Comments on: A random collection of bugs in Mathematica 7 and 7.0.1 http://www.walkingrandomly.com/?p=801 Because it's more fun than getting there in a straight line. Sun, 05 Sep 2010 12:28:36 +0000 http://wordpress.org/?v=2.9.1 hourly 1 By: Mike Croucher http://www.walkingrandomly.com/?p=801&cpage=1#comment-24399 Mike Croucher Sat, 15 May 2010 19:24:58 +0000 http://www.walkingrandomly.com/?p=801#comment-24399 Hi Grant You are correct. I copied the 'correct expression' from Maple and from my own testing it appears that you are right concerning the different conventions between the two packages. Let's take x=2 for example. In Mathematica 7.0 I get the result of 0.706094 for the integrand using NIntegrate but my 'correct expression' evaluates to 0.799487 at x=2. oops! However, if you evaluate the 'correct expression' for x=2 in Maple 13 then you get 0.706094 which agrees with Mathematica's NIntegrate. So, the 'correct expression' is correct if you use Maple's definition of EllipticK but it is incorrect if you use Mathematica's. Furthermore, I need to check my work more carefully in future. It's still a Mathematica 7 bug for Integrate though :) I'll leave the article as it stands so that the comments make sense in the future. Well spotted and thanks for commenting. Cheers, Mike PS. I also note that I didn't swap Maple's EllipticK() to Mathematica's EllipticK[]. I was clearly having a bad day! Hi Grant

You are correct. I copied the ‘correct expression’ from Maple and from my own testing it appears that you are right concerning the different conventions between the two packages.

Let’s take x=2 for example. In Mathematica 7.0 I get the result of 0.706094 for the integrand using NIntegrate but my ‘correct expression’ evaluates to 0.799487 at x=2. oops!

However, if you evaluate the ‘correct expression’ for x=2 in Maple 13 then you get 0.706094 which agrees with Mathematica’s NIntegrate.

So, the ‘correct expression’ is correct if you use Maple’s definition of EllipticK but it is incorrect if you use Mathematica’s. Furthermore, I need to check my work more carefully in future. It’s still a Mathematica 7 bug for Integrate though :)

I’ll leave the article as it stands so that the comments make sense in the future. Well spotted and thanks for commenting.

Cheers,
Mike

PS. I also note that I didn’t swap Maple’s EllipticK() to Mathematica’s EllipticK[]. I was clearly having a bad day!

]]> By: Grant Keady http://www.walkingrandomly.com/?p=801&cpage=1#comment-24187 Grant Keady Wed, 12 May 2010 09:13:01 +0000 http://www.walkingrandomly.com/?p=801#comment-24187 While I can see there is an Integrate bug in your "Integrate bug 1", I'm not sure that your "correct expression" (as I read it on 12 May 2010) is "correct". The numbers seem to differ from what one gets from NIntegrate. I noted elsewhere that there appear to have been different conventions in Maple and Mathematica concerning the EllipticK function. (I was asked by SIAM to do a book review, but I don't think it will be published...) http://school.maths.uwa.edu.au/~keady/CAS/siam10keady2.pdf I haven't checked in detail, and I could have made a mistake, or the cut-and-paste from the web page into Mathematica might have some subtle error. Would like you to check. Thanks While I can see there is an Integrate bug in your “Integrate bug 1″, I’m not sure
that your “correct expression” (as I read it on 12 May 2010) is “correct”.
The numbers seem to differ from what one gets from NIntegrate.
I noted elsewhere that there appear to have been different conventions in Maple and
Mathematica concerning the EllipticK function.
(I was asked by SIAM to do a book review, but I don’t think it will be published…)
http://school.maths.uwa.edu.au/~keady/CAS/siam10keady2.pdf

I haven’t checked in detail, and I could have made a mistake, or the cut-and-paste
from the web page into Mathematica might have some subtle error.
Would like you to check. Thanks

]]> By: Sander Huisman http://www.walkingrandomly.com/?p=801&cpage=1#comment-17643 Sander Huisman Tue, 24 Nov 2009 21:38:27 +0000 http://www.walkingrandomly.com/?p=801#comment-17643 Another bug, but was known (according to Rob Raguet-Schofield, Twitter: @ragfield): \[Alpha] // TeXForm \[Beta] // TeXForm (or anything expression for that matter) only outputs the last one. Same holds for CForm and FortranForm (probably they internally use the same mechanism...) Another bug, but was known (according to Rob Raguet-Schofield, Twitter: @ragfield):

\[Alpha] // TeXForm
\[Beta] // TeXForm
(or anything expression for that matter)

only outputs the last one.
Same holds for CForm and FortranForm (probably they internally use the same mechanism…)

