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Alternates and Experiments
Differential Operator Tables • Conjunction PQR
Version 1
LaTeX Tables
JPG Images
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Version 4
LaTeX Tables
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%d
![\begin{array}{|*{8}{c}|} \multicolumn{8}{c}{\text{Enlargement Map} ~ \mathrm{E}(pqr)} \\[4pt] \hline &&&&&&& \\ \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} & \texttt{~} p \texttt{~~} q \texttt{~(} r \texttt{)} & \texttt{~} p \texttt{~(} q \texttt{)~} r \texttt{~} & \texttt{~} p \texttt{~(} q \texttt{)(} r \texttt{)} & \texttt{(} p \texttt{)~} q \texttt{~~} r \texttt{~} & \texttt{(} p \texttt{)~} q \texttt{~(} r \texttt{)} & \texttt{(} p \texttt{)(} q \texttt{)~} r \texttt{~} & \texttt{(} p \texttt{)(} q \texttt{)(} r \texttt{)} \\ \hline &&&&&&& \\ \texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)} &&&&&&& \\ & \texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)} \mathrm{d}r &&&&&& \\ && \texttt{(} \mathrm{d}p \texttt{)} \mathrm{d}q \texttt{(} \mathrm{d}r \texttt{)} &&&&& \\ &&& \texttt{(} \mathrm{d}p \texttt{)} \mathrm{d}q \, \mathrm{d}r &&&& \\ &&&& \mathrm{d}p \texttt{(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)} &&& \\ &&&&& \mathrm{d}p \texttt{(} \mathrm{d}q \texttt{)} \mathrm{d}r && \\ &&&&&& \mathrm{d}p \, \mathrm{d}q \texttt{(} \mathrm{d}r \texttt{)} & \\ &&&&&&& \mathrm{d}p \, \mathrm{d}q \, \mathrm{d}r \\ \hline \end{array}](https://s0.wp.com/latex.php?latex=%5Cbegin%7Barray%7D%7B%7C%2A%7B8%7D%7Bc%7D%7C%7D++%5Cmulticolumn%7B8%7D%7Bc%7D%7B%5Ctext%7BEnlargement+Map%7D+%7E+%5Cmathrm%7BE%7D%28pqr%29%7D+%5C%5C%5B4pt%5D++%5Chline+%26%26%26%26%26%26%26+%5C%5C++%5Ctexttt%7B%7E%7D+p+%5Ctexttt%7B%7E%7E%7D+q+%5Ctexttt%7B%7E%7E%7D+r+%5Ctexttt%7B%7E%7D+%26++%5Ctexttt%7B%7E%7D+p+%5Ctexttt%7B%7E%7E%7D+q+%5Ctexttt%7B%7E%28%7D+r+%5Ctexttt%7B%29%7D+%26++%5Ctexttt%7B%7E%7D+p+%5Ctexttt%7B%7E%28%7D+q+%5Ctexttt%7B%29%7E%7D+r+%5Ctexttt%7B%7E%7D+%26++%5Ctexttt%7B%7E%7D+p+%5Ctexttt%7B%7E%28%7D+q+%5Ctexttt%7B%29%28%7D+r+%5Ctexttt%7B%29%7D+%26++%5Ctexttt%7B%28%7D+p+%5Ctexttt%7B%29%7E%7D+q+%5Ctexttt%7B%7E%7E%7D+r+%5Ctexttt%7B%7E%7D+%26++%5Ctexttt%7B%28%7D+p+%5Ctexttt%7B%29%7E%7D+q+%5Ctexttt%7B%7E%28%7D+r+%5Ctexttt%7B%29%7D+%26++%5Ctexttt%7B%28%7D+p+%5Ctexttt%7B%29%28%7D+q+%5Ctexttt%7B%29%7E%7D+r+%5Ctexttt%7B%7E%7D+%26++%5Ctexttt%7B%28%7D+p+%5Ctexttt%7B%29%28%7D+q+%5Ctexttt%7B%29%28%7D+r+%5Ctexttt%7B%29%7D+%5C%5C++%5Chline+%26%26%26%26%26%26%26+%5C%5C++%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%29%28%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%29%28%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%29%7D++%26%26%26%26%26%26%26+%5C%5C+%26++%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%29%28%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%29%7D+%5Cmathrm%7Bd%7Dr++%26%26%26%26%26%26+%5C%5C+%26%26++%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%29%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%29%7D++%26%26%26%26%26+%5C%5C+%26%26%26++%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%29%7D+%5Cmathrm