Hello Martin > Hi Kurt, > > In simpler terms: PermutationGroup and GroupPresentation are never going to > implement the category 'Group' because in PermutationGroup and > GroupPresentation > % represents the whole group whereas in Group % represents an element of the > group.
Indeed. Since PermutationGroup is a list of permutations (Permutation) it's obviously not a group -- the suffix is misleading. At least we have Permutation(Integer) has Group => true, as it should be. Apparently the word problem for permutation groups can be solved by the routines in permgrps. > > However, we could implement category 'Group' by having a domain called 'Word' > (over Symbols or Permutations) where the multiplication operation is the > concatenation of words with simplification given by the relations. > That's what had I in mind. I erroneously assumed that your "GroupPresentation" implements a group in the literallly sense, e.g. to get answers to queries like a*b^2=b*a^2? If you inherit from Group then you will get *,1,inv for free. So the domain "Word" will actually be a group. > It seems to me that such a proposed domain would help simplify existing and > proposed code as follows: > > 1) Tidy up some of the local functions in PermutationGroup which work with > words > in an ad hoc and messy way. > 2) Would simplify my conversion from PermutationGroup to GroupPresentation > which > uses words. > 3) Be a basis for examples such as LyndonWord That would undoubtedly be useful. On the other hand, if you implement (faithfully) GroupPresentation <--> PermutationGroup then we'll have the same functionality - in disguise though. I admit that I like the symbolic representation with equations much more than using NNI for fp groups, but that's a matter of taste. > > Martin B > -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
