issymmorph for individual SymOperations can be wrong

[thchr]

The trouble is that we currently assume that if op $= (W|w)$ has nonzero part $w$ and is in a primitive setting, then it is necessarily a nonsymmorphic operation: but that is not true in general. Rather, $w$ could simply indicate where the rotation axis/mirror plane is.

As an example, in SG 120, we have:

julia> sg = spacegroup(120)
julia> psg = primitivize(sg)
julia> op = psg[7]
{2₁₁₂|½,½,0} ─────── (-x+z+1/2,-y+z+1/2,z)
 ┌ -1  0  1 ╷ 1/2 ┐
 │  0 -1  1 ┆ 1/2 │
 └  0  0  1 ╵   0 ┘

Now, for a proper nonsymmorphic operation, if we apply it n times (with n denoting rotation order), it must become a pure, nonzero translation - but here, instead, we have:

julia> compose(op, op, false)
1 ──────────────────────────────── (x,y,z)
 ┌ 1  0  0 ╷ 0 ┐
 │ 0  1  0 ┆ 0 │
 └ 0  0  1 ╵ 0 ┘

What we probably need to do is compute the intrinsic translation part of w, what ITA calls $w_g = w - w_l$. See e.g., Section 11.2.

[hongyi-zhao]

See here and here for related discussions.