# User:Jon Awbrey/TABLES

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Note. Spacing may vary depending on the Wikimedia installation. The Wiki Table + TeX Cell formats below are the ones that currently work at the English Wikiversity, though they look a little uneven here.

## Differential Logic

### Tacit Extension

#### Wiki Table

 $\boldsymbol\varepsilon (pq)\!$ $=\!$ $p\!$ $\cdot\!$ $q\!$ $\cdot\!$ $\texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)}\!$ $+\!$ $p\!$ $\cdot\!$ $q\!$ $\cdot\!$ $\texttt{(} \mathrm{d}p \texttt{)} ~~ \mathrm{d}q ~~\!$ $+\!$ $p\!$ $\cdot\!$ $q\!$ $\cdot\!$ $~~ \mathrm{d}p ~~ \texttt{(} \mathrm{d}q \texttt{)}\!$ $+\!$ $p\!$ $\cdot\!$ $q\!$ $\cdot\!$ $~~ \mathrm{d}p ~~~~ \mathrm{d}q ~~\!$

#### TeX Array

 $\begin{array}{r*{8}{c}} \boldsymbol\varepsilon (pq) & = & p & \cdot & q & \cdot & \texttt{(} \mathrm{d}p \texttt{)} & \cdot & \texttt{(} \mathrm{d}q \texttt{)} \\[4pt] & + & p & \cdot & q & \cdot & \texttt{(} \mathrm{d}p \texttt{)} & \cdot & \mathrm{d}q \\[4pt] & + & p & \cdot & q & \cdot & \mathrm{d}p & \cdot & \texttt{(} \mathrm{d}q \texttt{)} \\[4pt] & + & p & \cdot & q & \cdot & \mathrm{d}p & \cdot & \mathrm{d}q \end{array}\!$

### Enlargement Map

#### Wiki Table

 $\mathrm{E}(pq)\!$ $=\!$ $p\!$ $\cdot\!$ $q\!$ $\cdot\!$ $\texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)}\!$ $+\!$ $p\!$ $\cdot\!$ $\texttt{(} q \texttt{)}\!$ $\cdot\!$ $\texttt{(} \mathrm{d}p \texttt{)} ~~ \mathrm{d}q ~~\!$ $+\!$ $\texttt{(} p \texttt{)}\!$ $\cdot\!$ $q\!$ $\cdot\!$ $~~ \mathrm{d}p ~~ \texttt{(} \mathrm{d}q \texttt{)}\!$ $+\!$ $\texttt{(} p \texttt{)}\!$ $\cdot\!$ $\texttt{(} q \texttt{)}\!$ $\cdot\!$ $~~ \mathrm{d}p ~~~~ \mathrm{d}q ~~\!$

#### TeX Array 1

 $\begin{array}{r*{8}{c}} \mathrm{E}(pq) & = & p & \cdot & q & \cdot & \texttt{(} \mathrm{d}p \texttt{)} & \cdot & \texttt{(} \mathrm{d}q \texttt{)} \\[4pt] & + & p & \cdot & \texttt{(} q \texttt{)} & \cdot & \texttt{(} \mathrm{d}p \texttt{)} & \cdot & \mathrm{d}q \\[4pt] & + & \texttt{(} p \texttt{)} & \cdot & q & \cdot & \mathrm{d}p & \cdot & \texttt{(} \mathrm{d}q \texttt{)} \\[4pt] & + & \texttt{(} p \texttt{)} & \cdot & \texttt{(} q \texttt{)} & \cdot & \mathrm{d}p & \cdot & \mathrm{d}q \end{array}\!$

