On Fri, Feb 4, 2022 at 4:40 AM 'Michel VAN DEN BERGH' via sage-support <sage-support@googlegroups.com> wrote: > > Dear all, > > I need to do something which I thought would be quite simple. I have free > groups > F, G with generators x1,x2,x3,x4 and x,y respectively and I need to compute > the image of an element under the homomorphism F-->G:x1->x, x2->y, x3->x, > x4->y. > > I could not find anything in the manual about morphisms between free groups. > I tried subs, but that does not work since the parents of the elements of F > and G are (of course) different. > > The workaround I used is to work in the free group H with generators > x1,x2,x3,x4,x,y and to use subs. However this is also inconvenient since I > need the action of the braid group with 4 strands on F. It does not act on H > because of the limitation "#strands=#generators". > > So this means I have to use only part of the braid group with 6 strands. > > In the end it all works but it is terribly hacky for some which seems to be a > very clean thing to do. > > I would be grateful for any suggestions.
Michel: One idea is to check out https://doc.sagemath.org/html/en/reference/groups/sage/groups/braid.html Another idea is to download braid-1.1.tar.gz, untar in the pkg subdirectory and type LoadPackage("braid"); FYI, the pkg subdir is inside sage-9*/local/share/gap You can find a pdf manual for the braid package at https://arxiv.org/abs/math/0304376 Currently, the link to braid-1.1.tar.gz at https://www.gap-system.org/Packages/undep.html is bad but I have a copy. Just email me privately. - David > Michel > > > -- > You received this message because you are subscribed to the Google Groups > "sage-support" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-support+unsubscr...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sage-support/f7d460d0-390b-455d-ae90-72b105e8e926n%40googlegroups.com. -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/CAEQuuAVmSsLxS%2Bi50JNUqrK%3DUm%3DquJaZ2ueNuedAVzr6xKSMzQ%40mail.gmail.com.
