Thanks a lot for the answers ,makes more sense to me now . Just thought of
asking this because I realized that there are some use cases of the above .
A simple one being that some expressions of the form Product( f(x) , (x ,
1 ,oo)).doit() which would eventually diverge could return oo instead of
returning self like
x = Symbol('x' ,integer =True, Positive=True)
Product( x , (x , 1 ,oo)).doit()
Product(1 +1/x**S(2/3) , (x, 1 ,oo)).doit()
As these calculations would involve 1**oo in the code workflow , returning
1 instead of nan would solve the problem as per our convenience but wasn't
sure if it's correct in all Mathematical aspects !!!!!
What I personally felt or rather what I used to believe without much
mathematical insight was that
" anything tending to 1 and not exactly 1" raised to the power of "
anything tending to oo (always the case as oo is not exact /defined )"
should give nan and correctly represents an Indeterminant form .
Like we do in case of limits
In [32]: limit((1 + 1/n**2)**n, n, oo)
Out[32]: 1
Here the expression tends to 1 and is not exactly 1 .
But .....
" exact 1 " raise to the power of "anything tending to infinity" would be 1
!!!
I will surely give more thought about this considering mathematical
correctness and other aspects!
On Sun, 7 Nov 2021, 00:07 Chris Smith, <[email protected]> wrote:
> There are ways to protect the path leading to `1**oo` but the expression
> itself is agnostic to path. An appeal that it give 1 has been made here:
> https://github.com/sympy/sympy/pull/21619
>
> /c
>
> On Saturday, November 6, 2021 at 11:55:14 AM UTC-5 [email protected]
> wrote:
>
>> I am just a hobby mathematician, but it seems to me like this:
>>
>> 1^oo := lim(1^n) = lim(1) = 1.
>>
>> The other 'limits' seem to me to be an inadmissible 'exchange' of limits:
>> 1 != (1 + 1/n) for any finite n
>>
>> On Sat 6. Nov 2021 at 14:15, Oscar Benjamin <[email protected]>
>> wrote:
>>
>>> On Sat, 6 Nov 2021 at 11:58, Anderson Bhat <[email protected]> wrote:
>>> >
>>> > Hello guys , I am working on couple of Pr's extending the
>>> functionality of the doit method in the concrete module , I noticed that
>>> one inconsistency leads to couple of errors . Product(1, (n, 1, oo)).doit()
>>> returns 1 and 1**oo returns NaN. Other integers work as expected . These
>>> expressions are equivalent right ??? or am I missing something !
>>>
>>> The expression 1**oo is indeterminate because there are different ways
>>> that you could arrive at this form that have different limits:
>>>
>>> In [31]: limit((1 + 1/n)**n, n, oo)
>>> Out[31]: ℯ
>>>
>>> In [32]: limit((1 + 1/n**2)**n, n, oo)
>>> Out[32]: 1
>>>
>>> In [33]: limit((1 + 1/sqrt(n))**n, n, oo)
>>> Out[33]: ∞
>>>
>>> The product in your case defines a particular limit so it is not
>>> indeterminate:
>>>
>>> In [38]: Product(1, (n, 1, m)).doit()
>>> Out[38]: 1
>>>
>>> In [39]: limit(Product(1, (n, 1, m)).doit(), m, oo)
>>> Out[39]: 1
>>>
>>> --
>>> Oscar
>>>
>>> --
>>> You received this message because you are subscribed to the Google
>>> Groups "sympy" group.
>>> To unsubscribe from this group and stop receiving emails from it, send
>>> an email to [email protected].
>>> To view this discussion on the web visit
>>> https://groups.google.com/d/msgid/sympy/CAHVvXxTS%2BA32brrRS7xZ7Rr7kJ%2BLG%2BxJ6Jre1sys8_iHVzZ7tg%40mail.gmail.com
>>> .
>>>
>> --
>> Best regards,
>>
>> Peter Stahlecker
>>
> --
> You received this message because you are subscribed to the Google Groups
> "sympy" group.
> To unsubscribe from this group and stop receiving emails from it, send an
> email to [email protected].
> To view this discussion on the web visit
> https://groups.google.com/d/msgid/sympy/3204172b-dd2b-4356-9bd8-d96fbfe09a5fn%40googlegroups.com
> <https://groups.google.com/d/msgid/sympy/3204172b-dd2b-4356-9bd8-d96fbfe09a5fn%40googlegroups.com?utm_medium=email&utm_source=footer>
> .
>
--
You received this message because you are subscribed to the Google Groups
"sympy" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To view this discussion on the web visit
https://groups.google.com/d/msgid/sympy/CACK4JX_PMZ_PGUM_L%3DrpiQKoMtH-sVHHJ9JtW0bk15e5uLZ9AA%40mail.gmail.com.
