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In the past I was using * for SeitzOperators' operations:

Base.:*(m::SeitzOperator, c::CrystalCoord) = CrystalCoord((m.data*[c; 1])[1:3])
Base.:*(a::SeitzOperator, b::SeitzOperator) = SeitzOperator(a.data * b.data)

But they can be ambiguous: where is

Base.:*(c::CrystalCoord, m::SeitzOperator)

?

Besides, I need to define a type CrystalCoord. But then I realized I could just use function-like objects onto an AbstractVector:

(::SeitzOperator)(v::AbstractVector)

which follows CoordinateTransformations.jl design.

It's more common to use degrees instead of radians in crystallography. Besides, sin and cos on floating point number is less accurate.

julia> sin(pi / 2)
1.0

julia> cos(pi / 2)
6.123233995736766e-17

julia> sind(90)
1.0

julia> cosd(90)
0.0

julia> tan(pi / 4)
0.9999999999999999

julia> tand(45)
1.0

julia> cot(pi / 4)
1.0000000000000002

julia> cotd(45)
1.0

julia> cos(pi)
-1.0

julia> sin(pi)
1.2246467991473532e-16

julia> cosd(180)
-1.0

julia> sind(180)
0.0