sage/rings/number_field/number_field_element_quadratic.pyx:7: DeprecationWarning: invalid escape sequence '\Q'
  """
sage/rings/number_field/number_field_element_quadratic.pyx:7: DeprecationWarning: invalid escape sequence '\Q'
  """
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Cell In [5], line 1
----> 1 QuaternionOrder(A, [Integer(1), Integer(3)*i, Integer(1)/Integer(2)*w + Integer(1)/Integer(2) + (Integer(3)/Integer(2)*w + Integer(1))*i + Integer(1)/Integer(2)*j, Integer(1)/Integer(2)*w + (Integer(3)/Integer(2)*w - Integer(1)/Integer(2))*i + Integer(1)/Integer(2)*k])

File /usr/lib/python3.10/site-packages/sage/algebras/quatalg/quaternion_algebra.py:1417, in QuaternionOrder.__init__(self, A, basis, check)
   1414     raise ValueError("lattice must contain 1")
   1416 # check if multiplicatively closed
-> 1417 Y = matrix(QQ, 16, 4, [(x*y).coefficient_tuple()
   1418                        for x in basis for y in basis])
   1419 X = M.solve_left(Y)
   1420 if any(a not in O for x in X for a in x):

File /usr/lib/python3.10/site-packages/sage/matrix/constructor.pyx:643, in sage.matrix.constructor.matrix (build/cythonized/sage/matrix/constructor.c:2731)()
    641 """
    642 immutable = kwds.pop('immutable', False)
--> 643 M = MatrixArgs(*args, **kwds).matrix()
    644 if immutable:
    645     M.set_immutable()

File /usr/lib/python3.10/site-packages/sage/matrix/args.pyx:667, in sage.matrix.args.MatrixArgs.matrix (build/cythonized/sage/matrix/args.c:8012)()
    665             break
    666 else:
--> 667     M = self.space(self, coerce=convert)
    668
    669 # Also store the matrix to support multiple calls of matrix()

File /usr/lib/python3.10/site-packages/sage/structure/parent.pyx:900, in sage.structure.parent.Parent.__call__ (build/cythonized/sage/structure/parent.c:9485)()
    898         return mor._call_(x)
    899     else:
--> 900         return mor._call_with_args(x, args, kwds)
    901
    902 raise TypeError(_LazyString(_lazy_format, ("No conversion defined from %s to %s", R, self), {}))

File /usr/lib/python3.10/site-packages/sage/structure/coerce_maps.pyx:180, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_with_args (build/cythonized/sage/structure/coerce_maps.c:5265)()
    178     print(type(C), C)
    179     print(type(C._element_constructor), C._element_constructor)
--> 180 raise
    181
    182

File /usr/lib/python3.10/site-packages/sage/structure/coerce_maps.pyx:170, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_with_args (build/cythonized/sage/structure/coerce_maps.c:5055)()
    168         return C._element_constructor(x)
    169     else:
--> 170         return C._element_constructor(x, **kwds)
    171 else:
    172     if len(kwds) == 0:

File /usr/lib/python3.10/site-packages/sage/matrix/matrix_space.py:925, in MatrixSpace._element_constructor_(self, entries, **kwds)
    815 def _element_constructor_(self, entries, **kwds):
    816     """
    817     Construct an element of ``self`` from ``entries``.
    818
   (...)
    923         False
    924     """
--> 925     return self.element_class(self, entries, **kwds)

File /usr/lib/python3.10/site-packages/sage/matrix/matrix_rational_dense.pyx:192, in sage.matrix.matrix_rational_dense.Matrix_rational_dense.__init__ (build/cythonized/sage/matrix/matrix_rational_dense.cpp:4962)()
    190 ma = MatrixArgs_init(parent, entries)
    191 cdef Rational z
--> 192 for t in ma.iter(coerce, True):
    193     se = <SparseEntry>t
    194     z = <Rational>se.entry

File /usr/lib/python3.10/site-packages/sage/matrix/args.pyx:521, in iter (build/cythonized/sage/matrix/args.c:6532)()
    519 x = next(row)
    520 if convert and self.need_to_convert(x):
--> 521     x = self.base(x)
    522 if sparse:
    523     yield make_SparseEntry(i, j, x)

File /usr/lib/python3.10/site-packages/sage/structure/parent.pyx:898, in sage.structure.parent.Parent.__call__ (build/cythonized/sage/structure/parent.c:9458)()
    896 if mor is not None:
    897     if no_extra_args:
--> 898         return mor._call_(x)
    899     else:
    900         return mor._call_with_args(x, args, kwds)

File /usr/lib/python3.10/site-packages/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_ (build/cythonized/sage/structure/coerce_maps.c:4734)()
    159             print(type(C), C)
    160             print(type(C._element_constructor), C._element_constructor)
--> 161         raise
    162
    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):

File /usr/lib/python3.10/site-packages/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_ (build/cythonized/sage/structure/coerce_maps.c:4626)()
    154 cdef Parent C = self._codomain
    155 try:
--> 156     return C._element_constructor(x)
    157 except Exception:
    158     if print_warnings:

File /usr/lib/python3.10/site-packages/sage/rings/rational.pyx:538, in sage.rings.rational.Rational.__init__ (build/cythonized/sage/rings/rational.cpp:6529)()
    536     """
    537     if x is not None:
--> 538         self.__set_value(x, base)
    539
    540 def __reduce__(self):

File /usr/lib/python3.10/site-packages/sage/rings/rational.pyx:626, in sage.rings.rational.Rational.__set_value (build/cythonized/sage/rings/rational.cpp:7657)()
    624
    625         elif hasattr(x, "_rational_"):
--> 626             set_from_Rational(self, x._rational_())
    627
    628         elif isinstance(x, tuple) and len(x) == 2:

File /usr/lib/python3.10/site-packages/sage/rings/number_field/number_field_element_quadratic.pyx:1713, in sage.rings.number_field.number_field_element_quadratic.NumberFieldElement_quadratic._rational_ (build/cythonized/sage/rings/number_field/number_field_element_quadratic.cpp:15940)()
   1711 cdef Rational res
   1712 if mpz_cmp_ui(self.b, 0)!=0:
-> 1713     raise TypeError("Unable to coerce %s to a rational" % self)
   1714 else:
   1715     res = <Rational>Rational.__new__(Rational)

TypeError: Unable to coerce 1/2*w + 1/2 to a rational