MalDun's Mathblog

The Computational Sage project

The goal of the computational sage project is not to replace sage, but more to give home for packages and extensions for sagemath, which are important or useful for computational mathematics (numerics, symbolic computation, scientific computing, parallel computing etc), but cannot merged into sage because they perhaps are not stable enough, or other reasons like lacking support for certain distributions, or are not wanted in the community.
Another goal is to try to “stabalize” these packages, and introduce them with bugfixes into sagemath to reach more users, and help the sage project.
I’m doing this myself and encourage other users to do this also.

It is also a goal to merge back packages from the FEMhub project into sage, and provide bleeding edge/more actual packages for certain packages like numpy or scipy.

Since I’m aware that some things are not liked by the communities of these projects, I started this project with the thought that other researchers share the same problems, and want to provide their experimental packages to other users, but they don’t get accepted by the community, or it will take at least months or even years to get it into the system.

I personally think that provide stable systems is important and correct, but also provide the possibilty for use of unstable packages at own knowledge and risk.

As a rule Packages which are “stabelized” and merged into sage will be deleted from the project hosing page.

Everyone who wants to help out is welcome.

Filed in Uncategorized 1 year, 8 months ago

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The Sage spectral methods Toolbox – A little dream of myself…

Since I do a lot with spectral methods recently in optimization, and began to write the whole thing in Sage, I started to think about writing a spectral methods toolbox for it.

The plan is to provide an open source tool box for work with Spectral Methods or hiqh order Spectral Element Methods. The user should be able to use

Fast Polynomial Transformations
Symbolic Methods for evaluating recursive Formulas, for e.g. Galerkin matrices
Filters
etc.

Why Sage? Because it has a strong symbolic component and and uses SciPy/NumPy as numeric foundation. That’s a good starting point for the crossover of symbolic and numeric methods. Till now I use mathematica for the symbolic stuff, but I hope to get indepentend of this to provide a free alternative (also then I have a chance to learn a lot of new stuff *g*). There should be no missunderstanding: I really like mathematica and I use it a lot, but it is very expensive (in fact too expensive for private use), and all libraries are closed…

The next thing is: it is quite a lot of work to communicate between GNU Octave and mathematica, and the next issue is: MAtlab/Octave is not object oriented, what is a problem from the desing point of view….

A first step in this direction is already done, by helping Burcin Erocal with a new implementation of the orthogonal polynomials:

http://trac.sagemath.org/sage_trac/ticket/9706

The package reached already beta status (in my opinion) , and will hopefully added soon to Sage.

Filed in Uncategorized 1 year, 9 months ago

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The proof of Murphy’s Law

Actually I found out, that Murphy’s Law “Anything that can go wrong, will go wrong.” is just a corollary of the Borel-Cantelli Lemma: [url]http://en.wikipedia.org/wiki/Borel%E2%80%93Cantelli_lemma[/url]

The proof is rather simple: We take a series $(A_n)_{n \in \mathbb{N}}$ of certain events, for example programming a code, or a process that repeats frequently. Then when ist can go wrong means that there exists a probabillity $\epsilon > 0$ that one of the events will go wrong. Now $\sum _{n=1}^{\infty} P(A_n)= \sum _{n=1}^{\infty} \epsilon = \infty$ . Now the Borel Cantelli Lemma states that the probability that infinitely many of them occur is 1. (This is even more, because it means also that infinetly many of them go wrong)

Filed in Uncategorized 2 years ago

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Awakening

Yippie, since WordPress finally supports LaTex, now this Blog’s getting finally a meaning!

I introduce me now to the world.

Im an Austrian mathematican. I’m currently making my PhD. thesis in Optimal Control Theory.

My research interest is in short Computational mathematics. I often wondered what my specific mathematical interest is, because there are so much different topics. But recently I found out that my personal interest is how can I compute certain things. Therefore I’m interested in

-Analysis (including functional analysis and topology)

-Algebra

-Numerical mathematics and approximation theory

-Symbolic computation

-Mathematical physics and some fields of engineering

-Non-linear optimization

-Asymptotics

other interests are: history, philosophy (especially scientific methods), programming, and other nerdish things like manga and anime