Concatenation product is well defined but not well implemented in Sage. If u is infinite then uv = u for any (finite or infinite) word v. It is not a free monoid anymore.
That being said, you can build the algebra on finite words, the one on infinite words (which is really stupid) and the one on all words. I guess only the first one matters. The shuffle algebra is not well defined on infinite words (the product becomes an infinite sum). So please turn infinite=False in both situations. Vincent 2014/1/5, Nathann Cohen <nathann.co...@gmail.com>: > Hmmmmmmmm... I just had Nicolas on the phone who told me that both can be > changed to "finite words only". Aaaaaaaaaand he had Florent around to > confirm. > > I also think that the concatenation product is not well defined. And I > actually wrote that in the patch already :-/ > > On the other hand I did not touch the Shuffle Product. > > Well, tell me what you think ^^; > > Nathann > > > On 5 January 2014 19:09, Darij Grinberg <darijgrinb...@gmail.com> wrote: > >> Huh? I thought shuffle does not work (because 1111... sh 1111... would >> be a sum of infinitely many identical words), but uv is well-defined >> (and equals u when u is infinite)? >> >> On Sun, Jan 5, 2014 at 7:08 PM, Christian Stump >> <christian.st...@gmail.com> wrote: >> >> Yes, but it's associative, so it works... (Except I don't expect it to >> >> have much of a use.) >> > >> > >> > can you be more specific? How is the product uv defined? I see that you >> have >> > a shuffle product defined, but I don't see that you have >> > concatenation... >> > >> > Thanks, Christian >> > >> > -- >> > You received this message because you are subscribed to the Google >> > Groups >> > "sage-combinat-devel" group. >> > To unsubscribe from this group and stop receiving emails from it, send >> > an >> > email to sage-combinat-devel+unsubscr...@googlegroups.com. >> > To post to this group, send email to >> sage-combinat-devel@googlegroups.com. >> > Visit this group at http://groups.google.com/group/sage-combinat-devel. >> > For more options, visit https://groups.google.com/groups/opt_out. >> >> -- >> You received this message because you are subscribed to a topic in the >> Google Groups "sage-combinat-devel" group. >> To unsubscribe from this topic, visit >> https://groups.google.com/d/topic/sage-combinat-devel/zdN44XJZu5s/unsubscribe >> . >> To unsubscribe from this group and all its topics, send an email to >> sage-combinat-devel+unsubscr...@googlegroups.com. >> To post to this group, send email to >> sage-combinat-devel@googlegroups.com. >> Visit this group at http://groups.google.com/group/sage-combinat-devel. >> For more options, visit https://groups.google.com/groups/opt_out. >> > > -- > You received this message because you are subscribed to the Google Groups > "sage-combinat-devel" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-combinat-devel+unsubscr...@googlegroups.com. > To post to this group, send email to sage-combinat-devel@googlegroups.com. > Visit this group at http://groups.google.com/group/sage-combinat-devel. > For more options, visit https://groups.google.com/groups/opt_out. > -- You received this message because you are subscribed to the Google Groups "sage-combinat-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-combinat-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-combinat-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-combinat-devel. For more options, visit https://groups.google.com/groups/opt_out.
