Two Dimensional rules for case statements structures.

Two Dimensional rules for case statements structures. Locale: nemeth, Style: Verbose.

{\begin{cases} x = y \\ 5 x - y = 4 \end{cases}

⠨⠠⠷⠭⠀⠨⠅⠀⠽⠀⠀⠀⠀⠀
⠨⠠⠷⠼⠢⠭⠤⠽⠀⠨⠅⠀⠼⠲

Two Dimensional rules for tabular layout equation. Locale: nemeth, Style: Verbose.

0	$\begin{matrix} e_{1} & = (100 \dots 00)^{t} \\ e_{2} & = (010 \dots 00)^{t} \\ ⋮ \\ e_{n} & = (000 \dots 01)^{t} \end{matrix}$	⠸⠰⠑⠂⠀⠀⠀⠨⠅⠀⠷⠂⠴⠴⠀⠄⠄⠄⠀⠴⠴⠾⠘⠞⠐ ⠸⠰⠑⠆⠀⠀⠀⠨⠅⠀⠷⠴⠂⠴⠀⠄⠄⠄⠀⠴⠴⠾⠘⠞⠐ ⠄⠄⠄⠀⠀⠀ ⠸⠰⠑⠰⠝⠐⠀⠨⠅⠀⠷⠴⠴⠴⠀⠄⠄⠄⠀⠴⠂⠾⠘⠞
1	$\begin{matrix} x_{2} + x_{3} + x_{4} & = 0 \\ x_{1} + x_{2} + x_{5} & = 0 \\ x_{1} + x_{3} + x_{6} & = 0 . \end{matrix}$	⠭⠆⠬⠭⠒⠬⠭⠲⠀⠨⠅⠀⠼⠴⠀ ⠭⠂⠬⠭⠆⠬⠭⠢⠀⠨⠅⠀⠼⠴⠀ ⠭⠂⠬⠭⠒⠬⠭⠖⠀⠨⠅⠀⠼⠴⠲
2	$\begin{matrix} 0 + H = 3 + H = {0, 3} \\ 1 + H = 4 + H = {1, 4} \\ 2 + H = 5 + H = {2, 5} . \end{matrix}$	⠼⠴⠬⠠⠓⠀⠨⠅⠀⠼⠒⠬⠠⠓⠀⠨⠅⠀⠨⠷⠴⠠⠀⠒⠨⠾⠀ ⠼⠂⠬⠠⠓⠀⠨⠅⠀⠼⠲⠬⠠⠓⠀⠨⠅⠀⠨⠷⠂⠠⠀⠲⠨⠾⠀ ⠼⠆⠬⠠⠓⠀⠨⠅⠀⠼⠢⠬⠠⠓⠀⠨⠅⠀⠨⠷⠆⠠⠀⠢⠨⠾⠲
3	$\begin{matrix} ϕ_{α} (f + g) = (f + g) (α) = f (α) + g (α) = ϕ_{α} (f) + ϕ_{α} (g) \\ ϕ_{α} (f g) = (f g) (α) = f (α) g (α) = ϕ_{α} (f) ϕ_{α} (g) \end{matrix}$	⠋⠰⠨⠁⠐⠷⠋⠬⠛⠾⠀⠨⠅⠀⠷⠋⠬⠛⠾⠷⠨⠁⠾⠀⠨⠅⠀⠋⠷⠨⠁⠾⠬⠛⠷⠨⠁⠾⠀⠨⠅⠀⠋⠰⠨⠁⠐⠷⠋⠾⠬⠋⠰⠨⠁⠐⠷⠛⠾ ⠋⠰⠨⠁⠐⠷⠋⠛⠾⠀⠨⠅⠀⠷⠋⠛⠾⠷⠨⠁⠾⠀⠨⠅⠀⠋⠷⠨⠁⠾⠛⠷⠨⠁⠾⠀⠨⠅⠀⠋⠰⠨⠁⠐⠷⠋⠾⠋⠰⠨⠁⠐⠷⠛⠾⠀⠀⠀⠀
4	$\begin{matrix} ϕ_{α} (f + g) = (f + g) (α) = f (α) + g (α) = ϕ_{α} (f) + ϕ_{α} (g) \\ ϕ_{α} (f g) = (f g) (α) = f (α) g (α) = ϕ_{α} (f) ϕ_{α} (g) \\ 2 ϕ_{α} (f) = 2 (f) (α) = f (2 α) = ϕ_{2 α} (f) \end{matrix}$	⠋⠰⠨⠁⠐⠷⠋⠬⠛⠾⠀⠨⠅⠀⠷⠋⠬⠛⠾⠷⠨⠁⠾⠀⠨⠅⠀⠋⠷⠨⠁⠾⠬⠛⠷⠨⠁⠾⠀⠨⠅⠀⠋⠰⠨⠁⠐⠷⠋⠾⠬⠋⠰⠨⠁⠐⠷⠛⠾ ⠋⠰⠨⠁⠐⠷⠋⠛⠾⠀⠨⠅⠀⠷⠋⠛⠾⠷⠨⠁⠾⠀⠨⠅⠀⠋⠷⠨⠁⠾⠛⠷⠨⠁⠾⠀⠨⠅⠀⠋⠰⠨⠁⠐⠷⠋⠾⠋⠰⠨⠁⠐⠷⠛⠾⠀⠀⠀⠀ ⠼⠆⠋⠰⠨⠁⠐⠷⠋⠾⠀⠨⠅⠀⠼⠆⠷⠋⠾⠷⠨⠁⠾⠀⠨⠅⠀⠋⠷⠆⠨⠁⠾⠀⠨⠅⠀⠋⠰⠆⠨⠁⠐⠷⠋⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Two Dimensional rules for matrix structures. Locale: nemeth, Style: Verbose.