#### TeX Array 2

 $\begin{array}{rcccccl} \mathrm{E}(pq) & = & p & \cdot & q & \cdot & \texttt{(} \mathrm{d}p \texttt{)} \texttt{(} \mathrm{d}q \texttt{)} \\[4pt] & + & p & \cdot & \texttt{(} q \texttt{)} & \cdot & \texttt{(} \mathrm{d}p \texttt{)} ~ \mathrm{d}q \\[4pt] & + & \texttt{(} p \texttt{)} & \cdot & q & \cdot & \mathrm{d}p ~ \texttt{(} \mathrm{d}q \texttt{)} \\[4pt] & + & \texttt{(} p \texttt{)} & \cdot & \texttt{(} q \texttt{)} & \cdot & \mathrm{d}p ~ \mathrm{d}q \end{array}\!$

### Difference Map

#### Wiki Table

 $\mathrm{D}(pq)\!$ $=\!$ $p\!$ $\cdot\!$ $q\!$ $\cdot\!$ $\texttt{((} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{))}\!$ $+\!$ $p\!$ $\cdot\!$ $\texttt{(} q \texttt{)}\!$ $\cdot\!$ $\texttt{(} \mathrm{d}p \texttt{)} ~~ \mathrm{d}q ~~\!$ $+\!$ $\texttt{(} p \texttt{)}\!$ $\cdot\!$ $q\!$ $\cdot\!$ $~~ \mathrm{d}p ~~ \texttt{(} \mathrm{d}q \texttt{)}\!$ $+\!$ $\texttt{(} p \texttt{)}\!$ $\cdot\!$ $\texttt{(} q \texttt{)}\!$ $\cdot\!$ $~~ \mathrm{d}p ~~~~ \mathrm{d}q ~~\!$

#### TeX Array

 $\begin{array}{rcccccl} \mathrm{D}(pq) & = & p & \cdot & q & \cdot & \texttt{((} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{))} \\[4pt] & + & p & \cdot & \texttt{(} q \texttt{)} & \cdot & \texttt{(} \mathrm{d}p \texttt{)} ~ \mathrm{d}q \\[4pt] & + & \texttt{(} p \texttt{)} & \cdot & q & \cdot & \mathrm{d}p ~ \texttt{(} \mathrm{d}q \texttt{)} \\[4pt] & + & \texttt{(} p \texttt{)} & \cdot & \texttt{(}q \texttt{)} & \cdot & \mathrm{d}p ~ \mathrm{d}q \end{array}\!$

### Tangent Map

#### Wiki Table

 $\mathrm{d}(pq)\!$ $=\!$ $p\!$ $\cdot\!$ $q\!$ $\cdot\!$ $\texttt{(} \mathrm{d}p \texttt{,} \mathrm{d}q \texttt{)}\!$ $+\!$ $p\!$ $\cdot\!$ $\texttt{(} q \texttt{)}\!$ $\cdot\!$ $\mathrm{d}q\!$ $+\!$ $\texttt{(} p \texttt{)}\!$ $\cdot\!$ $q\!$ $\cdot\!$ $\mathrm{d}p\!$ $+\!$ $\texttt{(} p \texttt{)}\!$ $\cdot\!$ $\texttt{(} q \texttt{)}\!$ $\cdot\!$ $0\!$

 $\texttt{(} \mathrm{d}p \texttt{,} \mathrm{d}q \texttt{)}\!$ $=\!$ $~~ \mathrm{d}p ~~ \texttt{(} \mathrm{d}q \texttt{)}\!$ $+\!$ $\texttt{(} \mathrm{d}p \texttt{)} ~~ \mathrm{d}q ~~\!$ $\mathrm{d}p\!$ $=\!$ $~~ \mathrm{d}p ~~~~ \mathrm{d}q ~~\!$ $+\!$ $~~ \mathrm{d}p ~~ \texttt{(} \mathrm{d}q \texttt{)}\!$ $\mathrm{d}q\!$ $=\!$ $~~ \mathrm{d}p ~~~~ \mathrm{d}q ~~\!$ $+\!$ $\texttt{(} \mathrm{d}p \texttt{)} ~~ \mathrm{d}q ~~\!$

