What I'm trying to say is that QQbar and NumberField aren't embedded in CC
in the same code path:
sage: SR(I).pyobject().parent().embeddings(CC)
[
Ring morphism:
From: Number Field in I with defining polynomial x^2 + 1
To: Complex Field with 53 bits of precision
Defn: I |--> -1.00000000000000*I,
Ring morphism:
From: Number Field in I with defining polynomial x^2 + 1
To: Complex Field with 53 bits of precision
Defn: I |--> 1.00000000000000*I
]
sage: K.<a> = NumberField(x^2+1, embedding=CC.gen())
sage: K.embeddings(CC)
[
Ring morphism:
From: Number Field in a with defining polynomial x^2 + 1
To: Complex Field with 53 bits of precision
Defn: a |--> -1.00000000000000*I,
Ring morphism:
From: Number Field in a with defining polynomial x^2 + 1
To: Complex Field with 53 bits of precision
Defn: a |--> 1.00000000000000*I
]
sage: QQbar.embeddings(CC)
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
<ipython-input-53-8c92918ea5ef> in <module>()
----> 1 QQbar.embeddings(CC)
/home/vbraun/Code/sage/src/sage/structure/parent.pyx in
sage.structure.parent.Parent.__getattr__
(/home/vbraun/Code/sage/src/build/cythonized/sage/structure/parent.c:8043)()
853 return self.__cached_methods[name]
854 except KeyError:
--> 855 attr = getattr_from_other_class(self,
self._category.parent_class, name)
856 self.__cached_methods[name] = attr
857 return attr
/home/vbraun/Code/sage/src/sage/structure/misc.pyx in
sage.structure.misc.getattr_from_other_class
(/home/vbraun/Code/sage/src/build/cythonized/sage/structure/misc.c:1667)()
251 dummy_error_message.cls = type(self)
252 dummy_error_message.name = name
--> 253 raise dummy_attribute_error
254 try:
255 attribute = getattr(cls, name)
AttributeError: 'AlgebraicField_with_category' object has no attribute
'embeddings'
and the crash is from working with QQbar, not the NumberField
sage: bool(SR(K.gen()) == I)
True
sage: bool(SR(QQbar.gen()) == I)
CRASH
On Sunday, January 17, 2016 at 9:49:13 PM UTC, William wrote:
>
> On Sun, Jan 17, 2016 at 1:42 PM, Volker Braun <[email protected]
> <javascript:>> wrote:
> > AlgebraicField = QQbar is a separate implementation from NumberField.
> The
> > number field embeddings refer to the latter only.
> >
>
> I don't understand. The first three examples at
>
>
> http://doc.sagemath.org/html/en/reference/number_fields/sage/rings/number_field/number_field_morphisms.html
>
>
> are of equipping a number field with an embedding in QQbar.
>
> William
>
> >
> > On Sunday, January 17, 2016 at 6:37:14 PM UTC, William wrote:
> >>
> >> Hi,
> >>
> >> Does anybody understand number field embeddings
> >>
> >>
> http://doc.sagemath.org/html/en/reference/number_fields/sage/rings/number_field/number_field_morphisms.html
>
> >>
> >> and whether the default I in SR (i.e., NumberField(x^2+1)) is equipped
> >> with any embeddings. The above reference manual shows how to make
> >> number fields with embeddings, but I couldn't see how to query a
> >> number field for its embeddings. Obviously, I could figure this out
> >> by reading the source, but I'm don't have time right now. I'm curious
> >> though, since I want to talk about this in my grad course on
> >> Wednesday, and it's relevant to the bug.
> >>
> >> I'm posting worksheets like this for my class:
> >>
> >>
> >>
> https://cloud.sagemath.com/projects/b85dd1b3-3f5f-4c2d-b503-242612561b9e/files/lectures/2016-01-15/2016-01-15-part0-QQbar.sagews
>
> >>
> >> On Sun, Jan 17, 2016 at 10:27 AM, Volker Braun <[email protected]>
> wrote:
> >> > SR is special in that it wraps various other rings:
> >> >
> >> > sage: wrapped_qqbar = SR(QQbar(I))
> >> > sage: wrapped_qqbar.parent()
> >> > Symbolic Ring
> >> > sage: wrapped_qqbar.pyobject()
> >> > 1*I
> >> > sage: wrapped_qqbar.pyobject().parent()
> >> > Algebraic Field
> >> >
> >> > You don't gain anything from wrapping stuff in SR; ideally you can
> avoid
> >> > it
> >> > in your code.
