File "sage/matrix/matrix_integer_dense.pyx", line 4182, in sage.matrix.matrix_integer_dense.Matrix_integer_dense.__invert__ return A / d File "sage/structure/element.pyx", line 4145, in sage.structure.element.Matrix.__truediv__ return coercion_model.bin_op(left, right, truediv) File "sage/structure/coerce.pyx", line 1221, in sage.structure.coerce.CoercionModel.bin_op action = self.get_action(xp, yp, op, x, y) File "sage/structure/coerce.pyx", line 1759, in sage.structure.coerce.CoercionModel.get_action action = self.discover_action(R, S, op, r, s) File "sage/structure/coerce.pyx", line 1927, in sage.structure.coerce.CoercionModel.discover_action right_mul = self.get_action(R, S, mul) File "sage/structure/coerce.pyx", line 1759, in sage.structure.coerce.CoercionModel.get_action action = self.discover_action(R, S, op, r, s) File "sage/structure/coerce.pyx", line 1900

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Variable 'X' referenced here was set only in doctest marked '# needs sage.rings.number_field'

Variable 'M' referenced here was set only in doctest marked '# needs sage.combinat sage.libs.pari'

Variable 'L' referenced here was set only in doctest marked '# needs sage.rings.number_field'

Variable 'b' referenced here was set only in doctest marked '# needs numpy'

Variable 'pi_def' referenced here was set only in doctest marked '# needs sage.libs.pari sage.symbolic'

Variable 'O' referenced here was set only in doctest marked '# needs sage.rings.finite_rings sage.rings.function_field'

Variable 'F' referenced here was set only in doctest marked '# needs sage.rings.finite_rings'

Variable 'F' referenced here was set only in doctest marked '# needs sage.rings.finite_rings'

Variable 'H' referenced here was set only in doctest marked '# optional - gap_package_polycyclic'