Macro for entering permutations in cycle notation

[danielrademacher]

Resolves oscar-system/GAP.jl#420
Resolves #1189

[thofma]

Would be good if there were some tests with invalid input, e.g. @perm (-1, 1) or @perm 10 [(1 11)].

[fingolfin]

Thank you!! Great work. Still some changes would be good

[danielrademacher]

I also added a check for

@perm ()

But than an error occurs for cperm

cperm([])
ERROR: MethodError: no method matching cperm(::Vector{Any})
Closest candidates are:
  cperm(::AbstractVector{T}...) where T<:Union{Integer, fmpz} at ~/.julia/dev/Oscar/src/Groups/perm.jl:214
  cperm(::PermGroup, ::AbstractVector{T}...) where T<:Union{Integer, fmpz} at ~/.julia/dev/Oscar/src/Groups/perm.jl:226

Is this intended?

[fingolfin]

You could just let ores start out as an empty vector and then do push!(ores, ...), then you don't need i.

[fingolfin]

This calls symmetric_group again and again, which isn't great, as we create a new group object each time. This could be improved by using let block; but I don't want to complicate things even further, so I suggest we first iron out everything else and get this merged, then we can worry about fine tuning.

Just for the record, here is what I'd do: I'd only collect the res values here:

Suggested change

	ores[i] = esc(:(Oscar.cperm(symmetric_group($n),$(res...))))
	ores[i] = esc(:( [$(res...)] ))

Then, the final return of this macro could look something like this:

return quote
   let g = symmetric_group($n)
       [ cperm(g, pi) for pi in [$(ores...)] ]
   end
end

Note: normally we'd have to worry that g and pi could clash with symbols defined by the programmer in the surrounding code, and referenced in the permutation expression. This is where the esc function comes into play: we applied it to the expressions we got from the user, but not to the outer expression above. This leads to the Julia macro hygiene functionality kicking in, which determines that g and pi (unlike symmetric_group and cperm) are not known variables, and replaces them by special generated names. You can check the effect of this via macroexpand:

julia> g = 7  # introduce a variable g and use it in the macro expression:
7

julia> macroexpand(Main, :( Oscar.@perm 14 [
                     (g,9)
                     (1,2)(10,11)
                    ]))
quote
    let var"#332#g" = Oscar.symmetric_group(14)
        [Oscar.cperm(var"#332#g", var"#333#pi"...) for var"#333#pi" = [[[g, 9]], [[1, 2], [10, 11]]]]
    end
end

[fingolfin]

Thanks!