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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