%7Bd%7Dq+%5C%2C+%5Cmathrm%7Bd%7Dr++%26%26%26%26+%5C%5C+%26%26%26%26++%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%29%28%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%29%7D++%26%26%26+%5C%5C+%26%26%26%26%26++%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%29%7D+%5Cmathrm%7Bd%7Dr+%26%26+%5C%5C++%26%26%26%26%26%26+%5Cmathrm%7Bd%7Dp+%5C%2C+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dr++%5Ctexttt%7B%29%7D+%26+%5C%5C+%26%26%26%26%26%26%26++%5Cmathrm%7Bd%7Dp+%5C%2C+%5Cmathrm%7Bd%7Dq+%5C%2C+%5Cmathrm%7Bd%7Dr+%5C%5C++%5Chline++%5Cend%7Barray%7D&bg=ffffff&fg=000000&s=0&c=20201002)
![\begin{array}{|*{8}{c}|} \multicolumn{8}{c}{\text{Tacit Extension} ~ \boldsymbol\varepsilon (pqr)} \\[4pt] \hline &&&&&&& \\ \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} & \texttt{~} p \texttt{~~} q \texttt{~(} r \texttt{)} & \texttt{~} p \texttt{~(} q \texttt{)~} r \texttt{~} & \texttt{~} p \texttt{~(} q \texttt{)(} r \texttt{)} & \texttt{(} p \texttt{)~} q \texttt{~~} r \texttt{~} & \texttt{(} p \texttt{)~} q \texttt{~(} r \texttt{)} & \texttt{(} p \texttt{)(} q \texttt{)~} r \texttt{~} & \texttt{(} p \texttt{)(} q \texttt{)(} r \texttt{)} \\ \hline &&&&&&& \\ \texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)} &&&&&&& \\ \texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~} &&&&&&& \\ \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)} &&&&&&& \\ \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~} &&&&&&& \\ \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)} &&&&&&& \\ \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~} &&&&&&& \\ \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)} &&&&&&& \\ \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~} &&&&&&& \\ \hline \end{array}](https://s0.wp.com/latex.php?latex=%5Cbegin%7Barray%7D%7B%7C%2A%7B8%7D%7Bc%7D%7C%7D++%5Cmulticolumn%7B8%7D%7Bc%7D%7B%5Ctext%7BTacit+Extension%7D+%7E+%5Cboldsymbol%5Cvarepsilon+%28pqr%29%7D+%5C%5C%5B4pt%5D++%5Chline+%26%26%26%26%26%26%26+%5C%5C++%5Ctexttt%7B%7E%7D+p+%5Ctexttt%7B%7E%7E%7D+q+%5Ctexttt%7B%7E%7E%7D+r+%5Ctexttt%7B%7E%7D+%26++%5Ctexttt%7B%7E%7D+p+%5Ctexttt%7B%7E%7E%7D+q+%5Ctexttt%7B%7E%28%7D+r+%5Ctexttt%7B%29%7D+%26++%5Ctexttt%7B%7E%7D+p+%5Ctexttt%7B%7E%28%7D+q+%5Ctexttt%7B%29%7E%7D+r+%5Ctexttt%7B%7E%7D+%26++%5Ctexttt%7B%7E%7D+p+%5Ctexttt%7B%7E%28%7D+q+%5Ctexttt%7B%29%28%7D+r+%5Ctexttt%7B%29%7D+%26++%5Ctexttt%7B%28%7D+p+%5Ctexttt%7B%29%7E%7D+q+%5Ctexttt%7B%7E%7E%7D+r+%5Ctexttt%7B%7E%7D+%26++%5Ctexttt%7B%28%7D+p+%5Ctexttt%7B%29%7E%7D+q+%5Ctexttt%7B%7E%28%7D+r+%5Ctexttt%7B%29%7D+%26++%5Ctexttt%7B%28%7D+p+%5Ctexttt%7B%29%28%7D+q+%5Ctexttt%7B%29%7E%7D+r+%5Ctexttt%7B%7E%7D+%26++%5Ctexttt%7B%28%7D+p+%5Ctexttt%7B%29%28%7D+q+%5Ctexttt%7B%29%28%7D+r+%5Ctexttt%7B%29%7D+%5C%5C++%5Chline+%26%26%26%26%26%26%26+%5C%5C++%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%29%28%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%29%28%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%29%7D+%26%26%26%26%26%26%26+%5C%5C++%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%29%28%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