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Having both programmed my share of c++ and studied some beginners group theory some year ago, I got curious about this...

Is there any particularly popular template based (object oriented) design pattern for systematically programming any kind of stuff related to group theory?

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    $\begingroup$ I think this is too general a question. "Abstract algebraic concepts" is just too unspecified to allow saying anything about representation with templates. $\endgroup$ – Wolfgang Bangerth Nov 27 '17 at 20:05
  • $\begingroup$ Ok I can scratch the abstract algebraic concepts and stick with group theory. But I had enough of trouble to manage to find tags to fit the question already. $\endgroup$ – mathreadler Nov 27 '17 at 20:14
  • $\begingroup$ A comment rather than an answer: translating the math. structure into templates, though natural, is not always beneficial to software design (sometimes it's good, sometimes it makes it more complicated with no benefit) $\endgroup$ – BrunoLevy Nov 28 '17 at 15:55
  • $\begingroup$ @BrunoLevy : Yes I know it is not always beneficial. But I would suspect something with so many rules and structures as algebra would benefit from it. $\endgroup$ – mathreadler Nov 28 '17 at 17:10
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Chapters 6 and 7 of Stepanov and Rose's book From Mathematics to generic programming deal precisely with what you asked. The first author is the designer of the C++ Standard Template Library.

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  • $\begingroup$ Clever choices, definitely. Almost mindblastingly clever. Almost presidentially clever, even. $\endgroup$ – mathreadler Nov 27 '17 at 21:26
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An earlier alternative to Stepanov's treatment of abstract algebra (including groups) is the one given in Barton and Nackman's "Scientific and Engineering C++".

In more modern c++, the boost concept checking library would seem to be a quite natural means of modularising the hierarchy of algebraic types (semigroups, monoids, groups etc).

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