Posts Tagged ‘magma’

Computational Algebra Systems

December 10, 2009

I use computational algebra systems in my research. I previously used Magma, but I now use GAP. I find that the documentation for Magma is nicer. I find that GAP is cheaper (free), and I like the fact that it is open source. The functionality is similar in both systems, although there are minor differences.

I use these systems as a lab of sorts. I study objects called “groups.” GAP and Magma give me an environment where I can study the properties of groups. I liken this to how a scientist works: she observes something in a lab, thinks of a question, creates a hypothesis, tests the hypothesis, and then either has a result or creates a new hypothesis.

I find that GAP and Magma are useful in formulating questions and testing hypotheses—they are my lab. While a scientist could think of a question while observing chimps, this is tougher to do with abstract objects. GAP and Magma make this possible, and can further test the hypothesis by checking many examples.

Of course, once this is done, I need to leave the computer and figure out exactly why the hypothesis is true—I need to prove the result. But computational algebra systems help me know what I should try to prove.

Tip of the Day

October 12, 2009

My thesis advisor gave me a great piece of advice: never leave the office without giving your computer something to do.

Since then, I have tried to have a program running overnight whenever possible. This is not the greenest thing to do, but it is productive. Here are two things that I do regularly.

  1. I use the computational algebra system GAP in my research, and I try to have a program running whenever I am not at the computer.
  2. I participate in the Great Internet Mersenne Prime Search (GIMPS) to use my computer to find large primes.

Frankly, I haven’t been very good about having GAP programs run. However, it is very easy to search for primes–GIMPS has programs that are foolproof.