%29%7E%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%7E%7D+%26%26%26%26%26%26%26+%5C%5C++%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%29%7E%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%7E%28%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%29%7D+%26%26%26%26%26%26%26+%5C%5C++%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%29%7E%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%7E%7E%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%7E%7D+%26%26%26%26%26%26%26+%5C%5C++%5Ctexttt%7B%7E%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%7E%28%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%29%28%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%29%7D+%26%26%26%26%26%26%26+%5C%5C++%5Ctexttt%7B%7E%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%7E%28%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%29%7E%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%7E%7D+%26%26%26%26%26%26%26+%5C%5C++%5Ctexttt%7B%7E%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%7E%7E%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%7E%28%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%29%7D+%26%26%26%26%26%26%26+%5C%5C++%5Ctexttt%7B%7E%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%7E%7E%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%7E%7E%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%7E%7D+%26%26%26%26%26%26%26+%5C%5C++%5Chline++%5Cend%7Barray%7D&bg=ffffff&fg=000000&s=0&c=20201002)
![\begin{array}{|*{8}{c}|} \multicolumn{8}{c}{\text{Difference Map} ~ \mathrm{D}(pqr)} \\[4pt] \hline &&&&&&& \\ \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} & \texttt{~} p \texttt{~~} q \texttt{~(} r \texttt{)} & \texttt{~} p \texttt{~(} q \texttt{)~} r \texttt{~} & \texttt{~} p \texttt{~(} q \texttt{)(} r \texttt{)} & \texttt{(} p \texttt{)~} q \texttt{~~} r \texttt{~} & \texttt{(} p \texttt{)~} q \texttt{~(} r \texttt{)} & \texttt{(} p \texttt{)(} q \texttt{)~} r \texttt{~} & \texttt{(} p \texttt{)(} q \texttt{)(} r \texttt{)} \\ \hline &&&&&&& \\ 0 &&&&&&& \\ \texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~} & \texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)} \mathrm{d}r &&&&&& \\ \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)} && \texttt{(} \mathrm{d}p \texttt{)} \mathrm{d}q \texttt{(} \mathrm{d}r \texttt{)} &&&&& \\ \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~} &&& \texttt{(} \mathrm{d}p \texttt{)} \mathrm{d}q \, \mathrm{d}r &&&& \\ \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)} &&&& \mathrm{d}p \texttt{(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)} &&& \\ \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~} &&&&& \mathrm{d}p \texttt{(} \mathrm{d}q \texttt{)} \mathrm{d}r && \\ \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)} &&&&&& \mathrm{d}p \, \mathrm{d}q \texttt{(} \mathrm{d}r \texttt{)} & \\ \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~} &&&&&&& \mathrm{d}p \, \mathrm{d}q \, \mathrm{d}r \\ \hline \end{array}](https://s0.wp.com/latex.php?latex=%5Cbegin%7Barray%7D%7B%7C%2A%7B8%7D%7Bc%7D%7C%7D++%5Cmulticolumn%7B8%7D%7Bc%7D%7B%5Ctext%7BDifference+Map%7D+%7E+%5Cmathrm%7BD%7D%28pqr%29%7D+%5C%5C%5B4pt%5D++%5Chline+%26%26%26%26%26%26%26+%5C%5C++%5Ctexttt%7B%7E%7D+p+%5Ctexttt%7B%7E%7E%7D+q+%5Ctexttt%7B%7E%7E%7D+r+%5Ctexttt%7B%7E%7D+%26++%5Ctexttt%7B%7E%7D+p+%5Ctexttt%7B%7E%7E%7D+q+%5Ctexttt%7B%7E%28%7D+r+%5Ctexttt%7B%29%7D+%26++%5Ctexttt%7B%7E%7D+p+%5Ctexttt%7B%7E%28%7D+q+%5Ctexttt%7B%29%7E%7D+r+%5Ctexttt%7B%7E%7D+%26++%5Ctexttt%7B%7E%7D+p+%5Ctexttt%7B%7E%28%7D+q+%5Ctexttt%7B%29%28%7D+r+%5Ctexttt%7B%29%7D+%26++%5Ctexttt%7B%28%7D+p+%5Ctexttt%7B%29%7E%7D+q+%5Ctexttt%7B%7E%7E%7D+r+%5Ctexttt%7B%7E%7D+%26++%5Ctexttt%7B%28%7D+p+%5Ctexttt%7B%29%7E%7D+q+%5Ctexttt%7B%7E%28%7D+r+%5Ctexttt%7B%29%7D+%26++%5Ctexttt%7B%28%7D+p+%5Ctexttt%7B%29%28%7D+q+%5Ctexttt%7B%29%7E%7D+r+%5Ctexttt%7B%7E%7D+%26++%5Ctexttt%7B%28%7D+p+%5Ctexttt%7B%29%28%7D+q+%5Ctexttt%7B%29%28%7D+r+%5Ctexttt%7B%29%7D+%5C%5C++%5Chline+%26%26%26%26%26%26%26+%5C%5C++0+%26%26%26%26%26%26%26+%5C%5C++%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%29%28%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%29%7E%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%7E%7D++%26+%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%29%28%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%29%7D+%5Cmathrm%7Bd%7Dr+%26%26%26%26%26%26+%5C%5C++%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%29%7E%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%7E%28%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%29%7D++%26%26+%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%29%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%29%7D+%26%26%26%26%26+%5C%5C++%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%29%7E%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%7E%7E%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%7E%7D++%26%26%26+%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%29%7D+%5Cmathrm%7Bd%7Dq+%5C%2C+%5Cmathrm%7Bd%7Dr+%26%26%26%26+%5C%5C++%5Ctexttt%7B%7E%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%7E%28%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%29%28%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%29%7D++%26%26%26%26+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%29%28%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%29%7D+%26%26%26+%5C%5C++%5Ctexttt%7B%7E%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%7E%28%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%29%7E%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%7E%7D++%26%26%26%26%26+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%29%7D+%5Cmathrm%7Bd%7Dr+%26%26+%5C%5C++%5Ctexttt%7B%7E%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%7E%7E%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%7E%28%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%29%7D++%26%26%26%26%26%26+%5Cmathrm%7Bd%7Dp+%5C%2C+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%29%7D+%26+%5C%5C++%5Ctexttt%7B%7E%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%7E%7E%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%7E%7E%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%7E%7D++%26%26%26%26%26%26%26+%5Cmathrm%7Bd%7Dp+%5C%2C+%5Cmathrm%7Bd%7Dq+%5C%2C+%5Cmathrm%7Bd%7Dr+%5C%5C++%5Chline++%5Cend%7Barray%7D&bg=ffffff&fg=000000&s=0&c=20201002)
