Dear Hongyi, there are several GAP packages dealing with crystallographic groups in one way or another. Have you had a look at those? From a quick look:
https://www.gap-system.org/Packages/cryst.html https://www.gap-system.org/Packages/crystcat.html https://www.gap-system.org/Packages/aclib.html Also, be advised that putting copyrighted material such as PDF of books still under copyright protection on GitHub is illegal in most jurisdictions. Please refrain from posting links to such illegal offerings here. Best regards Max -- Prof. Dr. Max Horn TU Kaiserslautern Fachbereich Mathematik Tel. (+49) 631 205-2730 _______________________________________________ Forum mailing list Forum@gap-system.org https://mail.gap-system.org/mailman/listinfo/forum