Computational Algebra Systems

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.

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5 Responses to “Computational Algebra Systems”

  1. dhdung1309 Says:

    I am just a beginner in using GAP. I just computed some basic computations in Groups. But I need to master it for my future research. I hope I may learn some more tips from you.



  2. juan Says:


    How do you compare them to PARI?
    Which one is faster or has more functions implemented?


    • bretbenesh Says:

      Hi Juan,

      Sorry! I am not familiar with PARI, and I do not know which is faster.

      Let me know if you find out, please.

      • juan Says:

        OK, I’ll do.
        I would like to find a software able to calculate 7^7^7^7^7 (mod 17), that’s 7^^5 (mod 17), or something like 8^7^6^5^4^3^2 (mod 37). But everything I’ve tried produces an overflow.

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