Nicer syntax for entering permutations

[fingolfin]

Right now, you may see something like this in a REPL or notebook:

julia> G
<permutation group of size 645120 with 9 generators>

julia> gens(G)
9-element Vector{PermGroupElem}:
 (1,10)
 (2,11)
 (3,12)
 (4,13)
 (5,14)
 (6,8)
 (7,9)
 (1,2,3,4,5,6,7)(8,9,10,11,12,13,14)
 (1,2)(10,11)

But how can you enter this group again, given just this output?

One idea would be to write a macro which can take a single permutation or a list and turn them into OSCAR permutation (we already had a similar idea for GAP.jl, see See also oscar-system/GAP.jl#420)

So then you could perhaps write

gens = @perm 14 [
  (1,10)
 (2,11)
 (3,12)
 (4,13)
 (5,14)
 (6,8)
 (7,9)
 (1,2,3,4,5,6,7)(8,9,10,11,12,13,14)
 (1,2)(10,11)
]

and it would produce the list of permutations as elements of sym(14). Alternatively the first argument 14 could be omitted (then just take the maximum of all occurring moved points), or could be an existing permutation group.

(Of course instead of returning a list of permutations, it could also directly return a permutation group. I just figured being able to deal with a list of permutations is more general).

In principle it is clear to me how to implement this, but I figured it would be good to first get some feedback, perhaps people have better ideas for the syntax of this, which I'd like to hear before working on that macro :-)

[rfourquet]

If not following the exact math notation is acceptable, you could also steal the {} syntax (e.g. [{1, 10}, {2, 11}, ...]), and allow direct input with a macro via SafeREPL ;-)

[fingolfin]

@rfourquet I am not sure I follow, what is the proposal in terms for the way one enters the permutations (ignoring completely how this is implemented for the moment?) Would it just replace ( and ) by { and } and otherwise look identical? Or something else?

[thofma]

Just for the record:

julia> using AbstractAlgebra

julia> perm"(1,2)(3,4)"
(1,2)(3,4)

[rfourquet]

Would it just replace ( and ) by { and } and otherwise look identical?

Yes. But this syntax can be used only through a macro, so it would look like @perm [{1, 10}, {1, 2}{10, 11}] in regular code (or without the comma, e.g. {1 10}), but the @perm can be omitted in the REPL (but saving on typing @perm would be useful only if you input a lot of permutations.