The equations in the gyroid paper involve .real and .imag extraction of real number from complex number.
The term e(power(i*theta) = cos(theta) + i*sin(theta) also must have .real and .imag applied at some point.
The paper ignores this, or has typo omitting when to apply this. I am trying some permutations...

Maybe doing the D and P surfaces will help with understanding. Cos(0) = 1, and i*Sin(PI/2) = i, so only a sign change is possible.
- Brian