Re: [sage-devel] Incorrect result for `sum(1/factorial(n**2),n,1,oo)`
On Fri, Apr 26, 2024 at 2:24 PM Georgi Guninski wrote: > > On Thu, Feb 15, 2024 at 2:27 AM Dima Pasechnik wrote: > > > > I've filed https://sourceforge.net/p/maxima/bugs/4262/ > > > > Is maxima supported? > There is no progress on their bug system for more than 2 months. not many people are involved, and some bugs stay open for years there. > SEGV is not pleasant, but incorrect symbolic result casts doubts about > all symbolic sage computations, especially those that can't be > verified numerically. > > -- > You received this message because you are subscribed to the Google Groups > "sage-devel" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-devel+unsubscr...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sage-devel/CAGUWgD_MWht0_wBwXXsH-c%3DpKGSXUCgNBEbKq4PyLRc3g5k%3D_Q%40mail.gmail.com. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAAWYfq0mzJCU2MOhgGFKZCfwNtMU0J3cuOmddWxGY6dEqqi9PA%40mail.gmail.com.
Re: [sage-devel] Incorrect result for `sum(1/factorial(n**2),n,1,oo)`
On Thu, Feb 15, 2024 at 2:27 AM Dima Pasechnik wrote: > > I've filed https://sourceforge.net/p/maxima/bugs/4262/ > Is maxima supported? There is no progress on their bug system for more than 2 months. SEGV is not pleasant, but incorrect symbolic result casts doubts about all symbolic sage computations, especially those that can't be verified numerically. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD_MWht0_wBwXXsH-c%3DpKGSXUCgNBEbKq4PyLRc3g5k%3D_Q%40mail.gmail.com.
Re: [sage-devel] Incorrect result for `sum(1/factorial(n**2),n,1,oo)`
I've filed https://sourceforge.net/p/maxima/bugs/4262/
On Wed, Feb 14, 2024 at 7:14 PM Dima Pasechnik wrote:
>
>
> On Wed, Feb 14, 2024 at 6:12 PM Oscar Benjamin
> wrote:
>
>> Maxima's simplify_sum function produces something similar looking:
>>
>> (%i4) load("simplify_sum");
>> (%o4) "/usr/share/maxima/5.45.1/share/solve_rec/simplify_sum.mac"
>>
>> (%i5) sum(1/factorial(n^2), n, 1, inf), simpsum;
>> (%o5) 'sum(1/(n^2)!,n,1,inf)
>>
>> (%i6) simplify_sum(%);
>>
>
> Oh, I see - I missed an explicit call to simplify_sum.
>
> 1/'product(n^2+%,%,1,2*n+1) non-rational term ratio to nusum
>> 1/'product(n^2+%,%,1,2*n+1) non-rational term ratio to nusum
>> (%o6) %f[1,4]([1],[1-%i,%i+1,1-sqrt(2)*%i,sqrt(2)*%i+1],1)
>>
>
> It seems to be a bug in simplify_sum() - nusum can't do it (
> "non-rational term ratio to nusum")
> indeed, it's obvious that the sum is not hypergeometric, as the consequent
> terms ratio is not of the right type,
> so it does try something more clever - but fails.
>
> Dima
>
>>
>> --
>> Oscar
>>
>> On Wed, 14 Feb 2024 at 17:52, Dima Pasechnik wrote:
>> >
>> > It appears to come from Maxima, but I have trouble reproducing this in
>> Maxima.
>> > Perhaps it's a bug in the Maxima interface?
>> > Is there a direct way to see how Maxima is called in this instance?
>> >
>> > Dima
>> >
>> >
>> > On Mon, Feb 12, 2024 at 2:53 PM Georgi Guninski
>> wrote:
>> >>
>> >> There is discussion about this on mathoverlow [1]:
>> >>
>> >> The closed form of `sum(1/factorial(n**2),n,1,oo)` doesn't appear
>> >> correct and it contradicts numerical computations, including
>> verification
>> >> with mpmath.
>> >>
>> >> Session:
>> >>
>> >> sage: import mpmath
>> >> sage: su4=sum(1/factorial(n**2),n,1,oo);su4
>> >> hypergeometric((1,), (-I + 1, I + 1, -I*sqrt(2) + 1, I*sqrt(2) + 1), 1)
>> >> sage: CC(su4)
>> >> 1.17227289255719 - 7.88860905221012e-31*I
>> >> sage: mpmath.hyper((1,), (-I + 1, I + 1, -I*sqrt(2) + 1, I*sqrt(2) +
>> 1), 1)
>> >> mpc(real='1.1722728925571919', imag='-6.9025329206838533e-31')
>> >> sage: su5=sum(1/factorial(i**2) for i in range(1,100))
>> >> sage: CC(su5)
>> >> 1.04166942239864
>> >>
>> >> sage: mpmath.nsum(lambda n: 1/mpmath.gamma(1+n**2),[1,mpmath.inf])
>> >> mpf('1.0416694223986369')
>> >>
>> >>
>> >> [1]:
>> https://mathoverflow.net/questions/463964/factorial-series-jd-sum-n-1-infty-frac1nd-and-hypergeometric-fu
>> >>
>> >> --
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>> Groups "sage-devel" group.
