Re: Mathematica goes Bad
- To: mathgroup at smc.vnet.net
- Subject: [mg59465] Re: [mg59422] Mathematica goes Bad
- From: stephen layland <layland at wolfram.com>
- Date: Wed, 10 Aug 2005 02:57:10 -0400 (EDT)
- References: <200508090730.DAA19089@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
and thus spake Igor Touzov [2005.08.09 @ 03:31]:
> I am using Mathematica second year already, and found that each consequative
> version cuts off something good from what mathematica used to be.
>
> Contacting technical support only results in open ticket that never gets
> closed.
>
> Here some simple example you can run for youself:
> Timing[
> Limit[ (a ^2 k ^2 ArcTan[ ( (-a ^2 ) Cot[ [Theta]] - w y
> Tan[ [Theta]] ) / (a @ (a ^2 + ((w - y) ) ^2 + y ^2
> Tan[ [Theta]] ^2 ) )]
> Sin[2 [Theta]] ) / (2 + 2 k ^2 Sin[ [Theta]] ^2 ), [Theta] -> 0]] )
Perhaps you meant:
(a^2 k^2 ArcTan[(-a^2 Cot[\[Theta]] - w y Tan[\[Theta]])/(
a (a^2 + ((w - y))^2 + y^2 (Tan[\[Theta]])^2))] Sin[2 \[Theta]])/(2 +
2 k^2 (Sin[\[Theta]])^2)
of which the limit _does_ take longer on version 5.1 and 5.2. This
seems to be because the Direction->Automatic is doing something
different. You might try experimenting some:
In[1]:= x=(a^2 k^2 ArcTan[(-a^2 Cot[\[Theta]] - w y Tan[\[Theta]])/(
a (a^2 + ((w - y))^2 + y^2 (Tan[\[Theta]])^2))] Sin[2
\[Theta]])/(2 +
2 k^2 (Sin[\[Theta]])^2);
In[2]:= Limit[x,\[Theta]->0]//Timing
Out[2]= {11.69 Second, 0}
In[3]:= Limit[x,\[Theta]->0,Direction->-1]//Timing
-16
Out[3]= {2.14238 10 Second, 0}
> Timing[
> Limit[ArcTan[ (a ((a k - w + y) ) Cot[ [Theta]] + k y ^2 Tan[
> [Theta]] ) / (y @ (a ^2 + ((w - y) ) ^2 + y ^2 Tan[ [Theta]] ^2 ) )],
> k -> (+ [Infinity] ), Direction -> 1]] )
This is also messed up, i presume due to problems with cut and pasting
inline formatted mathematica frontend text and someone else stripping \
characters. Try resending in InputForm. It's possible that this Limit
can also be fixed with some tweaking, or it's possible that this is a
bug.
> In version 5.0 computing following
>
> {Limit[ArcTan[k ], k -> + [Infinity], Direction -> -1],
> Limit[ArcTan[k ], k -> + [Infinity], Direction -> 1]} results in accurate
>
> {-(Pi/2), Pi/2}
> while doing the same in version 5.2 gives you absurd {(Pi/2), Pi/2}.
I get Pi/2 (wihtout parens) for both directions:
In[5]:= Limit[ArcTan[k],k->Infinity,Direction->#]&/@{-1,1}
Pi Pi
Out[5]= {--, --}
2 2
At the risk of showing my mathematical weakness, isn't this correct, though?
Taking the limit as k approaches infinity from the right of infinity, should
still converge to Pi/2, no? It's been a while since my epsilon delta proofs,
so i could be wrong. It works for arbitrary q though:
In[6]:= Limit[ArcTan[k],k->q,Direction->#]&/@{-1,1}
Out[6]= {ArcTan[q],ArcTan[q]}
Hardly rigorous, but to my naive mind it would seem like 5.0 was wrong.
> I could continue with list of examples that shows much more. But it only
> proofs the fact that whoever makes these changes in old good mathematica
> should be discharged. If some day I will get response from technical support
> that contains something meaningful I will post an update. Till then I would
> advise every body not to trust in results you get.
That's quite a broad conclusion you're jumping to on minimal evidence.
All programs have bugs, it looks like you might have found one with
Limit. You should know that not _any_ computer algebra software can be
100% right all the time. We're just right more than other people! :)
I would invest more time to working with other aspects of Mathematica
before prematurely concluding:
"each consequative[sic] version cuts off something good from
what mathematica used to be"
and asking that intelligent people be canned, without whom you would
have had no Mathematica to complain about anyway.
--
/*------------------------------*\
| stephen layland |
| Documentation Programmer |
| http://members.wri.com/layland |
\*------------------------------*/
- References:
- Mathematica goes Bad
- From: "Igor Touzov" <igor@nc.rr.com>
- Mathematica goes Bad