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Basic Linear Array Separator Matrix Notation, abbreviated as blaSMN, is the third component of Separator Matrix Notation.
blaSMN features groups of two numbers separated by a comma as separators.
@ = Any separator of the same kind in any one expression.
Elipses between two symbols can also indicate that there are only two symbols in total in that group of symbols.
Rule 1: All rules of xSMN apply to blaSMN.
Rule 2a: a(0,0)b = a((...(a)...)")a w/ b () layers.
Rule 2b: a(d,c)b = a(d,c1)(d,c1)...(d,c1)a w/ b parasegs.
(Ex: @(a+1)(a)(a)...(a)(a) = @(a+1)(a)(a+1) also applies to (b,@(a+1)(a)(a)...(a)(a) = (b,@(a+1)(a)(a+1))
Rule 3a: (@,(@,(@,(...,(@,0)...) = (@,(@+1,0))
Rule 3b: (@,(0,0),0),0)...),0) = (@+1,0)
Rule 4a: ((...(0,0),0)...) = ((0,0))
Rule â€¦
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Welcome to the Master Analysis of Separator Matrix Notation! Currently, the analysis contains parts of SMN that have not been defined yet.
Separator Matrix Notation Paraseg Cluster & Limit Indicators Approx FGH & Comparables
(0) \(f_3(n)\)  Tetration
(0) (0) \(f_4(n)\)  Pentation
(0) (0) (0) \(f_5(n)\)  Hexation
(0) (0) (0) (0) \(f_6(n)\)  Heptation
(0) (0) (0) (0) (0) \(f_7(n)\)  Octation
(0)(0) \(f_\omega(n)\)  Arrow Notation, Ackermann Function, HyperE Notation, SteinhausMoser Notation, Basic R Function
(0)(0) (0) \(f_{\omega+1}(n)\)  Expansion
(0)(0) (0) (0) \(f_{\omega+2}(n)\)  Multiexpansion
(0)(0) (0)(0) \(f_{\omega2}(n)\)
(0)(0) (0)(0) (0) \(f_{\omega2+1}(n)\)  Explosion
(0)(0) (0)(0) (0)(0) \(f_{\omega3}(n)\)  Detonation
(0)(0) (0)â€¦
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Extended Separator Matrix Notation, abbreviated as xSMN, is the second component of Separator Matrix Notation.
Hence the name, xSMN is a basic extension to bSMN, using nested parentheses and separating symbols.
@ = Any separator of the same kind in any one expression.
Elipses between two symbols can also indicate that there are only two symbols in total in that group of symbols.
Rule 1: All rules of bSMN apply to xSMN.
Rule 2: a(...(b)...)a w/ n ()s = a(...(0)...)a w/ n+1 ()s*
Rule 3a: a(...(a)...)a w/ b parenthesis nests = a(0(0))b
Rule 3b: a(c(...(a)...))a w/ b parenthesis nests = a(c+1(0))b
Rule 3c: a(b(0))a = a((0)(0))b
Rule 3d: a(...(b)(b)(b)...(b...))a w/ c b's = a(...(b+1)"...)c
Rule 3e: b((a+1)(a)(a)...(a))b w/ c a's = b((a+1)(a)(a+1))c
Rule â€¦
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Basic Separator Matrix Notation, abbreviated as bSMN, is the first component of Separator Matrix Notation.
Hence the name, the basic concept of bSMN works with a hierarchy of many different types of separators.
@ = Any separator of the same kind in any one expression.
Rules numbered 1 are full expression rules. Rules numbered 2 are separator rules. Those separators are put into expressions, just like the ones in rules numbered 1. Rules numbered 3 are lexical rules.
Rule 1a: a(0)b = a^^b
Rule 1b: a@a@a...@a w/ b a's = a@(0)b
In the rules below, the indeterminately long strings of parasegs (each item that is enclosed in parentheses along with the parantheses themselves is called a paraseg) are all part of the expression a@b, so the ellipses denotâ€¦
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Welcome to my new notation, Separator Matrix Notation.
Idea conceived in January 2016. Began prototypes in March 2016. Named in September 2016.
Basic Separator Matrix Notation (bSMN)
Extended Separator Matrix Notation (xSMN)
Basic Linear Array Separator Matrix Notation (blaSMN)
Extended Linear Array Separator Matrix Notation (xlaSMN)
MultiComma Array Separator Matrix Notation (mcaSMN)
Fancy Bracet Separator Matrix Notation (fbSMN)
Basic HyphenNumeral Separator Matrix Notation (bhnSMN)
Extended HyphenNumeral Separator Matrix Notation (xhnSMN)
Complex Hyphenation Separator Matrix Notation (chSMN)
Hyphenated Array Separator Matrix Notation (haSMN)
HigherOrderHyphen Separator Matrix Notation (hohSMN)
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