Ultimate Extensible Array Notation
Pre-Definition
Ultimate Extensible Array Notation (UEAN) is a collab made by 6 peoples, including me, Alemagno, Username, CatIsFluffy, Chronolegends, and Simple_Art.
- Basic (Made by Username)
- Hyperbasic (Made by Username)
- Linear (Made by me)
- Quadratic (Made by CatIsFluffy)
- Polynominal (Made by Simple_Art)
- Row Dotted
- Grid Dotted
- Multidotted
- Separators
Also, here is the sheet we are doing other stuff of UEAN.
This sheet shows these tabs, Welcome, Definition, FAQ, Analysis, and Values. That's it.
NOTE: ^ will uses for the rules starting with Arrowed and the expression expansion (A^B will be B groups of A strings).
Definition
Basic
Basic UEAN is the first extension of UEAN, made by Username.
There is only 1 rule, the base rule: a[0] = 10^a.
Hyperbasic
Hyperbasic UEAN is the second extension of UEAN, made by Username.
- a[0] = 10^a
- a[n] (if n > 0) = a'([n-1])^a'
'(A)^(B)' will change into (A)(A)(A)... with B '(A)'s.
Linear
Linear UEAN is the third extension of UEAN, made by me.
- a[0] = 10^a
- a[n #] (if n > 0) = a'([n-1 #])^a'
- Where # is the rest of the arrays.
- a['(0,)^b' n #] = a['(0,)^(b-1)' a,n-1 #]
- Where b can be anything.
The last entry of 0 can be removed.
Quadratic
Quadratic UEAN is the fourth extension of UEAN, made by CatIsFluffy.
- a[0] = 10^a
- a[n #] (if n > 0) = a'([n-1 #])^a'
- a[% 0,n #] = a[% a,n-1 #]
- Where % is the groups of '0,' or '0,,'.
- a[% 0,,n #] = a[% '(0,)^a'1,,n-1 #]
All of ',0,,'s can be reduce to ',,'s.
Polynomial
Polynomial UEAN is the fifth extension of UEAN, made by Simple_Art.
- a[0] = 10^a
- a[n #] (if n > 0) = a'([n-1 #])^a'
- a[% 0,n #] = a[% a,n-1 #]
- Where % is the groups of any '0'(,)^n''.
- a[% 0',^x'y #] = a[% '(0',^(x-1)')^a'1',^x'y-1 #]
All of '',^a'0,^b''s can be reduce to ',^b's, if b > a.
Dotted
Dotted UEAN is the sixth extension of UEAN, made by Chronolegends.
- a[0] = 10^a
- a[n #] (if n > 0) = a'([n-1 #])^a'
- a[% 0,n #] = a[% a,n-1 #]
- Where % is the groups of any '0'(,)^n'' or '0:'.
- a[% 0',^x'y #] = a[% '(0',^(x-1)')^a'1',^x'y-1 #]
- a[% 0;n #] = a[% 0',^a'1;n-1 #]
All of '',^a'0;'s can be reduce to ';'s.
Row Dotted
Row Dotted UEAN is the seventh extension of UEAN, made by me.
Now we can define separators because it will get more complex. Either ,^n or ,^m;, where n >= 1 and m >= 0 are vaild.
,^n is next separator of ,^(n-1), ; is next separator of all commas, and ,^n; is next separator of ,^(n-1);. Let N(A) will be next separator of A.
- a[0] = 10^a
- a[n #] (if n > 0) = a'([n-1 #])^a'
- a[% 0,n #] = a[% a,n-1 #]
- Where % is the groups of any '0&', where & can be any separator.
- a[% 0 N(&) x #] = a[% '(0 &)^a'1 N(&) x-1 #]
- a[% 0;n #] = a[% 0',^a'1;n-1 #]
All of 'A 0 B's can be reduce to 'B's, if B > A.
Grid Dotted
Grid Dotted UEAN is the eighth extension of UEAN.
Either ,^n or ,^x;,^y, where n >= 1 and x & y >= 0 are vaild.
- a[0] = 10^a
- a[n #] (if n > 0) = a'([n-1 #])^a'
- a[% 0,n #] = a[% a,n-1 #]
- Where % is the groups of any '0&', where & can be any separator.
- a[% 0 N(&) x #] = a[% '(0 &)^a'1 N(&) x-1 #]
- a[% 0;n #] = a[% 0',^a'1;n-1 #]
- a[% 0 ;,^m n #] = a[% 0 ',^a';,^m-1 1 ;,^m n-1 #]
Multidotted
Multidotted UEAN is the ninth extension of UEAN.
Either ,^n or ,^m;A, where n >= 1, m >= 0, and A which is vaild separator, are vaild.
- a[0] = 10^a
- a[n #] (if n > 0) = a'([n-1 #])^a'
- a[% 0,n #] = a[% a,n-1 #]
- Where % is the groups of any '0&', where & can be any separator.
- a[% 0 N(&) x #] = a[% '(0 &)^a'1 N(&) x-1 #]
- a[% 0 ;^m n #] = a[% 0 ;^m-1',^a' 1 ;^m n-1 #]
- a[% 0 ;^m N(&) n #] = a[% 0 ;^m-1',^a'; & 1 ;^m N(&) n-1 #]