![\begin{array}{|*{8}{c}|} \multicolumn{8}{c}{\text{Enlargement Map} ~ \mathrm{E}(pqr)} \\[4pt] \hline &&&&&&& \\ \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} & \texttt{(} p \texttt{)~} q \texttt{~~} r \texttt{~} & \texttt{~} p \texttt{~(} q \texttt{)~} r \texttt{~} & \texttt{~} p \texttt{~~} q \texttt{~(} r \texttt{)} & \texttt{(} p \texttt{)(} q \texttt{)~} r \texttt{~} & \texttt{(} p \texttt{)~} q \texttt{~(} r \texttt{)} & \texttt{~} p \texttt{~(} q \texttt{)(} r \texttt{)} & \texttt{(} p \texttt{)(} q \texttt{)(} r \texttt{)} \\ \hline &&&&&&& \\ \texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)} &&&&&&& \\ & \mathrm{d}p \texttt{(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)} &&&&&& \\ && \texttt{(} \mathrm{d}p \texttt{)} \mathrm{d}q \texttt{(} \mathrm{d}r \texttt{)} &&&&& \\ &&& \texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)} \mathrm{d}r &&&& \\ &&&& \mathrm{d}p ~ \mathrm{d}q \texttt{(} \mathrm{d}r \texttt{)} &&& \\ &&&&& \mathrm{d}p \texttt{(} \mathrm{d}q \texttt{)} \mathrm{d}r && \\ &&&&&& \texttt{(} \mathrm{d}p \texttt{)} \mathrm{d}q ~ \mathrm{d}r & \\ &&&&&&& \mathrm{d}p ~ \mathrm{d}q ~ \mathrm{d}r \\ \hline \end{array}](https://s0.wp.com/latex.php?latex=%5Cbegin%7Barray%7D%7B%7C%2A%7B8%7D%7Bc%7D%7C%7D++%5Cmulticolumn%7B8%7D%7Bc%7D%7B%5Ctext%7BEnlargement+Map%7D+%7E+%5Cmathrm%7BE%7D%28pqr%29%7D+%5C%5C%5B4pt%5D++%5Chline+%26%26%26%26%26%26%26+%5C%5C++%5Ctexttt%7B%7E%7D+p+%5Ctexttt%7B%7E%7E%7D+q+%5Ctexttt%7B%7E%7E%7D+r+%5Ctexttt%7B%7E%7D+%26++%5Ctexttt%7B%28%7D+p+%5Ctexttt%7B%29%7E%7D+q+%5Ctexttt%7B%7E%7E%7D+r+%5Ctexttt%7B%7E%7D+%26++%5Ctexttt%7B%7E%7D+p+%5Ctexttt%7B%7E%28%7D+q+%5Ctexttt%7B%29%7E%7D+r+%5Ctexttt%7B%7E%7D+%26++%5Ctexttt%7B%7E%7D+p+%5Ctexttt%7B%7E%7E%7D+q+%5Ctexttt%7B%7E%28%7D+r+%5Ctexttt%7B%29%7D+%26++%5Ctexttt%7B%28%7D+p+%5Ctexttt%7B%29%28%7D+q+%5Ctexttt%7B%29%7E%7D+r+%5Ctexttt%7B%7E%7D+%26++%5Ctexttt%7B%28%7D+p+%5Ctexttt%7B%29%7E%7D+q+%5Ctexttt%7B%7E%28%7D+r+%5Ctexttt%7B%29%7D+%26++%5Ctexttt%7B%7E%7D+p+%5Ctexttt%7B%7E%28%7D+q+%5Ctexttt%7B%29%28%7D+r+%5Ctexttt%7B%29%7D+%26++%5Ctexttt%7B%28%7D+p+%5Ctexttt%7B%29%28%7D+q+%5Ctexttt%7B%29%28%7D+r+%5Ctexttt%7B%29%7D+%5C%5C++%5Chline+%26%26%26%26%26%26%26+%5C%5C++%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%29%28%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%29%28%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%29%7D++%26%26%26%26%26%26%26+%5C%5C+%26++%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%29%28%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%29%7D++%26%26%26%26%26%26+%5C%5C+%26%26++%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%29%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%29%7D++%26%26%26%26%26+%5C%5C+%26%26%26++%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%29%28%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%29%7D+%5Cmathrm%7Bd%7Dr++%26%26%26%26+%5C%5C+%26%26%26%26++%5Cmathrm%7Bd%7Dp+%7E+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%29%7D++%26%26%26+%5C%5C+%26%26%26%26%26++%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%29%7D+%5Cmathrm%7Bd%7Dr++%26%26+%5C%5C+%26%26%26%26%26%26++%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%29%7D+%5Cmathrm%7Bd%7Dq+%7E+%5Cmathrm%7Bd%7Dr++%26+%5C%5C+%26%26%26%26%26%26%26++%5Cmathrm%7Bd%7Dp+%7E+%5Cmathrm%7Bd%7Dq+%7E+%5Cmathrm%7Bd%7Dr+%5C%5C++%5Chline++%5Cend%7Barray%7D&bg=ffffff&fg=000000&s=0&c=20201002)