> >> >
> >> > I opened http://trac.sagemath.org/ticket/19904 with a better
> testcase
> >> > for
> >> > the segfault
> >> >
> >> > sage: bool(SR(QQbar(I)) == I)
> >> > terminate called after throwing an instance of 'std::runtime_error'
> >> > what():
> >> >
> ------------------------------------------------------------------------
> >> >
> >> >
> /home/vbraun/Code/sage/local/lib/python2.7/site-packages/sage/ext/interrupt/interrupt.so(+0x3da5)[0x7f06b9187da5]
>
>
> >> >
> >> >
> /home/vbraun/Code/sage/local/lib/python2.7/site-packages/sage/ext/interrupt/interrupt.so(+0x3df7)[0x7f06b9187df7]
>
>
> >> >
> >> >
> /home/vbraun/Code/sage/local/lib/python2.7/site-packages/sage/ext/interrupt/interrupt.so(+0x644c)[0x7f06b918a44c]
>
>
> >> > /lib64/libpthread.so.0(+0x109f0)[0x7f06c8b0e9f0]
> >> > /lib64/libc.so.6(gsignal+0x38)[0x7f06c8068a98]
> >> > /lib64/libc.so.6(abort+0x16a)[0x7f06c806a69a]
> >> >
> >> >
> /home/vbraun/Code/sage/local/lib/libstdc++.so.6(__gnu_cxx::__verbose_terminate_handler()+0x15d)[0x7f06acab2ccd]
>
>
> >> >
> >> >
> /home/vbraun/Code/sage/local/lib/libstdc++.so.6(+0x5dd46)[0x7f06acab0d46]
> >> >
> >> >
> /home/vbraun/Code/sage/local/lib/libstdc++.so.6(+0x5dd91)[0x7f06acab0d91]
> >> >
> >> >
> /home/vbraun/Code/sage/local/lib/libstdc++.so.6(+0x5dfa9)[0x7f06acab0fa9]
> >> > /home/vbraun/Code/sage/local/lib/libpynac.so.0(py_error(char
> >> > const*)+0x70)[0x7f069376ede0]
> >> >
> >> >
> /home/vbraun/Code/sage/local/lib/libpynac.so.0(GiNaC::numeric::numeric(_object*,
>
>
> >> > bool)+0x1b8)[0x7f069376f9e8]
> >> >
> >> >
> /home/vbraun/Code/sage/local/lib/libpynac.so.0(GiNaC::numeric::add(GiNaC::numeric
>
>
> >> > const&) const+0x1fa)[0x7f0693776c6a]
> >> >
> >> >
> /home/vbraun/Code/sage/local/lib/libpynac.so.0(GiNaC::operator+(GiNaC::numeric
>
>
> >> > const&, GiNaC::numeric const&)+0x9)[0x7f069377a3a9]
> >> >
> >> >
> /home/vbraun/Code/sage/local/lib/libpynac.so.0(GiNaC::numeric::add_dyn(GiNaC::numeric
>
>
> >> > const&) const+0x39)[0x7f0693770889]
> >> >
> >> >
> /home/vbraun/Code/sage/local/lib/libpynac.so.0(GiNaC::expairseq::combine_overall_coeff(GiNaC::ex
>
>
> >> > const&)+0x1a)[0x7f06936d163a]
> >> >
> >> >
> /home/vbraun/Code/sage/local/lib/libpynac.so.0(GiNaC::expairseq::construct_from_2_ex(GiNaC::ex
>
>
> >> > const&, GiNaC::ex const&)+0x375)[0x7f06936d6515]
> >> >
> /home/vbraun/Code/sage/local/lib/libpynac.so.0(GiNaC::add::add(GiNaC::ex
> >> > const&, GiNaC::ex const&)+0x63)[0x7f06936a5a73]
> >> >
> >> >
> /home/vbraun/Code/sage/local/lib/libpynac.so.0(GiNaC::operator-(GiNaC::ex
> >> > const&, GiNaC::ex const&)+0x5f)[0x7f069377b0af]
> >> >
> >> >
> /home/vbraun/Code/sage/local/lib/libpynac.so.0(GiNaC::relational::decide()
> >> > const+0x46)[0x7f069378b886]
> >> >
> >> >
> /home/vbraun/Code/sage/local/lib/python2.7/site-packages/sage/symbolic/expression.so(+0x9ec48)[0x7f0693387c48]
>
>
> >> >
> >> >
> /home/vbraun/Code/sage/local/lib/libpython2.7.so.1.0(PyObject_IsTrue+0x37)[0x7f06c8dbaa57]
>
>
> >> >
> >> >
> /home/vbraun/Code/sage/local/lib/libpython2.7.so.1.0(+0x54e4e)[0x7f06c8d6fe4e]
>