0	$(\begin{matrix} a_{11} & a_{12} & \dots & a_{1, n - m} \\ a_{21} & a_{22} & \dots & a_{2, n - m} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ a_{m 1} & a_{m 2} & \dots & a_{m, n - m} \end{matrix})$	⠠⠷⠁⠂⠂⠀⠀⠀⠀⠁⠂⠆⠀⠀⠀⠀⠄⠄⠄⠀⠁⠰⠼⠂⠠⠀⠝⠤⠍⠐⠠⠾ ⠠⠷⠁⠆⠂⠀⠀⠀⠀⠁⠆⠆⠀⠀⠀⠀⠄⠄⠄⠀⠁⠰⠼⠆⠠⠀⠝⠤⠍⠐⠠⠾ ⠠⠷⠄⠄⠄⠀⠀⠀⠀⠄⠄⠄⠀⠀⠀⠀⠄⠄⠄⠀⠄⠄⠄⠀⠀⠀⠀⠀⠀⠀⠠⠾ ⠠⠷⠁⠰⠍⠐⠂⠐⠀⠁⠰⠍⠐⠆⠐⠀⠄⠄⠄⠀⠁⠰⠍⠠⠀⠝⠤⠍⠀⠀⠠⠾
1	$H x = (\begin{matrix} 0 \\ 0 \\ 0 \end{matrix}) and H y = (\begin{matrix} 1 \\ 0 \\ 1 \end{matrix}) .$	⠠⠓⠸⠰⠭⠀⠨⠅⠀⠠⠷⠼⠴⠠⠾⠁⠝⠙⠠⠓⠸⠰⠽⠀⠨⠅⠀⠠⠷⠼⠂⠠⠾⠲ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠷⠼⠴⠠⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠷⠼⠴⠠⠾⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠷⠼⠴⠠⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠷⠼⠂⠠⠾⠀
2	$H x = (\begin{matrix} 0 \\ 0 \\ 0 \end{matrix})$	⠠⠓⠸⠰⠭⠀⠨⠅⠀⠠⠷⠼⠴⠠⠾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠷⠼⠴⠠⠾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠷⠼⠴⠠⠾
3	$H y = (\begin{matrix} 1 \\ 0 \\ 1 \end{matrix})$	⠠⠓⠸⠰⠽⠀⠨⠅⠀⠠⠷⠼⠂⠠⠾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠷⠼⠴⠠⠾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠷⠼⠂⠠⠾
4	$H = (\begin{matrix} 1 & 1 & 1 & 0 & 0 \\ 0 & 1 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 & 1 \end{matrix})$	⠠⠓⠀⠨⠅⠀⠠⠷⠼⠂⠀⠼⠂⠀⠼⠂⠀⠼⠴⠀⠼⠴⠠⠾ ⠀⠀⠀⠀⠀⠀⠠⠷⠼⠴⠀⠼⠂⠀⠼⠴⠀⠼⠂⠀⠼⠴⠠⠾ ⠀⠀⠀⠀⠀⠀⠠⠷⠼⠂⠀⠼⠴⠀⠼⠴⠀⠼⠴⠀⠼⠂⠠⠾
5	$⟨ \begin{matrix} 1 \\ 2 \\ 3 \\ 4 \\ 5 \\ 6 \\ 7 \\ 8 \\ 9 \\ 10 \end{matrix} ⟩$	⠨⠨⠠⠷⠼⠂⠀⠨⠨⠠⠾ ⠨⠨⠠⠷⠼⠆⠀⠨⠨⠠⠾ ⠨⠨⠠⠷⠼⠒⠀⠨⠨⠠⠾ ⠨⠨⠠⠷⠼⠲⠀⠨⠨⠠⠾ ⠨⠨⠠⠷⠼⠢⠀⠨⠨⠠⠾ ⠨⠨⠠⠷⠼⠖⠀⠨⠨⠠⠾ ⠨⠨⠠⠷⠼⠶⠀⠨⠨⠠⠾ ⠨⠨⠠⠷⠼⠦⠀⠨⠨⠠⠾ ⠨⠨⠠⠷⠼⠔⠀⠨⠨⠠⠾ ⠨⠨⠠⠷⠼⠂⠴⠨⠨⠠⠾
6	$[\begin{matrix} 1 & 9 & - 13 \\ 20 & 5 & - 6 \end{matrix}]$	⠈⠠⠷⠼⠂⠀⠀⠼⠔⠀⠤⠼⠂⠒⠈⠠⠾ ⠈⠠⠷⠼⠆⠴⠀⠼⠢⠀⠤⠼⠖⠀⠈⠠⠾
7	$\| \begin{matrix} a & b \\ c & d \end{matrix} \|$	⠠⠳⠁⠀⠃⠠⠳ ⠠⠳⠉⠀⠙⠠⠳
