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 #]