Walking Randomly

There was a discussion recently on comp.soft-sys.math.mathematica about maintaining a user-led Mathematica bug list and various solutions were proposed.  I have no desire (and certainly no time) to even try to maintain a ‘proper’ bug database for Mathematica but I am interested in maintaining a list of bugs that I personally find interesting and that I would like to see explained or fixed.

This post is that list.

First – some answers to potential questions.

Why are you doing this?  I thought you liked Mathematica.

I love Mathematica but, like all pieces of software, it is not perfect.  I find (some of) the imperfections interesting and since I get lots of hits from google every month from people looking for bugs in MATLAB, Mathematica, Maple, Mathcad etc then I assume that I am not alone.  Every bug that I discuss here will be submitted to Wolfram Research and I will also update the page when the bug gets fixed.

I emailed/wrote a comment about a bug and you haven’t included it in the list. Why?

Sorry about that – please don’t take it personally.  I am low on time and may not have managed to verify the ‘bug’ or maybe it just didn’t tickle my fancy.  It’s also possible that I simply don’t understand the problem you are referring to and I will not post anything on here that I don’t at least think I understand.  Remember – I’m not trying to keep a list of all Mathematica bugs – just some of the ones that I find interesting.

One of the ‘bugs’ you posted is not a bug – you just misunderstood the situation.

Oops, sorry!  Please educate me so I can update it.

I think I have found a bug in Mathematica – what should I do?

In the first instance I suggest you post it to comp.soft-sys.math.mathematica – there are plenty of people there who know a lot about Mathematica and they (probably) will let you know if you really have found a bug or not. If everyone suspects that it is a bug then your next step is to report it to Wolfram.  Finally, if you think I’d like to know about it then feel free to leave a comment to this post or email me.

FullSimplify bug 1

Clear[n];
FullSimplify[n Exp[-n * 0.], Element[n, Integers]]

expected output:

n

actual output:

n/2

original source – here.

Integrate bug 1

Integrate[k^2 (k^2 - 1)/((k^2 - 1)^2 + x^2)^(3/2), {k, 0, Infinity},Assumptions -> x > 0]

Expected output:

1/2*1/(1+x^2)^(1/4)*EllipticK(1/2*2^(1/2)*(((1+x^2)^(1/2)+1)/(1+x^2)^(1/2))^(1/2))

Actual output:

EllipticK[(2*x)/(-I + x)]/(2*Sqrt[-1 - I*x])

Note that although the integrand is real for all k, Mathematica gives a complex result which is clearly wrong.  Original source – here.

Limit bug 1

Limit[EllipticTheta[3, 0, x], x -> 1, Direction -> 1]

Expected Output:

Infinity

Actual Output:

0

Original Source: here

Feel free to let me know of others that you find but please bear in mind the points at the beginning of this post.