(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
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