rewrite the definitions of groups in symmetry.jl

[kalmarek]

you can check the correctness of group definitions using

include(joinpath(pathof(GroupsCore), "..", "..", "test", "conformance_test.jl"))
let G = KleinGroup()
    test_Group_interface(G)
    test_GroupElement_interface(rand(G, 2)...)
    nothing
end
let G = KleinPermGroup()
    test_Group_interface(G)
    test_GroupElement_interface(rand(G, 2)...)
    nothing
end
let G = CyclicGroup(12)
    test_Group_interface(G)
    test_GroupElement_interface(rand(G, 2)...)
    nothing
end
let G = lattice1group(5)
    test_Group_interface(G)
    test_GroupElement_interface(rand(G, 2)...)
    nothing
end

[blegat]

Wow, that was fast. Was it incorrect before ?

[kalmarek]

yeah, I found them a bit earlier ;) took me ~2h to rewrite;

I'm not sure it was incorrect, it didn't pass the tests because of missing methods.

[kalmarek]

following interfaces is nice ;) everything is green here, locally ;)

[blegat]

So does that mean that SymbolicWedderburn was not running enough checks on the group ?

[blegat]

Maybe https://discourse.julialang.org/t/symmetry-sos-optimization-compatibility-issues/98057/6 has a similar issue, the group is not valid but with more checks an error would be thrown

[kalmarek]

SymbolicWedderburn doesn't do any checks per se (it does now for the group action);
Here I just made sure that our groups comply to the group interface. User should do that on his own, I suppose?

[blegat]

I think it's best if we do it by default and then the user can disable it with options. The power users will set the option to disable but the new user that does not know the option, he will also most probably have errors in the group ^^

[kalmarek]

ok, I'll think about it