On Sun, Aug 9, 2009 at 3:33 PM, Dr. David Kirkby <david.kirkby at onetel.net>wrote:
> William Stein wrote:
>
>
>>
>> On Sun, Aug 9, 2009 at 2:03 PM, Dr. David Kirkby <david.kirkby at onetel.net<mailto:
>> david.kirkby at onetel.net>> wrote:
>>
>>
>> Seen with Sage 4.1.1.rc0, with updated ECL 9.8.1 and Maxima 5.19.0.
>>
>> Should this be reported to the Maxima list?
>>
>> I've not created a trac ticket for this, as I don't know enough to fill
>> it in properly.
>>
>> File
>>
>> "/export/home/drkirkby/sage/sage-4.1.1.rc0/devel/sage/sage/symbolic/expression.pyx",
>> line 5329:
>> sage: solve(Q*sqrt(Q^2 + 2) - 1,Q)
>> Expected:
>> [Q == 1/sqrt(-sqrt(2) + 1), Q == 1/sqrt(sqrt(2) + 1)]
>> Got:
>> [Q == 1/sqrt(sqrt(2) + 1)]
>>
>>
>> This seems like a bug in Maxima to me, at first glance. For comparison,
>> here is what Mathematica does (which is the same as Sage right now):
>>
>> sage: var('Q')
>> Q
>> sage: m = mathematica(Q*sqrt(Q^2 + 2) == 1); m
>> Q*Sqrt[2 + Q^2] == 1
>> sage: m.Solve(Q)
>> {{Q -> Sqrt[-1 + Sqrt[2]]}, {Q -> (-I)*Sqrt[1 + Sqrt[2]]}}
>> sage: m.NSolve(Q)
>> {{Q -> 0. - 1.5537739740300396*I}, {Q -> 0.6435942529055826}}
>> sage: f = Q*sqrt(Q^2 + 2) - 1
>> sage: s = solve(Q*sqrt(Q^2 + 2) - 1,Q, solution_dict=True)
>> sage: N(s[0][Q])
>> 9.51412161947174e-17 - 1.55377397403004*I
>> sage: N(s[1][Q])
>> 0.643594252905583
>>
>> So I think this is a bug. It should return both solutions, but is only
>> returning the one real solution. Note that this is the behavior of the
>> default Maxima mode even in 5.16.3.
>> sage: !maxima
>> Maxima 5.16.3 http://maxima.sourceforge.net
>> Using Lisp ECL 9.4.1
>> Distributed under the GNU Public License. See the file COPYING.
>> Dedicated to the memory of William Schelter.
>> The function bug_report() provides bug reporting information.
>> (%i1) solve(Q*sqrt(Q^2+2)-1,Q)
>> ;
>> 1
>> (%o1) [Q = ------------]
>> 2
>> sqrt(Q + 2)
>>
>>
>> In fact, I can't coerce Maxima to return both solutions *no matter* what I
>> do, setting domain:complex, etc. Notice that in fact what Maxima does is
>> return the "solution" 'Q == 1/sqrt(Q^2 + 2)', which is no solution at all
>> since Q is in the right hand side. Sage (in expression.pyx in the
>> "if explicit_solutions is not False:" part of the code around line 5318),
>> looks at each solution, then calls Maxima's to_poly_solve on it.
>>
>> Here to_poly_solve is a function that is loaded when the maxima interface
>> initialization code is run, i.e., "load(topoly_solver)" is executed. The
>> maxima interface used by Sage's calculus code is started in calculus.py with
>> this line:
>>
>> maxima = Maxima(init_code = ['display2d:false; domain: complex; keepfloat:
>> true; load(topoly_solver)'],
>> script_subdirectory=None)
>>
>> So, my conclusion is that the topoly_solve package is somehow broken in
>> the new version of Maxima. In Maxima 5.16.3 we have:
>>
>> sage: !maxima
>> Maxima 5.16.3 http://maxima.sourceforge.net
>> Using Lisp ECL 9.4.1
>> Distributed under the GNU Public License. See the file COPYING.
>> Dedicated to the memory of William Schelter.
>> The function bug_report() provides bug reporting information.
>> (%i1) load(topoly_solver); domain:complex;
>> (%o1)
>> /Users/wstein/sage/build/64bit/sage/local/share/maxima/5.16.3/share/cont\
>> rib/topoly_solver.mac
>> (%i2) (%o2) complex
>> (%i3) to_poly_solve(Q = 1/sqrt(Q^2 + 2),Q);
>> Assuming that sqrt(Q^2+2) # 0
>> (%o3) [[Q = - sqrt(- sqrt(2) - 1)], [Q = sqrt(sqrt(2) - 1)]]
>>
>> Notice that we got both solutions! Does exactly the same input in Maxima
>> 5.19 not work right?
>>
>> William
>>
> No, I only get one solution:
He said it was fixed in 5.18. Maybe it is broken again in 5.19?
William
>
>
> (%i5) drkirkby at smudge:[~/sage/sage-4.1.1.rc0] $ ./local/bin/maxima
> ;;; Loading
> #P"/export/home/drkirkby/sage/sage-4.1.1.rc0/local/lib/ecl-9.8.1/defsystem.fas"
> ;;; Loading
> #P"/export/home/drkirkby/sage/sage-4.1.1.rc0/local/lib/ecl-9.8.1/cmp.fas"
> ;;; Loading
> #P"/export/home/drkirkby/sage/sage-4.1.1.rc0/local/lib/ecl-9.8.1/sysfun.lsp"
> Maxima 5.19.0 http://maxima.sourceforge.net
> Using Lisp ECL 9.8.1
> Distributed under the GNU Public License. See the file COPYING.
> Dedicated to the memory of William Schelter.
> The function bug_report() provides bug reporting information.
> (%i1) load(topoly_solver); domain:complex;
> (%o1)
> /export/home/drkirkby/sage/sage-4.1.1.rc0/local/share/maxima/5.19.0/shar\
> e/contrib/topoly_solver.mac
> (%o2) complex
> (%i3) to_poly_solve(Q = 1/sqrt(Q^2 + 2),Q);
> 1
> (%o3) [[Q = -----------------]]
> sqrt(sqrt(2) + 1)
> (%i4)
>
>
> With Mathematica 7 I get two solutions (not sure what version you are
> using).
>
> In[4]:= Solve[ Q Sqrt[Q^2 + 2] -1 ==0,Q]
>
> Out[4]= {{Q -> Sqrt[-1 + Sqrt[2]]}, {Q -> -I Sqrt[1 + Sqrt[2]]}}
>
>
> Anyway, it is time for me to go to bed now. If you want to look at the test
> log in Sage, it is here as an attachment. It is not on 't2' at this point.
>
> http://sagetrac.org/sage_trac/ticket/6709
>
>
> Dave
>
>
>
>
--
William Stein
Associate Professor of Mathematics
University of Washington
http://wstein.org