8	$A = (\begin{matrix} a & b \\ c & d \end{matrix})$	⠠⠁⠀⠨⠅⠀⠠⠷⠁⠀⠃⠠⠾ ⠀⠀⠀⠀⠀⠀⠠⠷⠉⠀⠙⠠⠾
9	$(\begin{matrix} a & b \\ c & d \end{matrix})$	⠠⠷⠁⠀⠃⠠⠾ ⠠⠷⠉⠀⠙⠠⠾
10	$[\begin{matrix} a & b \\ c & d \end{matrix}]$	⠈⠠⠷⠁⠀⠃⠈⠠⠾ ⠈⠠⠷⠉⠀⠙⠈⠠⠾
11	$\| \begin{matrix} a & b \\ c & d \end{matrix} \|$	⠠⠳⠁⠀⠃⠠⠳ ⠠⠳⠉⠀⠙⠠⠳
12	$(\begin{matrix} (\begin{matrix} a & b \\ c & d \end{matrix}) & r & s \\ 1 & 2 & 3 \end{matrix})$	⠠⠷⠠⠷⠁⠀⠃⠠⠾⠀⠗⠀⠀⠎⠀⠠⠾ ⠠⠷⠠⠷⠉⠀⠙⠠⠾⠀⠀⠀⠀⠀⠀⠠⠾ ⠠⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾ ⠠⠷⠼⠂⠀⠀⠀⠀⠀⠀⠼⠆⠀⠼⠒⠠⠾
13	$\begin{array}{r} (\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}) (\begin{array}{c} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{array}) (\begin{array}{c} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{array}) \\ (\begin{array}{c} 0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \end{array}) (\begin{array}{c} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array}) (\begin{array}{c} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \end{array}) \end{array}$	⠠⠷⠼⠂⠀⠼⠴⠀⠼⠴⠠⠾⠠⠷⠼⠂⠀⠼⠴⠀⠼⠴⠠⠾⠠⠷⠼⠴⠀⠼⠂⠀⠼⠴⠠⠾ ⠠⠷⠼⠴⠀⠼⠂⠀⠼⠴⠠⠾⠠⠷⠼⠴⠀⠼⠴⠀⠼⠂⠠⠾⠠⠷⠼⠂⠀⠼⠴⠀⠼⠴⠠⠾ ⠠⠷⠼⠴⠀⠼⠴⠀⠼⠂⠠⠾⠠⠷⠼⠴⠀⠼⠂⠀⠼⠴⠠⠾⠠⠷⠼⠴⠀⠼⠴⠀⠼⠂⠠⠾ ⠠⠷⠼⠴⠀⠼⠴⠀⠼⠂⠠⠾⠠⠷⠼⠴⠀⠼⠴⠀⠼⠂⠠⠾⠠⠷⠼⠴⠀⠼⠂⠀⠼⠴⠠⠾ ⠠⠷⠼⠂⠀⠼⠴⠀⠼⠴⠠⠾⠠⠷⠼⠴⠀⠼⠂⠀⠼⠴⠠⠾⠠⠷⠼⠴⠀⠼⠴⠀⠼⠂⠠⠾ ⠠⠷⠼⠴⠀⠼⠂⠀⠼⠴⠠⠾⠠⠷⠼⠂⠀⠼⠴⠀⠼⠴⠠⠾⠠⠷⠼⠂⠀⠼⠴⠀⠼⠴⠠⠾
14	$(\begin{matrix} 1 & x & y \\ 0 & 1 & z \\ 0 & 0 & 1 \end{matrix}) (\begin{matrix} 1 & x^{'} & y^{'} \\ 0 & 1 & z^{'} \\ 0 & 0 & 1 \end{matrix}) = (\begin{matrix} 1 & x + x^{'} & y + y^{'} + x z^{'} \\ 0 & 1 & z + z^{'} \\ 0 & 0 & 1 \end{matrix}) .$	⠠⠷⠼⠂⠀⠭⠀⠀⠽⠀⠠⠾⠠⠷⠼⠂⠀⠭⠘⠄⠐⠀⠽⠘⠄⠐⠠⠾⠀⠨⠅⠀⠠⠷⠼⠂⠀⠭⠬⠭⠘⠄⠐⠀⠽⠬⠽⠘⠄⠐⠬⠭⠵⠘⠄⠐⠠⠾⠲ ⠠⠷⠼⠴⠀⠼⠂⠀⠵⠀⠠⠾⠠⠷⠼⠴⠀⠼⠂⠀⠀⠀⠵⠘⠄⠐⠠⠾⠀⠀⠀⠀⠠⠷⠼⠴⠀⠼⠂⠀⠀⠀⠀⠀⠵⠬⠵⠘⠄⠐⠀⠀⠀⠀⠀⠀⠠⠾⠀ ⠠⠷⠼⠴⠀⠼⠴⠀⠼⠂⠠⠾⠠⠷⠼⠴⠀⠼⠴⠀⠀⠀⠼⠂⠀⠀⠠⠾⠀⠀⠀⠀⠠⠷⠼⠴⠀⠼⠴⠀⠀⠀⠀⠀⠼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠀

