I have an idea, if I define more precisely about 'z' ,allow it follow other modifier prefixes like(ff),(fs),s,(bs),and,(bb). default follow 's'. Now the Longnightflyer can be difined as N-[(z(ff)N)0]; the Longnightslider can be defined as N-[(z(sf)N)0]; the Shortnightflyer can be defined as N-[(z(bb)N)0]; the Shortnightflyer can be defined as N-[(z(sb)N)0]; the Nighrdueller can be defined as N-[(zN)0].
I have an idea, if I define more precisely about 'z' ,allow it follow other modifier prefixes like(ff),(fs),s,(bs),and,(bb). default follow 's'. Now the Longnightflyer can be difined as N-[(z(ff)N)0]; the Longnightslider can be defined as N-[(z(fs)N)0]; the Shortnightflyer can be defined as N-[(z(bb)N)0]; the Shortnightflyer can be defined as N-[(z(bs)N)0]; the Nighrdueller can be defined as N-[(zN)0].
If you need more precise notation, I think these notations will be more accurate: <4dl>:α,β: := <+-β;+-β>:α,β:+<+-β;+-α>:β,β:+<+-α;+-β>:β,β: <4ds>:α,β: := <+-α;+-α>:α,β:+<+-β;+-α>:α,α:+<+-α;+-β>:α,α: <3dl>:α,β: := <+-β;>:α,β:+<;+-β>:α,β:+<+-α;+-β>:0,β:+<+-β;+-α>:0,β:+<+-α;>:β,β:+<;+-α>:β,β:+<;<+-β;+-β>:0,α: <3ds>:α,β: := <+-α;>:α,β:+<;+-α>:α,β:+<+-α;+-β>:0,α:+<+-β;+-α>:0,α:+<+-β;>:α,α:+<;+-β>:α,α:+<+-α;+-α>:0,β:
there is a little wrong, Pawn could not go foward only if the drum has captured.
All the other attachments
Something about Crooked Pieces
Higher symmetry about 4D Move Operators
About giving Royal attribute to pieces