Dear Dima,
thanks for your input. Three additions: (i) I had overlooked that, but in
fact one can directly call the qepcad shell within sage by
'qepcad_console()'. (ii) The described error results from the frontend, it
apparently misinterprets the result returned by the qepcad backend if it
fails due to low memory. (iii) Indeed, I know msolve and it looks very
promising. The system I sent is not the one I actually wanted to study, it
resulted from reducing a bigger system which shows the unexpected behavior.
-- Peter Mueller
dim...@gmail.com schrieb am Dienstag, 12. Juli 2022 um 14:06:50 UTC+2:
> On Mon, Jul 11, 2022 at 8:24 PM 'Peter Mueller' via sage-support
> <sage-s...@googlegroups.com> wrote:
> >
> > OK, calling "sage -sh" and setting "export qe="~/local/sage/local"
> allows to start qepcad without relocating files. However, qepcad fails for
> this rather small example , telling "Failure occurred in: GCSI (final
> check) Reason for the failure: Too few cells reclaimed." So either (i)
> qepcad has a bug here, or (ii) qepcad's abilities are rather limited, or
> (iii) I'm not using it the right way. If (i) or (ii) applies, there is
> little hope for improvements, since the project seems to have abandoned in
> 2012.
>
> qepcad is certainly too old to be saved. One ought to implement
> cylindrical algebraic decomposition (CAD)
> in a modern way, e.g. in Sage...
>
> On a practical side of things, I'd have converted your system into a
> system of equations (using squares etc
> to model inequalities) and then looked for real solutions only (e.g.
> using msolve).
>
> HTH
> Dima
> >
> > dim...@gmail.com schrieb am Montag, 11. Juli 2022 um 19:11:08 UTC+2:
> >>
> >>
> >>
> >> On Mon, 11 Jul 2022, 17:04 'Peter Mueller' via sage-support, <
> sage-s...@googlegroups.com> wrote:
> >>>
> >>> Thanks for the suggestion, I wasn't aware of this feature. However,
> here it results in "Error HELPFRD: Could not open
> ~/local/sage/local/bin/qepcad/share/qepcad/qepcad.help". Unfortunately, the
> binary of qepcad is the file ~/local/sage/local/bin/qepcad, so I cannot
> symlink the existing help page (at
> ~/local/sage/local/share/qepcad/qepcad.help) to the place where qepcad is
> looking for it.
> >>
> >>
> >> you can move ~/local/sage/local/bin/qepcad
> >> somewhere (e.g. rename it) and create the necessary link.
> >>
> >>>
> >>>
> >>>
> >>> dim...@gmail.com schrieb am Montag, 11. Juli 2022 um 17:40:11 UTC+2:
> >>>>
> >>>>
> >>>>
> >>>> On Mon, 11 Jul 2022, 16:33 'Peter Mueller' via sage-support, <
> sage-s...@googlegroups.com> wrote:
> >>>>>
> >>>>> When running
> >>>>>
> >>>>> var('p1', 'p2', 'p3', 'q1', 'q2', 'q3')
> >>>>> qf = qepcad_formula
> >>>>> # q1 = p1
> >>>>> l = [p1+q1 == 1, 0 < p1, p1 < 1,
> >>>>> 0 <= p2, p2 <= 1, 0 <= q2, q2 <= 1,
> >>>>> p2 + p1*q1 + q2 == 1,
> >>>>> 0 <= p3, p3 <= 1, 0 <= q3, q3 <= 1,
> >>>>> p3 + p2*q1 + p1*q2 + q3 == 1]
> >>>>> F = qepcad_formula.and_(l)
> >>>>> qepcad(F, solution='any-point')
> >>>>>
> >>>>> I get the wrong answer
> >>>>>
> >>>>> ValueError: input formula is false everywhere
> >>>>>
> >>>>> However, this set of inequalities has solutions. In fact, if there
> were no solution, this should hold even more if we remove the comment in
> >>>>>
> >>>>> # q1 = p1
> >>>>>
> >>>>> above. However, doing that produces a correct solution
> >>>>>
> >>>>> {'p1': 1/2, 'p2': 0, 'p3': 0, 'q2': 3/4, 'q3': 5/8}.
> >>>>>
> >>>>> Am I doing something wrong? If it is a bug, then I don't know if
> comes from the interface to qepcad, or qepcad itself.
> >>>>
> >>>>
> >>>> you can try running qepcad standalone, at
> >>>> ./sage -sh
> >>>> prompt, and try reproducing...
> >>>>
> >>>>
> >>>> https://www.usna.edu/CS/qepcadweb/B/QEPCAD.html
> >>>>>
> >>>>>
> >>>>> I've tried the above example in Sage versions 9.6 and 9.7.beta3 on a
> linux machine.
> >>>>>
> >>>>> -- Peter Mueller
> >>>>>
> >>>>> --
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