User blog:Ynought/Extended degree function

If you haven't read the orginal one please read it first.Here is the lnk:[//googology.wikia.com/wiki/User_blog:Ynought/The_degree_function https://googology.wikia.com/wiki/User_blog:Ynought/The_degree_function]

In this extension i will extend \(t\) to enclude arrays.

The previous rules are still active here i will be listing the addded material:

Added terminology:


 * 1) is something well defined at this point.When this is in a place then that part with the # doesn't matter to the definition

The system is the current expression of \( [k]#\)

\(k\) is always the number in \([k]\)

\(C\) is the array in place of \(a_1\) for example \(C=(3,5,6,7,44,4)\) when \(A=(3,5,6,7,44,4)_#)\

\(C_n\) is the n-th element in \(C\) for example \(C=(3,5,6,7,44,4)\) then \(C_3\) is 6

\(D\) is the number of elements in \(C\)

\(E\) is the array in place of \(b_1\) for example \(E=(3,7,4,6,8,9)\) when \(A\)=\( (#)_{(3,7,4,6,8,9)} \)

\(E_n\) is the n-th element in \(E\) for example \(E=(3,7,4,6,8,9)\) then \(E_4\) is 6

Rules:

1.Start analysing every element in \(C\) from right to left

1.If there is a zero

1.Remove the zero along with the comma to the right if there is none then remove the one to the left

2.Add \(k\) to every first entry of the upper value of \(t\)

3. Add \(k\) to every lfirst entry of the lower value of \(t\)

4.Replace \(k\) by \(f(k)\)

2.Otherwise

1.replace \(C_D\) by \(C_D-1\)

2.replace every other \(C_i\) with the current system with \(C_i\) decreased by one amd every other \(C_j\) increased by \(k\)

3.replace \(k\) by \(f(k)\)

2.start analysing every element in \(E\) from right to left

1.If there is a zero

1.Remove the zero along with the comma to the right if there is none then remove the one to the left

2.Add \(k\) to every first entry of the upper value of \(t\)

3. Add \(k\) to every lfirst entry of the lower value of \(t\)

4.Replace \(k\) by \(f(k)\)

2.Otherwise

1.replace \(E_D\) by \(E_D-1\)

2.replace every other \(E_i\) with the current system with \(E_i\) decreased by one amd every other \(E_j\) increased by \(k\)

3.replace \(k\) by \(f(k)\)