Thanks a lot for this answer. This is somewhat clearer for me. Now, I have
to understand coercions between THREE sets that a
(non-professionnal-mathematician) human thinks (vaguely) as one :
$\mathbb{C}$.
I suppose that's a price to pay for using Sage. Probably "obviously" the
Right Thing to a professional mathematician, but a (non-obvious) hurdle for
"engineering types" such as me.
Thanks again !
--
Emmanuel Charpentier
Le dimanche 17 janvier 2016 19:00:02 UTC+1, William a écrit :
>
> On Sun, Jan 17, 2016 at 9:39 AM, Emmanuel Charpentier
> <[email protected] <javascript:>> 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:
>
> They aren't the same. The "I" you're using everywhere is a number
> field element. However, when you do SR(...root in QQbar...), you're
> making a completely different and incompatible I. The notation
>
> SomeParent(...)
>
> is potentially dangerous: <rant> it means "make something in
> SomeParent from the input possibly without respecting the coercion
> model". It's what people do when the get frustrated -- it's a sort of
> automated version of copy/paste. It's like Magma's "SomeParent![crazy
> thing]", and is by far the most likely source of bugs in code.
> </rant>
>
> If you do:
>
> reset()
> a = (x^2+1).roots(ring=QQbar)[1][0]
> b = I.pyobject()
> a, b
> parent(a), parent(b)
>
> you'll see the two underlying elements that you're trying to mix.
> One is a number field element, and the other is an element of QQbar.
> Number fields elements don't mix with elements of QQbar without
> explicitly applying an embedding morphism.
>
> That said, I vaguely recall at some point that a fixed choice of
> embedding was something maybe added to number fields. It would likely
> make a lot more sense also for the I in SR to the one from QQbar
> rather than the one from NumberField(x^2+1). However, the one from
> NumberField(x^2+1) is a *lot* faster (orders of magnitude!), so it's
> no so clear.
>
> I'm not at all saying you haven't hit on a serious bug. However, the
> above remarks might help whoever works on it, maybe.
>
> William
>
> >
> > 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
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> > To unsubscribe from this group and stop receiving emails from it, send
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> > 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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