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I have been learning the book "Computer Algebra and Materials Physics" during this period of time.

In the chapter 9 titled by "Final Remarks", the author wrote the following:

In my article, I have omitted several important application of the group theory and the algebra. One of this is the treatment of magnetic or color groups. Also I omitted the treatment of Lie algebra, important in the spin system or the study of angular momentum. As for the former, a package of color groups is implemented in GAP (The Gap Group 2017).

Since there is no example, I am still confused about the magnetic space group creating in GAP. It's well known that there are 1651 types of magnetic space groups in total, as shown below:

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I'm not sure if all these groups can be created and manipulated in GAP currently. Any tips or examples will be appreciated.

Regards, HZ

Hongyi Zhao
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  • In GAP, type `?ColorGroup` - it will open manual from a package, that's how you will find out that it's a [Cryst package](https://www.gap-system.org/Packages/cryst.html) implementing this. Is this what you're looking for? – Olexandr Konovalov May 17 '22 at 10:15
  • I looked through [the presumably most related section](https://www.gap-system.org/Manuals/pkg/cryst/htm/CHAP002.htm#SECT010) to the discussion here. There are few examples there. I still haven't been able to create a specific color group myself for the time being. OTOH, the color group concept used in `Cryst` seems rather mathematical and general than the description used by ordinary physicists. – Hongyi Zhao May 17 '22 at 12:47

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