User:Jon Awbrey/TABLES

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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\!