>
> >> >
> >> >
> /home/vbraun/Code/sage/local/lib/libpython2.7.so.1.0(+0xbcb63)[0x7f06c8dd7b63]
>
>
> >> >
> >> >
> /home/vbraun/Code/sage/local/lib/libpython2.7.so.1.0(PyObject_Call+0x43)[0x7f06c8d6dc43]
>
>
> >> >
> >> >
> /home/vbraun/Code/sage/local/lib/libpython2.7.so.1.0(PyEval_EvalFrameEx+0x3b2e)[0x7f06c8e2228e]
>
>
> >> >
> >> >
> /home/vbraun/Code/sage/local/lib/libpython2.7.so.1.0(PyEval_EvalCodeEx+0x830)[0x7f06c8e255a0]
>
>
> >> >
> >> >
> /home/vbraun/Code/sage/local/lib/libpython2.7.so.1.0(PyEval_EvalCode+0x19)[0x7f06c8e256c9]
>
>
> >> >
> >> >
> /home/vbraun/Code/sage/local/lib/libpython2.7.so.1.0(PyEval_EvalFrameEx+0x58de)[0x7f06c8e2403e]
>
>
> >> >
> >> >
> /home/vbraun/Code/sage/local/lib/libpython2.7.so.1.0(PyEval_EvalCodeEx+0x830)[0x7f06c8e255a0]
>
>
> >> >
> >> >
> /home/vbraun/Code/sage/local/lib/libpython2.7.so.1.0(PyEval_EvalFrameEx+0x5936)[0x7f06c8e24096]
>
>
> >> >
> >> >
> /home/vbraun/Code/sage/local/lib/libpython2.7.so.1.0(PyEval_EvalCodeEx+0x830)[0x7f06c8e255a0]
>
>
> >> >
> >> >
> /home/vbraun/Code/sage/local/lib/libpython2.7.so.1.0(PyEval_EvalFrameEx+0x5936)[0x7f06c8e24096]
>
>
> >> >
> >> >
> /home/vbraun/Code/sage/local/lib/libpython2.7.so.1.0(PyEval_EvalCodeEx+0x830)[0x7f06c8e255a0]
>
>
> >> >
> >> >
> /home/vbraun/Code/sage/local/lib/libpython2.7.so.1.0(PyEval_EvalFrameEx+0x5936)[0x7f06c8e24096]
>
>
> >> >
> >> >
> /home/vbraun/Code/sage/local/lib/libpython2.7.so.1.0(PyEval_EvalCodeEx+0x830)[0x7f06c8e255a0]
>
>
> >> >
> >> >
> /home/vbraun/Code/sage/local/lib/libpython2.7.so.1.0(PyEval_EvalFrameEx+0x5936)[0x7f06c8e24096]
>
>
> >> >
> >> >
> /home/vbraun/Code/sage/local/lib/libpython2.7.so.1.0(PyEval_EvalCodeEx+0x830)[0x7f06c8e255a0]
>
>
> >> >
> >> >
> /home/vbraun/Code/sage/local/lib/libpython2.7.so.1.0(PyEval_EvalFrameEx+0x5936)[0x7f06c8e24096]
>
>
> >> >
> >> >
> /home/vbraun/Code/sage/local/lib/libpython2.7.so.1.0(PyEval_EvalCodeEx+0x830)[0x7f06c8e255a0]
>
>
> >> >
> >> >
> /home/vbraun/Code/sage/local/lib/libpython2.7.so.1.0(PyEval_EvalFrameEx+0x5936)[0x7f06c8e24096]
>
>
> >> >
> >> >
> /home/vbraun/Code/sage/local/lib/libpython2.7.so.1.0(PyEval_EvalCodeEx+0x830)[0x7f06c8e255a0]
>
>
> >> >
> >> >
> /home/vbraun/Code/sage/local/lib/libpython2.7.so.1.0(PyEval_EvalCode+0x19)[0x7f06c8e256c9]
>
>
> >> >
> >> >
> /home/vbraun/Code/sage/local/lib/libpython2.7.so.1.0(PyRun_FileExFlags+0x8a)[0x7f06c8e4949a]
>
>
> >> >
> >> >
> /home/vbraun/Code/sage/local/lib/libpython2.7.so.1.0(PyRun_SimpleFileExFlags+0xd7)[0x7f06c8e4aa27]
>
>
> >> >
> >> >
> /home/vbraun/Code/sage/local/lib/libpython2.7.so.1.0(Py_Main+0xc25)[0x7f06c8e60c25]
>
>
> >> > /lib64/libc.so.6(__libc_start_main+0xf0)[0x7f06c8054580]
> >> > python(_start+0x29)[0x400769]
> >> >
> >> >
> >> >
> >> >
> >> >
> >> > On Sunday, January 17, 2016 at 5:39:43 PM UTC, Emmanuel Charpentier
> >> > wrote:
> >> >>
> >> >> (Note : Question also asked on ask.sagemath.org, but crossposted
> >> >> because I
> >> >> found a way to CRASH sage...).
> >> >> I'm trying to understand coercions, and I'm hitting (repeatedly)
> >> >> something