]]> By: Sander Huisman http://www.walkingrandomly.com/?p=801&cpage=1#comment-17642 Sander Huisman Tue, 24 Nov 2009 21:32:22 +0000 http://www.walkingrandomly.com/?p=801#comment-17642 @Mike Luckily it is correct if you put 0 instead of 0. Who works with inexact numbers anyways ;-) :-) @Mike

Luckily it is correct if you put 0 instead of 0. Who works with inexact numbers anyways ;-) :-)

]]> By: Mike Croucher http://www.walkingrandomly.com/?p=801&cpage=1#comment-17627 Mike Croucher Tue, 24 Nov 2009 09:44:44 +0000 http://www.walkingrandomly.com/?p=801#comment-17627 @Sander I hadn't looked at it like that but you are right. It's all a bit strange. @Szabolcs - I agree, the occasional bug in Integrate is not surprising but still worth reporting I feel. They might never get fixed otherwise :) The RandomReal bug is very interesting! Thanks for letting me know abut it! Cheers, Mike @Sander I hadn’t looked at it like that but you are right. It’s all a bit strange.

@Szabolcs – I agree, the occasional bug in Integrate is not surprising but still worth reporting I feel. They might never get fixed otherwise :) The RandomReal bug is very interesting! Thanks for letting me know abut it!

Cheers,
Mike

]]> By: Szabolcs http://www.walkingrandomly.com/?p=801&cpage=1#comment-17612 Szabolcs Mon, 23 Nov 2009 20:25:44 +0000 http://www.walkingrandomly.com/?p=801#comment-17612 I think that the bugs that are really worth mentioning are the surprising ones. An incorrect answer to a symbolic definite integral shouldn't surprise anyone who has some experience with CASs. But a bug in a function like Sort[] or Tally[] is something really bad simply because it's unexpected... Mathematica 6 had a nasty Tally bug. (It appeared only when a custom comparison function was used.) It's fixed in 7. I think that the bugs that are really worth mentioning are the surprising ones. An incorrect answer to a symbolic definite integral shouldn’t surprise anyone who has some experience with CASs. But a bug in a function like Sort[] or Tally[] is something really bad simply because it’s unexpected… Mathematica 6 had a nasty Tally bug. (It appeared only when a custom comparison function was used.) It’s fixed in 7.

]]> By: Szabolcs http://www.walkingrandomly.com/?p=801&cpage=1#comment-17611 Szabolcs Mon, 23 Nov 2009 20:18:42 +0000 http://www.walkingrandomly.com/?p=801#comment-17611 Integration and taking limits can be complicated, and the validity of some of the steps these functions make during calculations can depend on difficult-to-impossible to test assumptions. So the occasional bug is not that surprising here. The FullSimplify bug is a bit more shocking than these. And here's one that was really unexpected for me: http://groups.google.com/group/comp.soft-sys.math.mathematica/browse_frm/thread/8a43649367ebcc21# In the example that was posted, Maximize[] re-seeds the RNG, so it'll always give the same sequence. That's nasty. Integration and taking limits can be complicated, and the validity of some of the steps these functions make during calculations can depend on difficult-to-impossible to test assumptions. So the occasional bug is not that surprising here. The FullSimplify bug is a bit more shocking than these. And here’s one that was really unexpected for me:

http://groups.google.com/group/comp.soft-sys.math.mathematica/browse_frm/thread/8a43649367ebcc21#

In the example that was posted, Maximize[] re-seeds the RNG, so it’ll always give the same sequence. That’s nasty.

]]> By: Sander Huisman http://www.walkingrandomly.com/?p=801&cpage=1#comment-17604 Sander Huisman Mon, 23 Nov 2009 17:54:13 +0000 http://www.walkingrandomly.com/?p=801#comment-17604 The first is the most interesting, as you give an inexact (approximate) input, that yields an exact (non-correct) output ! The first is the most interesting, as you give an inexact (approximate) input, that yields an exact (non-correct) output !

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