Fwd: [sage-release] Bug in limit?

[David Joyner]

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 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

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--
William (http://wstein.org)

[kcrisman]

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?

I've been wondering about this as well (also integrals) for some time.  Unfortunately I haven't had time to systematically try things out.   

[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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[Dima Pasechnik]

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

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

 

[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

[Dima Pasechnik]

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:

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

[William Stein]

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

William

[Nils Bruin]

On Monday, November 23, 2015 at 11:20:23 AM UTC-8, Dima Pasechnik wrote:

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

The stack overflow does happen in maxima, as you can see from the error messages that are printed upon failure in sage (the leading ";" gives a very lispy taste)

Indeed, if you execute

domain: complex;

limit(2/5*((3/4)^m - 1)*(a0 - 1000000) + 1/5*(3*(3/4)^m + 2)*a0,m,inf);

things go haywire. Indeed, it's not hard to see how this limit might be problematic when viewed in terms of multi-valued complex functions.

Maxima/SBCL fails a little less harshly, but still fails on a lisp error.

I'm not sure if with "domain: complex" (which sage uses in maxima) this limit makes sense, but the way maxima fails is definitely a reportable bug in maxima.



 

[Sergey Kirpichev]

On Monday, November 23, 2015 at 3:43:02 AM UTC+3, William wrote:

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

This is not a maxima bug:

 Maxima 5.34.1 http://maxima.sourceforge.net
using Lisp GNU Common Lisp (GCL) GCL 2.6.12 (a.k.a. GCL)
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) limit(2/5*((3/4)^m - 1)*(a0 - 1000000) + 1/5*(3*(3/4)^m + 2)*a0, m, inf);
(%o1)                               400000

or git version:
Maxima branch_5_37_base_186_gfa7cd4a http://maxima.sourceforge.net
using Lisp CLISP 2.49 (2010-07-07)
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) limit(2/5*((3/4)^m - 1)*(a0 - 1000000) + 1/5*(3*(3/4)^m + 2)*a0, m, inf);
(%o1)                               400000

In fact, limit algorithm implementation in sympy is known to be
broken.  (Hopefuly, this is fixed there:
https://github.com/skirpichev/omg/, but this is not sympy.)

At some point, presumably sympy will be uniformly better than maxima?

I think that as ex-dev of sympy I have good reasons to believe that
it's not the case..  Maxima community has less 1st year college students but
much more knowlegeable people.

[Sergey Kirpichev]

On Monday, November 23, 2015 at 10:38:39 PM UTC+3, Ondrej Certik wrote:

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

Maxima's, of course.  btw, sympy's answer is same:
 In [3]: limit(S(2)/5*((S(3)/4)**m - 1)*(a0 - 1000000) + S(1)/5*(3*(S(3)/4)**m + 2)*a0, m, oo)
Out[3]: 400000

I suspect just a typo in the William's reply.

[Dima Pasechnik]

On Tuesday, 24 November 2015 11:12:13 UTC, Sergey Kirpichev wrote:

On Monday, November 23, 2015 at 3:43:02 AM UTC+3, William wrote:

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

This is not a maxima bug:

 Maxima 5.34.1 http://maxima.sourceforge.net
using Lisp GNU Common Lisp (GCL) GCL 2.6.12 (a.k.a. GCL)
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) limit(2/5*((3/4)^m - 1)*(a0 - 1000000) + 1/5*(3*(3/4)^m + 2)*a0, m, inf);
(%o1)                               400000

If you first set domain to complex (and this is the setting Sage uses to call maxima), you get the same
error as from Sage. See https://groups.google.com/d/msg/sage-support/rAkql0-A6cM/8zPsNUsYCAAJ

 

[Dima Pasechnik]

On Tuesday, 24 November 2015 11:12:13 UTC, Sergey Kirpichev wrote:

yes, it was a typo - as confirmed by William: https://groups.google.com/d/msg/sage-support/rAkql0-A6cM/u4QxjVsXCAAJ

It seems that for some reason you haven't got the latest messages on this, or they were not
cross-posted as widely as some others.

 

 

[Sergey B Kirpichev]

On Tue, Nov 24, 2015 at 04:12:52AM -0800, Dima Pasechnik wrote:
> If you first set domain to complex (and this is the setting Sage uses to
> call maxima), you get the same error as from Sage.

I have seen this post. My messages arrive too late due to moderation, so
they a little dated. Sorry for that.