> >> >> that I do not understand.
> >> >>
> >> >> Let's try to find thge roots of a polynom. We can try equation
> solving
> >> >> (of
> >> >> a quartic, no less) :
> >> >>
> >> >> sage: w = x^4 - (1+3*i)*x^3 - (2-4*i)*x^2 + (6-2*i)*x - 4 - 4*i
> >> >> sage: S1=[t.rhs() for t in solve(w,x)];S1
> >> >> [-1/2*sqrt(2*I) + 3/2*I - 1/2, 1/2*sqrt(2*I) + 3/2*I - 1/2, -I + 1,
> I +
> >> >> 1]
> >> >> sage: bool(sqrt(2*I)==1+I)
> >> >> True
> >> >>
> >> >> Or we can try the roots of a polynomial :
> >> >>
> >> >> sage: S2=[SR(t[0]) for t in w.roots(ring=QQbar)];S2
> >> >> [-1 + 1*I, 2*I, 1 - 1*I, 1 + 1*I]
> >> >> sage: bool(sqrt(2*I)==1+I)
> >> >> True
> >> >> sage: S1R=[t.subs({sqrt(2*I):1+I}) for t in S1];S1R
> >> >> [I - 1, 2*I, -I + 1, I + 1]
> >> >>
> >> >> So far, so good. I'm convinced that these two solution lists are one
> >> >> and
> >> >> the same. But I can't find a way to convince Sage:
> >> >>
> >> >> sage: map(lambda t,u:t-u, S1R, S2)
> >> >>
> >> >>
> >> >>
> ---------------------------------------------------------------------------
> >> >> TypeError Traceback (most recent
> call
> >> >> last)
> >> >> <ipython-input-6-be2e4183b522> in <module>()
> >> >> ----> 1 map(lambda t,u:t-u, S1R, S2)
> >> >>
> >> >> <ipython-input-6-be2e4183b522> in <lambda>(t, u)
> >> >> ----> 1 map(lambda t,u:t-u, S1R, S2)
> >> >>
> >> >> /usr/local/sage-7.0/src/sage/structure/element.pyx in
> >> >> sage.structure.element.RingElement.__sub__
> >> >>
> >> >>
> (/usr/local/sage-7.0/src/build/cythonized/sage/structure/element.c:15995)()
> >> >> 1665 cdef long n
> >> >> 1666 if have_same_parent_c(left, right):
> >> >> -> 1667 return
> >> >> (<ModuleElement>left)._sub_(<ModuleElement>right)
> >> >> 1668 if PyInt_CheckExact(right):
> >> >> 1669 n = PyInt_AS_LONG(right)
> >> >>
> >> >> /usr/local/sage-7.0/src/sage/symbolic/expression.pyx in
> >> >> sage.symbolic.expression.Expression._sub_
> >> >>
> >> >>
> (/usr/local/sage-7.0/src/build/cythonized/sage/symbolic/expression.cpp:20844)()
>
>
> >> >> 2950
> relational_operator(_right._gobj))
> >> >> 2951 else:
> >> >> -> 2952 x = gsub(left._gobj, _right._gobj)
> >> >> 2953 return new_Expression_from_GEx(left._parent, x)
> >> >> 2954
> >> >>
> >> >> /usr/local/sage-7.0/src/sage/structure/element.pyx in
> >> >> sage.structure.element.RingElement.__add__
> >> >>
> >> >>
> (/usr/local/sage-7.0/src/build/cythonized/sage/structure/element.c:15852)()
> >> >> 1649 elif PyInt_CheckExact(left):
> >> >> 1650 return
> >> >> (<RingElement>right)._add_long(PyInt_AS_LONG(left))
> >> >> -> 1651 return coercion_model.bin_op(left, right, add)
> >> >> 1652
> >> >> 1653 cdef RingElement _add_long(self, long n):
> >> >>
> >> >> /usr/local/sage-7.0/src/sage/structure/coerce.pyx in
> >> >> sage.structure.coerce.CoercionModel_cache_maps.bin_op
> >> >>
> >> >>
> (/usr/local/sage-7.0/src/build/cythonized/sage/structure/coerce.c:9736)()
> >> >> 1067 # We should really include the underlying error.
> >> >> 1068 # This causes so much headache.
> >> >> -> 1069 raise TypeError(arith_error_message(x,y,op))
> >> >> 1070