Two Dimensional rules for table structures. Locale: nemeth, Style: Verbose.

0	$\begin{array}{lll} \cdot & 0 & 1 \\ 0 & 0 & 0 \\ 1 & 0 & 1 \end{array}$	⠡⠀⠀⠀⠼⠴⠀⠀⠼⠂ ⠐⠒⠀⠀⠐⠒⠀⠀⠐⠒ ⠼⠴⠀⠀⠼⠴⠀⠀⠼⠴ ⠼⠂⠀⠀⠼⠴⠀⠀⠼⠂
1	$\begin{array}{cccc} + & 0 & 1 & 2 \\ 0 & 0 & 1 & 2 \\ 1 & 1 & 2 & 0 \\ 2 & 2 & 0 & 1 \end{array}$	⠬⠀⠀⠀⠼⠴⠀⠀⠼⠂⠀⠀⠼⠆ ⠐⠒⠀⠀⠐⠒⠀⠀⠐⠒⠀⠀⠐⠒ ⠼⠴⠀⠀⠼⠴⠀⠀⠼⠂⠀⠀⠼⠆ ⠼⠂⠀⠀⠼⠂⠀⠀⠼⠆⠀⠀⠼⠴ ⠼⠆⠀⠀⠼⠆⠀⠀⠼⠴⠀⠀⠼⠂
2	$\begin{array}{ccc} N & (1 2) N \\ N & N & (1 2) N \\ (1 2) N & (1 2) N & N \end{array}$	⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠼⠂⠀⠼⠆⠾⠠⠝ ⠐⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒ ⠠⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠼⠂⠀⠼⠆⠾⠠⠝ ⠷⠼⠂⠀⠼⠆⠾⠠⠝⠀⠀⠷⠼⠂⠀⠼⠆⠾⠠⠝⠀⠀⠠⠝⠀⠀⠀⠀⠀⠀⠀
3	$\begin{array}{cccc} + & 0 + 3 Z & 1 + 3 Z & 2 + 3 Z \\ 0 + 3 Z & 0 + 3 Z & 1 + 3 Z & 2 + 3 Z \\ 1 + 3 Z & 1 + 3 Z & 2 + 3 Z & 0 + 3 Z \\ 2 + 3 Z & 2 + 3 Z & 0 + 3 Z & 1 + 3 Z \end{array}$	⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠴⠬⠒⠈⠰⠠⠵⠀⠀⠼⠂⠬⠒⠈⠰⠠⠵⠀⠀⠼⠆⠬⠒⠈⠰⠠⠵ ⠐⠒⠒⠒⠒⠒⠒⠒⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒ ⠼⠴⠬⠒⠈⠰⠠⠵⠀⠀⠼⠴⠬⠒⠈⠰⠠⠵⠀⠀⠼⠂⠬⠒⠈⠰⠠⠵⠀⠀⠼⠆⠬⠒⠈⠰⠠⠵ ⠼⠂⠬⠒⠈⠰⠠⠵⠀⠀⠼⠂⠬⠒⠈⠰⠠⠵⠀⠀⠼⠆⠬⠒⠈⠰⠠⠵⠀⠀⠼⠴⠬⠒⠈⠰⠠⠵ ⠼⠆⠬⠒⠈⠰⠠⠵⠀⠀⠼⠆⠬⠒⠈⠰⠠⠵⠀⠀⠼⠴⠬⠒⠈⠰⠠⠵⠀⠀⠼⠂⠬⠒⠈⠰⠠⠵