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>> an email to sage-devel+unsubscr...@googlegroups.com.
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>> .
>> >
>> > --
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>> .
>>
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>> .
>>
>
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Re: [sage-devel] Incorrect result for `sum(1/factorial(n**2),n,1,oo)`
On Wed, Feb 14, 2024 at 6:12 PM Oscar Benjamin
wrote:
> Maxima's simplify_sum function produces something similar looking:
>
> (%i4) load("simplify_sum");
> (%o4) "/usr/share/maxima/5.45.1/share/solve_rec/simplify_sum.mac"
>
> (%i5) sum(1/factorial(n^2), n, 1, inf), simpsum;
> (%o5) 'sum(1/(n^2)!,n,1,inf)
>
> (%i6) simplify_sum(%);
>
Oh, I see - I missed an explicit call to simplify_sum.
1/'product(n^2+%,%,1,2*n+1) non-rational term ratio to nusum
> 1/'product(n^2+%,%,1,2*n+1) non-rational term ratio to nusum
> (%o6) %f[1,4]([1],[1-%i,%i+1,1-sqrt(2)*%i,sqrt(2)*%i+1],1)
>
It seems to be a bug in simplify_sum() - nusum can't do it ( "non-rational
term ratio to nusum")
indeed, it's obvious that the sum is not hypergeometric, as the consequent
terms ratio is not of the right type,
so it does try something more clever - but fails.
Dima
>
> --
> Oscar
>
> On Wed, 14 Feb 2024 at 17:52, Dima Pasechnik wrote:
> >
> > It appears to come from Maxima, but I have trouble reproducing this in
> Maxima.
> > Perhaps it's a bug in the Maxima interface?
> > Is there a direct way to see how Maxima is called in this instance?
> >
> > Dima
> >
> >
> > On Mon, Feb 12, 2024 at 2:53 PM Georgi Guninski
> wrote:
> >>
> >> There is discussion about this on mathoverlow [1]:
> >>
> >> The closed form of `sum(1/factorial(n**2),n,1,oo)` doesn't appear
> >> correct and it contradicts numerical computations, including
> verification
> >> with mpmath.
> >>
> >> Session:
> >>
> >> sage: import mpmath
> >> sage: su4=sum(1/factorial(n**2),n,1,oo);su4
> >> hypergeometric((1,), (-I + 1, I + 1, -I*sqrt(2) + 1, I*sqrt(2) + 1), 1)
> >> sage: CC(su4)
> >> 1.17227289255719 - 7.88860905221012e-31*I
> >> sage: mpmath.hyper((1,), (-I + 1, I + 1, -I*sqrt(2) + 1, I*sqrt(2) +
> 1), 1)
> >> mpc(real='1.1722728925571919', imag='-6.9025329206838533e-31')
> >> sage: su5=sum(1/factorial(i**2) for i in range(1,100))
> >> sage: CC(su5)
> >> 1.04166942239864
> >>
> >> sage: mpmath.nsum(lambda n: 1/mpmath.gamma(1+n**2),[1,mpmath.inf])
> >> mpf('1.0416694223986369')
> >>
> >>
> >> [1]:
> https://mathoverflow.net/questions/463964/factorial-series-jd-sum-n-1-infty-frac1nd-and-hypergeometric-fu
> >>
> >> --
> >> You received this message because you are subscribed to the Google
> Groups "sage-devel" group.
> >> To unsubscribe from this group and stop receiving emails from it, send
> an email to sage-devel+unsubscr...@googlegroups.com.
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> .
> >
> > --
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> .
>
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> .
>
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Re: [sage-devel] Incorrect result for `sum(1/factorial(n**2),n,1,oo)`
Maxima's simplify_sum function produces something similar looking:
(%i4) load("simplify_sum");
(%o4) "/usr/share/maxima/5.45.1/share/solve_rec/simplify_sum.mac"
(%i5) sum(1/factorial(n^2), n, 1, inf), simpsum;
(%o5) 'sum(1/(n^2)!,n,1,inf)
(%i6) simplify_sum(%);
1/'product(n^2+%,%,1,2*n+1) non-rational term ratio to nusum
1/'product(n^2+%,%,1,2*n+1) non-rational term ratio to nusum
(%o6) %f[1,4]([1],[1-%i,%i+1,1-sqrt(2)*%i,sqrt(2)*%i+1],1)
--
Oscar
On Wed, 14 Feb 2024 at 17:52, Dima Pasechnik wrote:
>
> It appears to come from Maxima, but I have trouble reproducing this in Maxima.
