Re: [sage-support] Fwd: [sage-release] Bug in limit?

[William Stein]

This definitely looks like a bug. In the meantime, a workaround is to
use sympy:

sage: var('m a0')
(m, a0)
sage: x=2/5*((3/4)^m - 1)*(a0 - 1000000) + 1/5*(3*(3/4)^m + 2)*a0;x
2/5*((3/4)^m - 1)*(a0 - 1000000) + 1/5*(3*(3/4)^m + 2)*a0
sage: limit(x, m=oo)
[BAD]
sage: limit(x, m=oo, algorithm='sympy')
4000000

I wonder -- to what extent should we be using maxima by default still
for limits, instead of sympy...? At some point, presumably sympy will
be uniformly better than maxima?

Public worksheet:

https://cloud.sagemath.com/projects/4a5f0542-5873-4eed-a85c-a18c706e8bcd/files/support/2015-11-22-163829-limit.sagews

On Sun, Nov 22, 2015 at 2:00 PM, David Joyner <wdjo...@gmail.com> wrote:
> Forwarded to the correct list
>
> ---------- Forwarded message ----------
> From: G. M.-S. <list...@gmail.com>
> Date: Sun, Nov 22, 2015 at 4:34 PM
> Subject: [sage-release] Bug in limit?
> To: sage-r...@googlegroups.com
>
>
>
> Hello.
>
> This is my first post, please be indulgent.
>
> Is the following a bug?
>
> Thanks in advance.
>
> Guillermo Moreno-Socías
>
> ┌────────────────────────────────────────────────────────────────────┐
> │ SageMath Version 6.9, Release Date: 2015-10-10 │
> │ Type "notebook()" for the browser-based notebook interface. │
> │ Type "help()" for help. │
> └────────────────────────────────────────────────────────────────────┘
> sage: var('m a0')
> (m, a0)
> sage: x=2/5*((3/4)^m - 1)*(a0 - 1000000) + 1/5*(3*(3/4)^m + 2)*a0;x
> 2/5*((3/4)^m - 1)*(a0 - 1000000) + 1/5*(3*(3/4)^m + 2)*a0
> sage: limit(x,m=oo)
>
> ;;;
> ;;; Detected access to protected memory, also kwown as 'bus or
> segmentation fault'.
> ;;; Jumping to the outermost toplevel prompt
> ;;;
>
> (Note that if x is expanded then the limit is correctly calculated.)
>
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--
William (http://wstein.org)

[Aaron Meurer]

(note, I am not on the sage list or gms list, so this probably won't
make it there unless someone forwards it)

SymPy's limit primarily uses the Gruntz algorithm, which is fairly
capable. I'm not an expert on it, so others will be able to comment in
more detail, but as far as I know, it's mostly reliant on the ability
to compute series expansions, which SymPy has built up quite a bit.
Computing series expansions and limits with this algorithm was one of
the first things SymPy was able to do when Ondrej created it back in
2005 (IIRC), so it's fairly developed. I believe the algorithm has
some difficulties with expressions with trigonometric functions (but
again, others should comment on that).

What algorithms does Maxima implement? Does Sage generally only use
one backend or can it also use fallback mechanisms. SymPy should
generally raise NotImplementedError (or maybe another error if there
is a bug) if it can't compute a limit.

Aaron Meurer

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[Ondřej Čertík]

On Mon, Nov 23, 2015 at 12:20 PM, Dima Pasechnik <dim...@gmail.com> wrote:

>
>
> On Monday, 23 November 2015 00:43:02 UTC, William wrote:
>>
>> This definitely looks like a bug. In the meantime, a workaround is to
>> use sympy:
>>
>> sage: var('m a0')
>> (m, a0)
>> sage: x=2/5*((3/4)^m - 1)*(a0 - 1000000) + 1/5*(3*(3/4)^m + 2)*a0;x
>> 2/5*((3/4)^m - 1)*(a0 - 1000000) + 1/5*(3*(3/4)^m + 2)*a0
>> sage: limit(x, m=oo)
>> [BAD]
>> sage: limit(x, m=oo, algorithm='sympy')
>> 4000000
>>
>> I wonder -- to what extent should we be using maxima by default still
>> for limits, instead of sympy...? At some point, presumably sympy will
>> be uniformly better than maxima?
>
>

> the bug is not really in maxima, it's in Sage's interface to maxima:
>
> (%i7) limit(2/5*((3/4)^m - 1)*(a0 - 1000000) + 1/5*(3*(3/4)^m +
> 2)*a0,m,inf);
> (%o7) 400000

Note that William's result has one more zero in the answer... Which
one is correct?

Ondrej

>
> (this is with 'sage --maxima')
> probably extra maxima packages loaded along with maxima cause this OOM in
> Sage.

[William Stein]

On Mon, Nov 23, 2015 at 12:17 PM, Dima Pasechnik <dim...@gmail.com> wrote:

>
>
> On Monday, 23 November 2015 19:38:39 UTC, Ondrej Certik wrote:
>>
>> On Mon, Nov 23, 2015 at 12:20 PM, Dima Pasechnik <dim...@gmail.com> wrote:
>> >
>> >
>> > On Monday, 23 November 2015 00:43:02 UTC, William wrote:
>> >>
>> >> This definitely looks like a bug. In the meantime, a workaround is to
>> >> use sympy:
>> >>
>> >> sage: var('m a0')
>> >> (m, a0)
>> >> sage: x=2/5*((3/4)^m - 1)*(a0 - 1000000) + 1/5*(3*(3/4)^m + 2)*a0;x
>> >> 2/5*((3/4)^m - 1)*(a0 - 1000000) + 1/5*(3*(3/4)^m + 2)*a0
>> >> sage: limit(x, m=oo)
>> >> [BAD]
>> >> sage: limit(x, m=oo, algorithm='sympy')
>> >> 4000000
>> >>
>> >> I wonder -- to what extent should we be using maxima by default still
>> >> for limits, instead of sympy...? At some point, presumably sympy will
>> >> be uniformly better than maxima?
>> >
>> >
>> > the bug is not really in maxima, it's in Sage's interface to maxima:
>> >
>> > (%i7) limit(2/5*((3/4)^m - 1)*(a0 - 1000000) + 1/5*(3*(3/4)^m +
>> > 2)*a0,m,inf);
>> > (%o7) 400000
>>
>> Note that William's result has one more zero in the answer... Which
>> one is correct?
>
>

> one doesn't need a computer here :)
> lim_{m->oo} 2/5*((3/4)^m - 1)*(a0 - 1000000) + 1/5*(3*(3/4)^m + 2)*a0 =
> 2/5*(0 - 1)*(a0 - 10^6) + 1/5*(0 + 2)*a0=2*10^6/5 = 400000
>
> I don't know where extra 0 came from, I get the same answer as maxima or my
> pen:

Copy/paste error. I gave a link to the actual session where everything is fine.

William

>
> sage: x=2/5*((3/4)^m - 1)*(a0 - 1000000) + 1/5*(3*(3/4)^m + 2)*a0;x
> 2/5*((3/4)^m - 1)*(a0 - 1000000) + 1/5*(3*(3/4)^m + 2)*a0

> sage: limit(x, m=oo, algorithm="sympy")
> 400000
>
> Dima