![\begin{array}{|*{8}{c}|} \multicolumn{8}{c}{\text{Tacit Extension} ~ \boldsymbol\varepsilon (pqr)} \\[4pt] \hline &&&&&&& \\ \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} & \texttt{(} p \texttt{)~} q \texttt{~~} r \texttt{~} & \texttt{~} p \texttt{~(} q \texttt{)~} r \texttt{~} & \texttt{~} p \texttt{~~} q \texttt{~(} r \texttt{)} & \texttt{(} p \texttt{)(} q \texttt{)~} r \texttt{~} & \texttt{(} p \texttt{)~} q \texttt{~(} r \texttt{)} & \texttt{~} p \texttt{~(} q \texttt{)(} r \texttt{)} & \texttt{(} p \texttt{)(} q \texttt{)(} r \texttt{)} \\ \hline &&&&&&& \\ \texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)} &&&&&&& \\ \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)} &&&&&&& \\ \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)} &&&&&&& \\ \texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~} &&&&&&& \\ \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)} &&&&&&& \\ \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~} &&&&&&& \\ \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~} &&&&&&& \\ \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~} &&&&&&& \\ \hline \end{array}](https://s0.wp.com/latex.php?latex=%5Cbegin%7Barray%7D%7B%7C%2A%7B8%7D%7Bc%7D%7C%7D++%5Cmulticolumn%7B8%7D%7Bc%7D%7B%5Ctext%7BTacit+Extension%7D+%7E+%5Cboldsymbol%5Cvarepsilon+%28pqr%29%7D+%5C%5C%5B4pt%5D++%5Chline+%26%26%26%26%26%26%26+%5C%5C++%5Ctexttt%7B%7E%7D+p+%5Ctexttt%7B%7E%7E%7D+q+%5Ctexttt%7B%7E%7E%7D+r+%5Ctexttt%7B%7E%7D+%26++%5Ctexttt%7B%28%7D+p+%5Ctexttt%7B%29%7E%7D+q+%5Ctexttt%7B%7E%7E%7D+r+%5Ctexttt%7B%7E%7D+%26++%5Ctexttt%7B%7E%7D+p+%5Ctexttt%7B%7E%28%7D+q+%5Ctexttt%7B%29%7E%7D+r+%5Ctexttt%7B%7E%7D+%26++%5Ctexttt%7B%7E%7D+p+%5Ctexttt%7B%7E%7E%7D+q+%5Ctexttt%7B%7E%28%7D+r+%5Ctexttt%7B%29%7D+%26++%5Ctexttt%7B%28%7D+p+%5Ctexttt%7B%29%28%7D+q+%5Ctexttt%7B%29%7E%7D+r+%5Ctexttt%7B%7E%7D+%26++%5Ctexttt%7B%28%7D+p+%5Ctexttt%7B%29%7E%7D+q+%5Ctexttt%7B%7E%28%7D+r+%5Ctexttt%7B%29%7D+%26++%5Ctexttt%7B%7E%7D+p+%5Ctexttt%7B%7E%28%7D+q+%5Ctexttt%7B%29%28%7D+r+%5Ctexttt%7B%29%7D+%26++%5Ctexttt%7B%28%7D+p+%5Ctexttt%7B%29%28%7D+q+%5Ctexttt%7B%29%28%7D+r+%5Ctexttt%7B%29%7D+%5C%5C++%5Chline+%26%26%26%26%26%26%26+%5C%5C++%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%29%28%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%29%28%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%29%7D+%26%26%26%26%26%26%26+%5C%5C++%5Ctexttt%7B%7E%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%7E%28%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%29%28%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%29%7D+%26%26%26%26%26%26%26+%5C%5C++%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