> >> >> 1071 cpdef canonical_coercion(self, x, y):
> >> >>
> >> >> TypeError: unsupported operand parent(s) for '+': 'Number Field in I
> >> >> with
> >> >> defining polynomial x^2 + 1' and 'Algebraic Field'
> >> >>
> >> >> I do not understand this error : both S1R and S2 are composed of
> things
> >> >> belonging to SR :
> >> >>
> >> >> sage: map(lambda t:type(t), S1R)
> >> >> [<type 'sage.symbolic.expression.Expression'>,
> >> >> <type 'sage.symbolic.expression.Expression'>,
> >> >> <type 'sage.symbolic.expression.Expression'>,
> >> >> <type 'sage.symbolic.expression.Expression'>]
> >> >> sage: map(lambda t:type(t), S2)
> >> >> [<type 'sage.symbolic.expression.Expression'>,
> >> >> <type 'sage.symbolic.expression.Expression'>,
> >> >> <type 'sage.symbolic.expression.Expression'>,
> >> >> <type 'sage.symbolic.expression.Expression'>]
> >> >>
> >> >> The reverse conversion works, however :
> >> >>
> >> >> sage: map(lambda t,u:t-u, [QQbar(t) for t in S1R], [QQbar(t) for t
> in
> >> >> S2])
> >> >> [0, 0, 0, 0]
> >> >>
> >> >> Worse : testing directly for equality CRASHES Sage :
> >> >>
> >> >> sage: map(lambda t,u:bool(t==u), S1R, S2)
> >> >> terminate called after throwing an instance of 'std::runtime_error'
> >> >> what():
> >> >>
> >> >>
> ------------------------------------------------------------------------
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/python2.7/site-packages/sage/ext/interrupt/interrupt.so(+0x3c35)[0x7f3d47047c35]
>
>
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/python2.7/site-packages/sage/ext/interrupt/interrupt.so(+0x3c87)[0x7f3d47047c87]
>
>
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/python2.7/site-packages/sage/ext/interrupt/interrupt.so(+0x608c)[0x7f3d4704a08c]
>
>
> >> >> /lib/x86_64-linux-gnu/libpthread.so.0(+0x10670)[0x7f3d4edc4670]
> >> >> /lib/x86_64-linux-gnu/libc.so.6(gsignal+0x37)[0x7f3d4e337657]
> >> >> /lib/x86_64-linux-gnu/libc.so.6(abort+0x16a)[0x7f3d4e338a2a]
> >> >>
> >> >>
> >> >>
> /usr/lib/x86_64-linux-gnu/libstdc++.so.6(_ZN9__gnu_cxx27__verbose_terminate_handlerEv+0x15d)[0x7f3d3a9ad35d]
>
>
> >> >> /usr/lib/x86_64-linux-gnu/libstdc++.so.6(+0x8d3b6)[0x7f3d3a9ab3b6]
> >> >> /usr/lib/x86_64-linux-gnu/libstdc++.so.6(+0x8d401)[0x7f3d3a9ab401]
> >> >> /usr/lib/x86_64-linux-gnu/libstdc++.so.6(+0x8d619)[0x7f3d3a9ab619]
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/libpynac.so.2(_Z8py_errorPKc+0x49)[0x7f3d214029c9]
>
>
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/libpynac.so.2(_ZN5GiNaC7numericC1EP7_objectb+0x1b8)[0x7f3d21403508]
>
>
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/libpynac.so.2(_ZNK5GiNaC7numeric3addERKS0_+0x1c2)[0x7f3d214094f2]
>
>
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/libpynac.so.2(_ZN5GiNaCplERKNS_7numericES2_+0x9)[0x7f3d2140c569]
>
>
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/libpynac.so.2(_ZNK5GiNaC7numeric7add_dynERKS0_+0x2d)[0x7f3d2140405d]
>
>
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/libpynac.so.2(_ZN5GiNaC9expairseq21combine_overall_coeffERKNS_2exE+0x15)[0x7f3d2136f945]
