User:JonAwbrey/Tables

Differential Logic

Tacit Extension

Wiki Table

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

TeX Array

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

Enlargement Map

Wiki Table

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

TeX Array 1

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

TeX Array 2

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

Difference Map

Wiki Table

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

TeX Array

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

Tangent Map

Wiki Table

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

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

TeX Array

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

Remainder Map

Wiki Table

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

TeX Array

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

Fourier Analysis

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

Logical Implication

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

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