%29%7E%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%7E%28%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%29%7D+%26%26%26%26%26%26%26+%5C%5C++%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%29%28%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%29%7E%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%7E%7D+%26%26%26%26%26%26%26+%5C%5C++%5Ctexttt%7B%7E%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%7E%7E%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%7E%28%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%29%7D+%26%26%26%26%26%26%26+%5C%5C++%5Ctexttt%7B%7E%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%7E%28%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%29%7E%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%7E%7D+%26%26%26%26%26%26%26+%5C%5C++%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%29%7E%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%7E%7E%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%7E%7D+%26%26%26%26%26%26%26+%5C%5C++%5Ctexttt%7B%7E%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%7E%7E%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%7E%7E%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%7E%7D+%26%26%26%26%26%26%26+%5C%5C++%5Chline++%5Cend%7Barray%7D&bg=ffffff&fg=000000&s=0&c=20201002)
![\begin{array}{|*{8}{c}|} \multicolumn{8}{c}{\text{Difference Map} ~ \mathrm{D}(pqr)} \\[4pt] \hline &&&&&&& \\ \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} & \texttt{(} p \texttt{)~} q \texttt{~~} r \texttt{~} & \texttt{~} p \texttt{~(} q \texttt{)~} r \texttt{~} & \texttt{~} p \texttt{~~} q \texttt{~(} r \texttt{)} & \texttt{(} p \texttt{)(} q \texttt{)~} r \texttt{~} & \texttt{(} p \texttt{)~} q \texttt{~(} r \texttt{)} & \texttt{~} p \texttt{~(} q \texttt{)(} r \texttt{)} & \texttt{(} p \texttt{)(} q \texttt{)(} r \texttt{)} \\ \hline &&&&&&& \\ 0 &&&&&&& \\ \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)} & \mathrm{d}p \texttt{(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)} &&&&&& \\ \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)} && \texttt{(} \mathrm{d}p \texttt{)} \mathrm{d}q \texttt{(} \mathrm{d}r \texttt{)} &&&&& \\ \texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~} &&& \texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)} \mathrm{d}r &&&& \\ \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)} &&&& \mathrm{d}p ~ \mathrm{d}q \texttt{(} \mathrm{d}r \texttt{)} &&& \\ \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~} &&&&& \mathrm{d}p \texttt{(} \mathrm{d}q \texttt{)} \mathrm{d}r && \\ \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~} &&&&&& \texttt{(} \mathrm{d}p \texttt{)} \mathrm{d}q ~ \mathrm{d}r & \\ \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~} &&&&&&& \mathrm{d}p ~ \mathrm{d}q ~ \mathrm{d}r \\ \hline \end{array}](https://s0.wp.com/latex.php?latex=%5Cbegin%7Barray%7D%7B%7C%2A%7B8%7D%7Bc%7D%7C%7D++%5Cmulticolumn%7B8%7D%7Bc%7D%7B%5Ctext%7BDifference+Map%7D+%7E+%5Cmathrm%7BD%7D%28pqr%29%7D+%5C%5C%5B4pt%5D++%5Chline+%26%26%26%26%26%26%26+%5C%5C++%5Ctexttt%7B%7E%7D+p+%5Ctexttt%7B%7E%7E%7D+q+%5Ctexttt%7B%7E%7E%7D+r+%5Ctexttt%7B%7E%7D+%26++%5Ctexttt%7B%28%7D+p+%5Ctexttt%7B%29%7E%7D+q+%5Ctexttt%7B%7E%7E%7D+r+%5Ctexttt%7B%7E%7D+%26++%5Ctexttt%7B%7E%7D+p+%5Ctexttt%7B%7E%28%7D+q+%5Ctexttt%7B%29%7E%7D+r+%5Ctexttt%7B%7E%7D+%26++%5Ctexttt%7B%7E%7D+p+%5Ctexttt%7B%7E%7E%7D+q+%5Ctexttt%7B%7E%28%7D+r+%5Ctexttt%7B%29%7D+%26++%5Ctexttt%7B%28%7D+p+%5Ctexttt%7B%29%28%7D+q+%5Ctexttt%7B%29%7E%7D+r+%5Ctexttt%7B%7E%7D+%26++%5Ctexttt%7B%28%7D+p+%5Ctexttt%7B%29%7E%7D+q+%5Ctexttt%7B%7E%28%7D+r+%5Ctexttt%7B%29%7D+%26++%5Ctexttt%7B%7E%7D+p+%5Ctexttt%7B%7E%28%7D+q+%5Ctexttt%7B%29%28%7D+r+%5Ctexttt%7B%29%7D+%26++%5Ctexttt%7B%28%7D+p+%5Ctexttt%7B%29%28%7D+q+%5Ctexttt%7B%29%28%7D+r+%5Ctexttt%7B%29%7D+%5C%5C++%5Chline+%26%26%26%26%26%26%26+%5C%5C++0+%26%26%26%26%26%26%26+%5C%5C++%5Ctexttt%7B%7E%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%7E%28%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%29%28%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%29%7D+%26++%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%29%28%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%29%7D+%26%26%26%26%26%26+%5C%5C++%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%29%7E%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%7E%28%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%29%7D+%26%26++%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%29%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%29%7D+%26%26%26%26%26+%5C%5C++%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%29%28%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%29%7E%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%7E%7D+%26%26%26++%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%29%28%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%29%7D+%5Cmathrm%7Bd%7Dr+%26%26%26%26+%5C%5C++%5Ctexttt%7B%7E%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%7E%7E%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%7E%28%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%29%7D+%26%26%26%26++%5Cmathrm%7Bd%7Dp+%7E+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%29%7D+%26%26%26+%5C%5C++%5Ctexttt%7B%7E%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%7E%28%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%29%7E%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%7E%7D+%26%26%26%26%26++%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%29%7D+%5Cmathrm%7Bd%7Dr+%26%26+%5C%5C++%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%29%7E%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%7E%7E%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%7E%7D+%26%26%26%26%26%26++%5Ctexttt%7B%28%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%29%7D+%5Cmathrm%7Bd%7Dq+%7E+%5Cmathrm%7Bd%7Dr+%26+%5C%5C++%5Ctexttt%7B%7E%7D+%5Cmathrm%7Bd%7Dp+%5Ctexttt%7B%7E%7E%7D+%5Cmathrm%7Bd%7Dq+%5Ctexttt%7B%7E%7E%7D+%5Cmathrm%7Bd%7Dr+%5Ctexttt%7B%7E%7D+%26%26%26%26%26%26%26++%5Cmathrm%7Bd%7Dp+%7E+%5Cmathrm%7Bd%7Dq+%7E+%5Cmathrm%7Bd%7Dr+%5C%5C++%5Chline++%5Cend%7Barray%7D&bg=ffffff&fg=000000&s=0&c=20201002)
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