>
>
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/libpynac.so.2(_ZN5GiNaC9expairseq19construct_from_2_exERKNS_2exES3_+0x27d)[0x7f3d21374bed]
>
>
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/libpynac.so.2(_ZN5GiNaC3addC1ERKNS_2exES3_+0x63)[0x7f3d21346633]
>
>
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/libpynac.so.2(_ZN5GiNaCmiERKNS_2exES2_+0x5f)[0x7f3d2140d14f]
>
>
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/libpynac.so.2(_ZNK5GiNaC10relational6decideEv+0x3e)[0x7f3d2141bede]
>
>
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/python2.7/site-packages/sage/symbolic/expression.so(+0xa7108)[0x7f3d21039108]
>
>
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/libpython2.7.so.1.0(PyObject_IsTrue+0x37)[0x7f3d4f06fe17]
>
>
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/libpython2.7.so.1.0(+0x54eae)[0x7f3d4f025eae]
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/libpython2.7.so.1.0(+0xbc623)[0x7f3d4f08d623]
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/libpython2.7.so.1.0(PyObject_Call+0x43)[0x7f3d4f023a73]
>
>
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/libpython2.7.so.1.0(PyEval_EvalFrameEx+0x3a6e)[0x7f3d4f0d634e]
>
>
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/libpython2.7.so.1.0(PyEval_EvalCodeEx+0x81c)[0x7f3d4f0d928c]
>
>
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/libpython2.7.so.1.0(+0x835ac)[0x7f3d4f0545ac]
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/libpython2.7.so.1.0(PyObject_Call+0x43)[0x7f3d4f023a73]
>
>
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/libpython2.7.so.1.0(PyEval_CallObjectWithKeywords+0x47)[0x7f3d4f0d22e7]
>
>
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/libpython2.7.so.1.0(+0xfd564)[0x7f3d4f0ce564]
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/libpython2.7.so.1.0(PyEval_EvalFrameEx+0x5c8e)[0x7f3d4f0d856e]
>
>
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/libpython2.7.so.1.0(PyEval_EvalCodeEx+0x81c)[0x7f3d4f0d928c]
>
>
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/libpython2.7.so.1.0(PyEval_EvalCode+0x19)[0x7f3d4f0d93a9]
>
>
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/libpython2.7.so.1.0(PyEval_EvalFrameEx+0x5234)[0x7f3d4f0d7b14]
>
>
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/libpython2.7.so.1.0(PyEval_EvalCodeEx+0x81c)[0x7f3d4f0d928c]
>
>
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/libpython2.7.so.1.0(PyEval_EvalFrameEx+0x5a42)[0x7f3d4f0d8322]
>
>
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/libpython2.7.so.1.0(PyEval_EvalCodeEx+0x81c)[0x7f3d4f0d928c]
>
>
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/libpython2.7.so.1.0(PyEval_EvalFrameEx+0x5a42)[0x7f3d4f0d8322]
>
>
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/libpython2.7.so.1.0(PyEval_EvalCodeEx+0x81c)[0x7f3d4f0d928c]
>
>
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/libpython2.7.so.1.0(PyEval_EvalFrameEx+0x5a42)[0x7f3d4f0d8322]
>
>
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/libpython2.7.so.1.0(PyEval_EvalCodeEx+0x81c)[0x7f3d4f0d928c]
