Investigating the error shows that sympy didn't do anything with this sum:
671 try:
--> 672 return result._sage_()
673 except AttributeError:
674 raise AttributeError("Unable to convert SymPy result
(={}) into"
ipdb> p result
Sum(log(1 - 1/2**k), (k, 1, oo))
so while solving the "NotImplemented" error would be nice, it wouldn't get
you anything you didn't have already. The question then really is how to
*numerically* evaluate an infinite sum in sage. As shown above, one way
could be to use sympy for this. It may be that numerical sum evaluation
hasn't received much attention in sage. The link below also suggests using
sympy:
https://ask.sagemath.org/question/32122/how-to-evaluate-the-infinite-sum-of-12n-1-over-all-positive-integers/
I'm not sure how rigorous these methods are. You may have to do some
analysis yourself to guarantee an error bound.
On Tuesday, 10 December 2024 at 06:15:33 UTC-8 krts...@googlemail.com wrote:
> Thanks for investigating. I tried to use sympy this way:
>
> sum(log(1-2^-k),k,1,oo,algorithm="sympy")
>
> but this failed for other reasons (NotImplementedError: conversion to
> SageMath is not implemented)
>
>
>
> wdjo...@gmail.com schrieb am Dienstag, 10. Dezember 2024 um 14:58:49
> UTC+1:
>
>> On Tue, Dec 10, 2024 at 8:43 AM 'OHappyDay' via sage-support <
>> sage-s...@googlegroups.com> wrote:
>>
>>> I tried to evaluate the infinite product:
>>>
>>> prod((2^n-1)/2^n) (n=1,oo)
>>>
>>> by converting the product to a sum via logarithm:
>>>
>>> sum(log(1-2^-k),k,1,oo)
>>>
>>> The sum (and thus the product) should, according to WolframAlpha,
>>> converge with a final value of about
>>>
>>> -1.24206
>>>
>>
>> Sympy does it:
>>
>> sage: *from* *sympy* *import* oo, Sum, log, Product
>>
>> sage: p0 = Product((1-1/2^n), (n, 1, oo))
>>
>> sage: p0.evalf()
>>
>> 0.288788095086602
>>
>> sage: s0 = Sum( log(1-1/2^n), (n, 1, oo))
>>
>> sage: s0.evalf()
>>
>> -1.24206209481242
>>
>> sage: exp(-1.242) ## check
>> 0.288806027885956
>>
>>
>>>
>>> This video (https://www.youtube.com/watch?v=KDyHJlNkov8) indicates that
>>> the product converges with an irrational value.
>>>
>>> Sage reports that the sum is divergent.
>>>
>>> Ideas? Is this again a failure in Maxima?
>>>
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>>> .
>>>
>>
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