#### TeX Array

 $\begin{array}{rcccccc} \mathrm{d}(pq) & = & p & \cdot & q & \cdot & \texttt{(} \mathrm{d}p \texttt{,} \mathrm{d}q \texttt{)} \\[4pt] & + & p & \cdot & \texttt{(} q \texttt{)} & \cdot & \mathrm{d}q \\[4pt] & + & \texttt{(} p \texttt{)} & \cdot & q & \cdot & \mathrm{d}p \\[4pt] & + & \texttt{(} p \texttt{)} & \cdot & \texttt{(} q \texttt{)} & \cdot & 0 \end{array}\!$
 $\begin{matrix} \texttt{(} \mathrm{d}p \texttt{,} \mathrm{d}q \texttt{)} & = & \mathrm{d}p ~ \texttt{(} \mathrm{d}q \texttt{)} & + & \texttt{(} \mathrm{d}p \texttt{)} ~ \mathrm{d}q \\[4pt] dp & = & \mathrm{d}p ~ \mathrm{d}q & + & \mathrm{d}p ~ \texttt{(} \mathrm{d}q \texttt{)} \\[4pt] \mathrm{d}q & = & \mathrm{d}p ~ \mathrm{d}q & + & \texttt{(} \mathrm{d}p \texttt{)} ~ \mathrm{d}q \end{matrix}\!$

### Remainder Map

#### Wiki Table

 $\mathrm{r}(pq)\!$ $=\!$ $p\!$ $\cdot\!$ $q\!$ $\cdot\!$ $\mathrm{d}p ~ \mathrm{d}q\!$ $+\!$ $p\!$ $\cdot\!$ $\texttt{(} q \texttt{)}\!$ $\cdot\!$ $\mathrm{d}p ~ \mathrm{d}q\!$ $+\!$ $\texttt{(} p \texttt{)}\!$ $\cdot\!$ $q\!$ $\cdot\!$ $\mathrm{d}p ~ \mathrm{d}q\!$ $+\!$ $\texttt{(} p \texttt{)}\!$ $\cdot\!$ $\texttt{(} q \texttt{)}\!$ $\cdot\!$ $\mathrm{d}p ~ \mathrm{d}q\!$

#### TeX Array

 $\begin{array}{rcccccc} \mathrm{r}(pq) & = & p & \cdot & q & \cdot & \mathrm{d}p ~ \mathrm{d}q \\[4pt] & + & p & \cdot & \texttt{(} q \texttt{)} & \cdot & \mathrm{d}p ~ \mathrm{d}q \\[4pt] & + & \texttt{(} p \texttt{)} & \cdot & q & \cdot & \mathrm{d}p ~ \mathrm{d}q \\[4pt] & + & \texttt{(} p \texttt{)} & \cdot & \texttt{(} q \texttt{)} & \cdot & \mathrm{d}p ~ \mathrm{d}q \end{array}\!$

## Fourier Analysis

 $\begin{array}{|c||*{4}{c}|} \hline g & f_{8} & f_{4} & f_{2} & f_{1} \\ & \texttt{ } u \texttt{ } v \texttt{ } & \texttt{ } u \texttt{ (} v \texttt{)} & \texttt{(} u \texttt{) } v \texttt{ } & \texttt{(} u \texttt{)(} v \texttt{)} \\ \hline\hline f_{7} & 0 & 1 & 1 & 1 \\ f_{11} & 1 & 0 & 1 & 1 \\ f_{13} & 1 & 1 & 0 & 1 \\ f_{14} & 1 & 1 & 1 & 0 \\ \hline \end{array}\!$

## Logical Implication

 $\begin{array}{|c||cc|} \hline \texttt{=}\!\texttt{<} & 0 & 1 \\ \hline\hline 0 & 1 & 1 \\ 1 & 0 & 1 \\ \hline \end{array}\!$

 $\texttt{=}\!\texttt{<}\!$ $0\!$ $1\!$ $0\!$ $1\!$ $1\!$ $1\!$ $0\!$ $1\!$