Creation of a 4D number system without coordinates
Confugure: "Arial Unicode MS" 16
The "qabc" (quaternion abc)
qabc=.81
3$'o̥ḀB̥C̥D̥E̥F̥G̥H̥I̥J̥K̥L̥M̥N̥O̥P̥Q̥R̥S̥T̥U̥V̥W̥X̥Y̥Z̥o̟A̟B̟C̟D̟E̟F̟G̟H̟I̟J̟K̟L̟M̟N̟O̟P̟Q̟R̟S̟T̟U̟V̟W̟X̟Y̟Z̟o̠A̠B̠C̠D̠E̠F̠G̠H̠I̠J̠K̠L̠M̠N̠O̠P̠Q̠R̠S̠T̠U̠V̠W̠X̠Y̠Z̠
'
#qabc
81
d=:3 :'q,"1 y,"1 q=.39{a.' NB. display of quaternion
AfC=: 3 : 0 NB. conversion to "alfa system" from "coordinate form"
A=.4 0$0
while.+./0~:y do.y=.3%~y-j-3*j=2[A=.A,.~|.j=.3|y end.
qabc{~3#.|:A
)
NB. conversion to "coordinate form" from "alfa
system"
CfA=:3 :'3#.|.|:j-3*2=j=.3 3 3 3#:qabc i.y$~3,~3%~#y'
NB. Example no.1
d A1=:,AfC 2 3 8 2
'I̥D̟T̠'
CfA 'I̥D̟T̠'
2 3 8 2
NB. Example no.2
d A2=:,AfC _28 12 _6 11
'B̥U̟L̟B̠'
CfA 'B̥U̟L̟B̠'
_28 12 _6 11
NB. Example no.3
d A3=:,AfC 163 _89 _89 237
'A̟Z̥o̥X̠o̟M̥'
CfA 'A̟Z̥o̥X̠o̟M̥'
163 _89 _89 237
NB. Examles with single unicode
CfA 0{qabc
0 0 0 0
CfA 1{qabc
1 0 0 0
CfA 2{qabc
_1 0 0 0
CfA 78{qabc
0 _1 _1 _1
CfA 79{qabc
1 _1 _1 _1
CfA 80{qabc
_1 _1 _1 _1
qlist=:3 : 0 NB. display of the complete qabc
qList=:0 4$0
for_i.i.81 do.qList=:qList,CfA i{y end.
y,.'=',.3j0":qList
)
qlist qabc NB. equal or assignment virtually?
o̥= 0 0 0 0 NB. This is an isomorphism between digits
Ḁ= 1 0 0 0 NB. of two 4D vectorial number systems.
B̥= _1 0 0 0 NB. The first (left side) - without coordinates,
C̥= 0 1 0 0 NB. the second (right side) - with ones.
D̥= 1 1 0 0 NB. Both of them have basis(radix) = 3
E̥= _1 1 0 0 NB. and the _1 is displaised with 2 just as
F̥= 0 _1 0 0 NB. at the wellknown balanced ternary system.
G̥= 1 _1 0 0 NB. The four coordinates: x y z s,
H̥= _1 _1 0 0 NB. where the first three are the vector part
I̥= 0 0 1 0 NB. and the last is the scalar part of the
quaternion.
J̥= 1 0 1 0
K̥= _1 0 1 0
L̥= 0 1 1 0
M̥= 1 1 1 0
N̥= _1 1 1 0
O̥= 0 _1 1 0
P̥= 1 _1 1 0
Q̥= _1 _1 1 0
R̥= 0 0 _1 0
S̥= 1 0 _1 0
T̥= _1 0 _1 0
U̥= 0 1 _1 0
V̥= 1 1 _1 0
W̥= _1 1 _1 0
X̥= 0 _1 _1 0
Y̥= 1 _1 _1 0
Z̥= _1 _1 _1 0
o̟= 0 0 0 1
A̟= 1 0 0 1
B̟= _1 0 0 1
C̟= 0 1 0 1
D̟= 1 1 0 1
E̟= _1 1 0 1
F̟= 0 _1 0 1
G̟= 1 _1 0 1
H̟= _1 _1 0 1
I̟= 0 0 1 1
J̟= 1 0 1 1
K̟= _1 0 1 1
L̟= 0 1 1 1
M̟= 1 1 1 1
N̟= _1 1 1 1
O̟= 0 _1 1 1
P̟= 1 _1 1 1
Q̟= _1 _1 1 1
R̟= 0 0 _1 1
S̟= 1 0 _1 1
T̟= _1 0 _1 1
U̟= 0 1 _1 1
V̟= 1 1 _1 1
W̟= _1 1 _1 1
X̟= 0 _1 _1 1
Y̟= 1 _1 _1 1
Z̟= _1 _1 _1 1
o̠= 0 0 0 _1
A̠= 1 0 0 _1
B̠= _1 0 0 _1
C̠= 0 1 0 _1
D̠= 1 1 0 _1
E̠= _1 1 0 _1
F̠= 0 _1 0 _1
G̠= 1 _1 0 _1
H̠= _1 _1 0 _1
I̠= 0 0 1 _1
J̠= 1 0 1 _1
K̠= _1 0 1 _1
L̠= 0 1 1 _1
M̠= 1 1 1 _1
N̠= _1 1 1 _1
O̠= 0 _1 1 _1
P̠= 1 _1 1 _1
Q̠= _1 _1 1 _1
R̠= 0 0 _1 _1
S̠= 1 0 _1 _1
T̠= _1 0 _1 _1
U̠= 0 1 _1 _1
V̠= 1 1 _1 _1
W̠= _1 1 _1 _1
X̠= 0 _1 _1 _1
Y̠= 1 _1 _1 _1
Z̠= _1 _1 _1 _1
to be continued, feedback welcome
Istvan Kadar
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
