Mathematica goes Bad (Resend)
- To: mathgroup at smc.vnet.net
- Subject: [mg59431] Mathematica goes Bad (Resend)
- From: "igor" <igor at touzov.com>
- Date: Wed, 10 Aug 2005 02:55:12 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
[This is a resend of Igor's post to correct the input - moderator]
I am using Mathematica second year already, and found that each consecutive
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 yourself:
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]] )
It takes less then 1 ms on version 5.0, while for version 5.2 it will take
forever (40.328 Second).
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]]
It takes 76.782 Second is version 5.0, 100.187 Second in version 5.1.1 and
104.015 Second in version 5.2.
Not to mention it gives you some absurd results as well:
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 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.