> Perhaps it's a bug in the Maxima interface?
> Is there a direct way to see how Maxima is called in this instance?
>
> Dima
>
>
> On Mon, Feb 12, 2024 at 2:53 PM Georgi Guninski wrote:
>>
>> There is discussion about this on mathoverlow [1]:
>>
>> The closed form of `sum(1/factorial(n**2),n,1,oo)` doesn't appear
>> correct and it contradicts numerical computations, including verification
>> with mpmath.
>>
>> Session:
>>
>> sage: import mpmath
>> sage: su4=sum(1/factorial(n**2),n,1,oo);su4
>> hypergeometric((1,), (-I + 1, I + 1, -I*sqrt(2) + 1, I*sqrt(2) + 1), 1)
>> sage: CC(su4)
>> 1.17227289255719 - 7.88860905221012e-31*I
>> sage: mpmath.hyper((1,), (-I + 1, I + 1, -I*sqrt(2) + 1, I*sqrt(2) + 1), 1)
>> mpc(real='1.1722728925571919', imag='-6.9025329206838533e-31')
>> sage: su5=sum(1/factorial(i**2) for i in range(1,100))
>> sage: CC(su5)
>> 1.04166942239864
>>
>> sage: mpmath.nsum(lambda n: 1/mpmath.gamma(1+n**2),[1,mpmath.inf])
>> mpf('1.0416694223986369')
>>
>>
>> [1]:
>> https://mathoverflow.net/questions/463964/factorial-series-jd-sum-n-1-infty-frac1nd-and-hypergeometric-fu
>>
>> --
>> You received this message because you are subscribed to the Google Groups
>> "sage-devel" group.
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>> email to sage-devel+unsubscr...@googlegroups.com.
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>
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Re: [sage-devel] Incorrect result for `sum(1/factorial(n**2),n,1,oo)`
It appears to come from Maxima, but I have trouble reproducing this in
Maxima.
Perhaps it's a bug in the Maxima interface?
Is there a direct way to see how Maxima is called in this instance?
Dima
On Mon, Feb 12, 2024 at 2:53 PM Georgi Guninski wrote:
> There is discussion about this on mathoverlow [1]:
>
> The closed form of `sum(1/factorial(n**2),n,1,oo)` doesn't appear
> correct and it contradicts numerical computations, including verification
> with mpmath.
>
> Session:
>
> sage: import mpmath
> sage: su4=sum(1/factorial(n**2),n,1,oo);su4
> hypergeometric((1,), (-I + 1, I + 1, -I*sqrt(2) + 1, I*sqrt(2) + 1), 1)
> sage: CC(su4)
> 1.17227289255719 - 7.88860905221012e-31*I
> sage: mpmath.hyper((1,), (-I + 1, I + 1, -I*sqrt(2) + 1, I*sqrt(2) + 1), 1)
> mpc(real='1.1722728925571919', imag='-6.9025329206838533e-31')
> sage: su5=sum(1/factorial(i**2) for i in range(1,100))
> sage: CC(su5)
> 1.04166942239864
>
> sage: mpmath.nsum(lambda n: 1/mpmath.gamma(1+n**2),[1,mpmath.inf])
> mpf('1.0416694223986369')
>
>
> [1]:
> https://mathoverflow.net/questions/463964/factorial-series-jd-sum-n-1-infty-frac1nd-and-hypergeometric-fu
>
> --
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> .
>
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[sage-devel] Incorrect result for `sum(1/factorial(n**2),n,1,oo)`
There is discussion about this on mathoverlow [1]:
The closed form of `sum(1/factorial(n**2),n,1,oo)` doesn't appear
correct and it contradicts numerical computations, including verification
with mpmath.
Session:
sage: import mpmath
sage: su4=sum(1/factorial(n**2),n,1,oo);su4
hypergeometric((1,), (-I + 1, I + 1, -I*sqrt(2) + 1, I*sqrt(2) + 1), 1)
sage: CC(su4)
1.17227289255719 - 7.88860905221012e-31*I
sage: mpmath.hyper((1,), (-I + 1, I + 1, -I*sqrt(2) + 1, I*sqrt(2) + 1), 1)
mpc(real='1.1722728925571919', imag='-6.9025329206838533e-31')
sage: su5=sum(1/factorial(i**2) for i in range(1,100))
sage: CC(su5)
1.04166942239864
sage: mpmath.nsum(lambda n: 1/mpmath.gamma(1+n**2),[1,mpmath.inf])
mpf('1.0416694223986369')
[1]:
https://mathoverflow.net/questions/463964/factorial-series-jd-sum-n-1-infty-frac1nd-and-hypergeometric-fu
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