On Wed, Mar 24, 2021 at 3:59 PM slelievre <samuel.lelie...@gmail.com> wrote: > > 2021-03-24 14:53:06 UTC, Matt: >> >> How can I calculate the direct product of two groups and/or the direct sum? >> For example given: >> >> G.<x,y>=FreeGroup() >> H=G.quotient([x*y]) >> >> how do I calculate H+H and HxH? > > > Having defined `H`, you can type > > H. > > then hit the TAB key to see what methods are available. > > This reveals the methods `cartesian_product` > and `direct_product`, are they what you need? > > ``` > sage: G.<x, y> = FreeGroup() > sage: H = G.quotient([x*y]) > > sage: H.cartesian_product(H) > The Cartesian product of > (Finitely presented group < x, y | x*y >, > Finitely presented group < x, y | x*y >) > > sage: H.direct_product(H) > Finitely presented group < a, b, c, d | > a*b, c*d, a^-1*c^-1*a*c, a^-1*d^-1*a*d, > b^-1*c^-1*b*c, b^-1*d^-1*b*d > > ```
careful here, FreeGroup is not Abelian, you'll want to add commuting relations for all its generators. You might prefer AbelianGroup() to begin with. > > -- > 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/ec06a1f8-624a-4352-b968-ac451fa3847bn%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/CAAWYfq1Ey5ujUz5ygbXNHuJYpvN_8JGEyxKunJdVTAb2fhr38g%40mail.gmail.com.