Python

I recently got interested in singular perturbation theory , and to get help with the algebra, I turned to SymPy. I had tried to use Mathematica in graduate school in the early 90s, but the experience had been sufficiently frustrating that I had steered clear of computer algebra systems since.

SymPy presents itself as a “friendly”, less intimidating alternative, with a more familiar and conventional language and operating model.

Formal perturbation theory, and in particular singular perturbation theory, are standard topics in applied mathematics, but seem to be largely unknown outside that specific community. Which is a shame, because they are both useful, and intellectually fascinating.

Perturbation expansions, in particular for higher orders, have a reputation for being “cumbersome”, as the say: the algebra quickly becomes both tedious and error-prone. Which is true, but it turns out that the SymPy computer-algebra system can be put to good use in this context.

Every once in a while, I need to evaluate the normal distribution function $\Phi(x)$:

$$ \Phi(x) = \frac{1}{\sqrt{2 \pi}} \int_{-\infty}^x \! e^{-\frac{1}{2}t^2} \, dt $$

Unfortunately, it is not always available in the standard math libraries, and hence I have to implement a “good-enough” version myself. Here are some options.

How short can a complete, competitive sort algorithm be? Less than half a dozen lines? Maybe just 3 or 4?

Shuffling a collection of items is a surprisingly frequent task in programming: essentially, it comes up whenever a known input must be processed in random order. What is more, there is a delightful, three-line algorithm to accomplish this task correctly, in-place, and in optimal time. Unfortunately, this simple three-line solution seems to be insufficiently known, leading to various, less-than-optimal ad-hoc alternatives being used in practice — but that is entirely unnecessary!

Over the holidays, I sat down and wrote a casual turn-based strategy game. Aside from the obvious fun aspect, one major motivation was to gain experience with the pyglet game library, which I wanted to evaluate as a potentially general, light-weight GUI library for Python.

Over the holidays, I had the opportunity to work on a spare time project, and so I sat down and wrote a casual, turn-based strategy game; a variant (you might say: a clone) of the KDE game Konquest.

Finding a realistic (or at least, realistic looking) initial configuration of game objects or simulation particles can be a challenge. The desired configuration should appear to be both “random” and at the same time “spatially uniform”, without objects clustering together or overlapping.

I have started to get interested in Hidden Markov Models (HMM). As a warm-up, I prepared a pure Python implementation of the relevant algorithms (github).

Processing command-line arguments in ad-hoc python tools is one of those areas where I tend to just hack it together from scratch — simply because the effort of learning and understanding the relevant library packages not only seems to be more work than it is worth, but also and in particular more effort than “just doing it” by hand. I don’t want anything fancy, after all. I just want to get it done.