>
>
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/libpython2.7.so.1.0(PyEval_EvalFrameEx+0x5a42)[0x7f3d4f0d8322]
>
>
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/libpython2.7.so.1.0(PyEval_EvalCodeEx+0x81c)[0x7f3d4f0d928c]
>
>
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/libpython2.7.so.1.0(PyEval_EvalFrameEx+0x5a42)[0x7f3d4f0d8322]
>
>
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/libpython2.7.so.1.0(PyEval_EvalCodeEx+0x81c)[0x7f3d4f0d928c]
>
>
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/libpython2.7.so.1.0(PyEval_EvalFrameEx+0x5a42)[0x7f3d4f0d8322]
>
>
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/libpython2.7.so.1.0(PyEval_EvalCodeEx+0x81c)[0x7f3d4f0d928c]
>
>
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/libpython2.7.so.1.0(PyEval_EvalCode+0x19)[0x7f3d4f0d93a9]
>
>
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/libpython2.7.so.1.0(PyRun_FileExFlags+0x8a)[0x7f3d4f0fca9a]
>
>
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/libpython2.7.so.1.0(PyRun_SimpleFileExFlags+0xd7)[0x7f3d4f0fde47]
>
>
> >> >>
> >> >>
> >> >>
> /usr/local/sage-7.0/local/lib/libpython2.7.so.1.0(Py_Main+0xc3e)[0x7f3d4f1143ee]
>
>
> >> >>
> /lib/x86_64-linux-gnu/libc.so.6(__libc_start_main+0xf0)[0x7f3d4e324870]
> >> >> python(_start+0x29)[0x4006f9]
> >> >>
> >> >>
> ------------------------------------------------------------------------
> >> >> Attaching gdb to process id 11241.
> >> >>
> >> >> Saved trace to /home/charpent/.sage/crash_logs/sage_crash_qQFZhv.log
> >> >>
> >> >>
> ------------------------------------------------------------------------
> >> >> Unhandled SIGABRT: An abort() occurred in Sage.
> >> >> This probably occurred because a *compiled* component of Sage has a
> bug
> >> >> in it and is not properly wrapped with sig_on(), sig_off().
> >> >> Sage will now terminate.
> >> >>
> >> >>
> ------------------------------------------------------------------------
> >> >> Abandon
> >> >>
> >> >>
> >> > --
> >> > You received this message because you are subscribed to the Google
> >> > Groups
> >> > "sage-support" group.
> >> > To unsubscribe from this group and stop receiving emails from it,
> send
> >> > an
> >> > email to [email protected].
> >> > To post to this group, send email to [email protected].
> >> > Visit this group at https://groups.google.com/group/sage-support.
> >> > For more options, visit https://groups.google.com/d/optout.
> >>
> >>
> >>
> >> --
> >> William (http://wstein.org)
> >
> > --
> > You received this message because you are subscribed to the Google
> Groups
> > "sage-support" group.
> > To unsubscribe from this group and stop receiving emails from it, send
> an
> > email to [email protected] <javascript:>.
> > To post to this group, send email to [email protected]
> <javascript:>.
> > Visit this group at https://groups.google.com/group/sage-support.
> > For more options, visit https://groups.google.com/d/optout.
>
>
>
> --
> William (http://wstein.org)
>
--
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