Where is the design for the new assumptions-system coming from? Is the new
design based on academic papers, or on previous software, or being designed
from the ground up here? I'm interested in automated reasoning for its own
sake, but not an expert.
On Tuesday, August 18, 2020 at 2:08:37 PM UTC-7, Aaron Meurer wrote:
>
> summation() should probably have a conds argument similar to
> integrate() that lets you disable the piecewise.
>
> You can always manually extract it from the expression:
>
> >>> sympy.summation(sympy.S('z^k / k'), sympy.S('(k, 1,
> oo)')).args[0].args[0]
> -log(1 - z)
>
> Ideally refine() would let you do this, but it doesn't seem to work yet.
>
> Aaron Meurer
>
> On Tue, Aug 18, 2020 at 7:44 AM [email protected]
> <[email protected] <javascript:>> wrote:
> >
> > I'll try to clarify. Putting software aside momentarily, in pure math,
> for z real or complex with abs(z) < 1, for k from 1 to infinity, the
> following power-series summations hold:
> >
> > -log(1-x) = sum (z^k / k)
> > log(1-x) = sum(-1 * z^k / k)
> > log(1+x) = sum(-1 * z^k * (-1)^k / k)
> >
> > Maple and Mathematica can both do those, using their sum functions. (I'm
> not 100% confident in their handling of edge cases like z=-1 and z=+1, but
> my testing their has been haphazard.)
> >
> > I keep changing my story about Maxima, as I learn more about it.
> Yesterday I said Maxima cannot do those sums. Last night I learned Maxima
> can do them, via its "simplify_sum" feature, whose documentation is hidden
> in an obscure Chapter 84. Maxima manual's "Summation" chapter includes no
> mention of "simplify_sum". (I'm curious how many decades this Maxima
> documentation-bug has persisted without anyone simply moving "simplify_sum"
> to the chapter on sums. All 55 years of Maxima's history?)
> >
> > Sympy can sum those into Piecewise expressions:
> >
> > >>> sympy.summation(sympy.S('z^k / k'), sympy.S('(k, 1, oo)'))
> > Piecewise((-log(1 - z), (z >= -1) & (z < 1)), (Sum(z**k/k, (k, 1, oo)),
> True))
> > >>>
> >
> > The catch is, there's no way to ask Sympy "what's that Piecewise
> expression assuming abs(z) < 1"? Neither old nor new Sympy assumptions can
> express that query.
> >
> > I see two issues: Lack of functionality and room for
> documentation-improvement. I haven't designed and implemented my own
> assumptions-system, so I can't speak to its difficulty. Maxima's been
> worked on by countless geniuses for 55 years and still has an admittedly
> weak assumptions system; so maybe assumptions are especially hard for
> CAS-designers.
> >
> > The second issue is documentation. I have spent many months in many
> CAS's trying to sum the power series of log(1+x). I could have accomplished
> the same in a day is the CAS's had been documented better.
> >
> >
> > On Monday, August 17, 2020 at 11:00:47 PM UTC-7 [email protected]
> wrote:
> >>
> >> David,
> >>
> >> I'm not on this project, but I think it would save the devs time if you
> would specify the sum you are referring to.
> >>
> >> -- Kind Regards,
> >> Christian
> >>
> >> On Mon, Aug 17, 2020, 3:32 PM first last <[email protected]> wrote:
> >>>
> >>> P.S. Maxima and Axiom are also unable to do this sum. Mathematica and
> Maple are able to do it.
> >>>
> >>> On Monday, August 17, 2020 at 3:30:26 PM UTC-7, first last wrote:
> >>>>
> >>>> I'll take the response as, there's no way to get Sympy to do this
> sum.
> >>>>
> >>>> On Friday, August 14, 2020 at 4:17:20 PM UTC-7, David Bailey wrote:
> >>>>>
> >>>>> Dear group,
> >>>>>
> >>>>> Am I correct that the write-up about assumptions found here relates
> to the old-style assumptions:
> >>>>>
> >>>>> https://docs.sympy.org/latest/modules/assumptions/assume.html
> >>>>>
> >>>>> Is there any documentation relating to the new assumptions?
> >>>>>
> >>>>> It would be really helpful if the documentation for old or new
> assumptions indicated which type it related to.
> >>>>>
> >>>>> David
> >>>
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>
> >
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>
>
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