Mr. Marko Riedel

390 Reputation

11 years, 358 days
B.Sc. Computer Science UBC 1994, M.Sc. Computer Science UofT 1996.

closed form integral...

Maple

Dear friends,

every once in a while I come across an integral that Maple does not readily compute and post it here, so that your programmers may perhaps include it in the integration engine.

I am writing today concerning the integral int(x^q/(exp(x)-1), x=0..infinity); for q a real number. Maple can do this integral for rational q but not for irrational ones, e.g. try q=14/10 vs. q=sqrt(2). I hope you can make good use of this hint. The original computation...

automorphisms of the petersen graph...

Maple

Dear friends, I recently answered a query concerning the action of the automorphism group of the Petersen graph on its edges at math.stackexchange.com. The algorithm that I present is quite naive, but it does produce the desired result. I thought I would share it here because it makes a nice Maple programming exercise e.g. for a talented student at high school level. (I have always thought that Polya counting and permutation groups belong into the high school curriculum.) It makes extensive use of Maple's internal hash function for compound objects to efficiently compare them during the computation. It is quite interesting to observe how Maple does work hard for several minutes to do this computation and then comes up with the correct answer. (Obviously the core computation needs to be done only once.) Enjoy!

Best regards, Marko Riedel

If you come up with a better algorithm then please do share it at the stackexchange link.

Important update Mar 24 2016. The algorithm at the above post is middling to say the least, but can perhaps serve as an example of Maple computational techniques. There is an efficient algorithm including Maple code here at math.stackexchange.com.

calculating a sum symbolically...

Dear friends,

I have recently been calculating a sum from this link.

The problem here is to calculate the sum sum_{n>=1} (-1)^(n+1)/(n^2+a) with a some positive real number. You probably all agree that it is preferable to express it using elementary functions from basic calculus as opposed to the Gamma, Zeta and Digamma...

possible symbolic integration bug...

Dear friends,

I will present a series of commands for you to ponder that should speak for themselves.

```> q := n -> int(1/(1-2^n*exp(I*theta*n))^2*2*I*exp(I*theta), theta=0..2*Pi);
2 Pi
/
|          2 I exp(theta I)
q := n ->  |      ------------------------ dtheta
|            n                2
/       (1 - 2  exp(theta n I...```

more contour integration issues...

Maple

Hello all,

I recently helped someone with a contour integration problem, you may find my calculation at the following link. It occurred to me to test this integral with Maple and Mathematica.

For example,

`int(1/x^(1/3)/(x^2+2*x*cos(Pi/7)+1), x=0..infinity);`

produces an unusable output from Mathematica. Maple is a little better,...

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