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 >
```
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