User blog:GamesFan2000/Entry Swap Array Notation Extension

This is an extension of Entry Swap Array Notation. In this, I will add multidimensionality.

There are two new functions I will introduce: [] and. [] and are expansions of the separator function.

Rules
1 – {a(0)b}={a, a, ...b terms...a}

2 – {...a(0)b(0)c}={...a(0){b, b, ...c terms...b}}

3 – {...a[n]b}={...a(n-1)a(n-1)a...b (n-1)’s...(n-1)a}

4 – {...a(n)b}={...a[n]a[n]a...b [n]’s...[n]a}

5 – If a comma separates strings of multidimensional separators, i.e. {3(3)3, 10[5]20[6]8}, you solve the strings before you solve the main array. Likewise, if linear or multidimensional arrays are contained, they must be solved before you proceed with the main array.

Examples
{10(0)8}={10, 10, 10, 10, 10, 10, 10, 10}

{5[3]4[7]6}={5[3]4(6)4(6)4(6)4(6)4(6)4(6)4}

{4[10]8(11)9}={4[10]8[11]8[11]8[11]8[11]8[11]8[11]8[11]8[11]8[11]8}

This extension is right-associative: all and [] are solved right-to-left unless contained arrays are present.

The strength of this extension is heavily dependant on the first variable of the string, since that will eventually become the final array. If I could give an overall F(n) for this, it would be an n-length string of (n)’s, with n-length strings of [n]’s contained between the (n)’s, with n-length strings of (n-1)’s contained between the [n]’s, and so on.

As an example: F(2)={{{{{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}}(1){{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}}(1){{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}}}[2]{{{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}}(1){{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}}(1){{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}}}[2]{{{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}}(1){{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}}(1){{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}}}}(2){{{{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}}(1){{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}}(1){{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}}}[2]{{{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}}(1){{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}}(1){{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}}}[2]{{{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}}(1){{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}}(1){{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}}}}(2){{{{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}}(1){{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}}(1){{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}}}[2]{{{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}}(1){{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}}(1){{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}}}[2]{{{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}}(1){{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}}(1){{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}[1]{{{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}(0){{2, 2}, {2, 2}}}}}}}