ordex: Ordinal Expander in JavaScript

input:
 →











link of this notation

auto save link

syntax sugar:
1=(0,0,0)
n=(0,0,0)+...n's...+(0,0,0)
w=ω=(0,0,(0,0,0))
W=Ω=(0,(0,0,0),0)
e=ε0=(0,0,W)
z=ζ0=(0,0,(0,1,W))
G=Γ0=(0,0,(0,1,(0,1,W)))
 → output:


usage
  • This version can parse/compare/dom/expand the Kuma Kuma 3-ary psi notation.
  • The valid primitive charactors are "0", "(", "," and ")".
  • Write ψ_{X1}(X2,X3) as (X1,X2,X3). For example,
    0
    (0,0,0)
    (0,0,0)+(0,0,0)
    (0,0,0)+(0,0,0)+(0,0,0)
    (0,0,(0,0,0))
    (0,0,(0,0,0))+(0,0,0)
    (0,0,(0,0,0)+(0,0,0))
    (0,0,(0,0,(0,0,0)))
    (0,0,(0,(0,0,0),0))
    (0,0,((0,0,0),0,0))
    (0,0,(((0,0,0),0,0),0,0))
  • The syntax sugar 0,1,2,3,4,5,6,7,8,9,w=ω, e=ε0, z=ζ0, G=Γ0 and W=Ω are available.
    • 5
    w+4
    z+z+4
    (0,0,(0,W,0))
  • Spaces in a line or multiple lines or empty lines give you the multiple result at once. Like this:
    0 1 2 3 w+1    w+1+1  w+w
    (0,0,1)         (0,0,w)+w

    (0,0,(0,0,0))+1+1  W
parse
X returns parsed expression of the ordinal notation X by the system.
tree
It shows tree structor of the objects.
compare
it compares 2 ordinals when you put "X Y" in input box.
3      w
W+w    w+w+w+9
1      1
↓
3   <  w
W+w >  w+w+w+9
1   =  1
dom
It returns dom(X) into output box when you put "X" in input box.
0  1  3
w  W  W+w
(0,w,0) (0,W,0) (1,0,0)
↓
0  1  1
w  W  w
w  W  (1,0,0)
expand
It returns X[Y] into output box when you put "X Y" in input box.
w 3
w+5 3
(0,0,(0,0,w+5)) 3
(0,0,(0,0,w+w+2)) 3
(0,0,W) 3
(0,0,(0,1,W)) 3
(0,0,(0,W,0)) 3
(0,0,(W,0,0)) 3
↓
3
w+1+1+1+1
(0,0,(0,0,w+1+1+1+1)+(0,0,w+1+1+1+1)+(0,0,w+1+1+1+1))
(0,0,(0,0,w+w+1)+(0,0,w+w+1)+(0,0,w+w+1))
(0,0,(0,0,(0,0,w)))
(0,0,(0,1,(0,0,(0,1,(0,0,(0,1,(0,0,(0,1,1))))))))
(0,0,(0,(0,0,(0,(0,0,(0,e,0)),0)),0))
(0,0,((0,0,((0,0,((0,0,(1,0,0)),0,0)),0,0)),0,0))
link
Right click and copy this to get and share the parmalink of the notation you input.
auto save
When you check here and press any button, the URL is saved into your browser history.
example
There are some example sheet of the expansion or the correspondence to the other notations. "result" is the result of the expansion for the notations on the sheets.


ordex: Ordinal Expander in Javascript version 1.8
Original Kuma kuma 3-ary Psi(ja) (en) was invented by Kanrokoti(en/ja)
programmed by koteitan
Source code is on github
The program and the site is licensed by CC-BY-SA 3.0.