Work 9

Difference Map • Conjunction PQR

Version 1 (a)

\begin{array}{*{4}{l}}  \multicolumn{4}{l}{\mathrm{D}f(p, q, r, \mathrm{d}p, \mathrm{d}q, \mathrm{d}r) =}  \\[10pt]  &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~}  & + &  \texttt{~} p \texttt{~~} q \texttt{~(} r \texttt{)} \cdot  \texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~}  \\[10pt]  + &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)}  & + &  \texttt{~} p \texttt{~(} q \texttt{)~} r \texttt{~} \cdot  \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)}  \\[10pt]  + &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~}  & + &  \texttt{~} p \texttt{~(} q \texttt{)(} r \texttt{)} \cdot  \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~}  \end{array}
 
\begin{array}{*{4}{l}}  + &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)}  & + &  \texttt{(} p \texttt{)~} q \texttt{~~} r \texttt{~} \cdot  \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)}  \\[10pt]  + &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~}  & + &  \texttt{(} p \texttt{)~} q \texttt{~(} r \texttt{)} \cdot  \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~}  \\[10pt]  + &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)}  & + &  \texttt{(} p \texttt{)(} q \texttt{)~} r \texttt{~} \cdot  \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)}  \\[10pt]  + &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~}  & + &  \texttt{(} p \texttt{)(} q \texttt{)(} r \texttt{)} \cdot  \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~}  \end{array}

Version 1 (b)

\begin{array}{*{4}{l}}  \multicolumn{4}{l}{\mathrm{D}f(p, q, r, \mathrm{d}p, \mathrm{d}q, \mathrm{d}r) =}  \\[10pt]  &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~}  & + &  \texttt{(} p \texttt{)(} q \texttt{)(} r \texttt{)} \cdot  \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~}  \\[10pt]  + &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)}  & + &  \texttt{(} p \texttt{)(} q \texttt{)~} r \texttt{~} \cdot  \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)}  \\[10pt]  + &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~}  & + &  \texttt{(} p \texttt{)~} q \texttt{~(} r \texttt{)} \cdot  \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~}  \end{array}
 
\begin{array}{*{4}{l}}  + &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)}  & + &  \texttt{(} p \texttt{)~} q \texttt{~~} r \texttt{~} \cdot  \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)}  \\[10pt]  + &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~}  & + &  \texttt{~} p \texttt{~(} q \texttt{)(} r \texttt{)} \cdot  \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~}  \\[10pt]  + &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)}  & + &  \texttt{~} p \texttt{~(} q \texttt{)~} r \texttt{~} \cdot  \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)}  \\[10pt]  + &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~}  & + &  \texttt{~} p \texttt{~~} q \texttt{~(} r \texttt{)} \cdot  \texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~}\end{array}

Version 4

\begin{array}{*{4}{l}}  \multicolumn{4}{l}{\mathrm{D}f(p, q, r, \mathrm{d}p, \mathrm{d}q, \mathrm{d}r) =}  \\[10pt]  &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)}  & + &  \texttt{(} p \texttt{)~} q \texttt{~~} r \texttt{~} \cdot  \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)}  \\[10pt]  + &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)}  & + &  \texttt{~} p \texttt{~(} q \texttt{)~} r \texttt{~} \cdot  \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)}  \\[10pt]  + &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~}  & + &  \texttt{~} p \texttt{~~} q \texttt{~(} r \texttt{)} \cdot  \texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~}  \end{array}
 
\begin{array}{*{4}{l}}  + &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)}  & + &  \texttt{(} p \texttt{)(} q \texttt{)~} r \texttt{~} \cdot  \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)}  \\[10pt]  + &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~}  & + &  \texttt{(} p \texttt{)~} q \texttt{~(} r \texttt{)} \cdot  \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~}  \\[10pt]  + &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~}  & + &  \texttt{~} p \texttt{~(} q \texttt{)(} r \texttt{)} \cdot  \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~}  \\[10pt]  + &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~}  & + &  \texttt{(} p \texttt{)(} q \texttt{)(} r \texttt{)} \cdot  \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~}  \end{array}

Column Sum

\begin{array}{*{4}{c}}  \multicolumn{4}{l}{\mathrm{D}f(p, q, r, \mathrm{d}p, \mathrm{d}q, \mathrm{d}r) =}  \\[10pt]  &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~}  & \cdot &  \texttt{((} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{))}  \\[4pt]  + &  \texttt{(} p \texttt{)~} q \texttt{~~} r \texttt{~}  & \cdot &  \texttt{~~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)~}  \\[4pt]  + &  \texttt{~} p \texttt{~(} q \texttt{)~} r \texttt{~}  & \cdot &  \texttt{~(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)~}  \\[4pt]  + &  \texttt{~} p \texttt{~~} q \texttt{~(} r \texttt{)}  & \cdot &  \texttt{~(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~~}  \\[4pt]  + &  \texttt{(} p \texttt{)(} q \texttt{)~} r \texttt{~}  & \cdot &  \texttt{~~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)~}  \\[4pt]  + &  \texttt{(} p \texttt{)~} q \texttt{~(} r \texttt{)}  & \cdot &  \texttt{~~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~~}  \\[4pt]  + &  \texttt{~} p \texttt{~(} q \texttt{)(} r \texttt{)}  & \cdot &  \texttt{~(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~~}  \\[4pt]  + &  \texttt{(} p \texttt{)(} q \texttt{)(} r \texttt{)}  & \cdot &  \texttt{~~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~~}  \end{array}

Row Sum

Version 1

\begin{array}{*{4}{c}}  \multicolumn{4}{l}{\mathrm{D}f(p, q, r, \mathrm{d}p, \mathrm{d}q, \mathrm{d}r) =}  \\[10pt]  &  p \texttt{~} q \texttt{~} r  & \cdot &  \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~}  \\[4pt]  + &  p \texttt{~} q  & \cdot &  \texttt{~} \mathrm{d}r \texttt{~(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)}  \\[4pt]  + &  p \texttt{~} r  & \cdot &  \texttt{~} \mathrm{d}q \texttt{~(} \mathrm{d}p \texttt{)(} \mathrm{d}r \texttt{)}  \\[4pt]  + &  q \texttt{~} r  & \cdot &  \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)}  \\[4pt]  + &  \texttt{((} p \texttt{,} q \texttt{))} ~ r  & \cdot &  \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)}  \\[4pt]  + &  \texttt{((} p \texttt{,} r \texttt{))} ~ q  & \cdot &  \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}r \texttt{~(} \mathrm{d}q \texttt{)}  \\[4pt]  + &  \texttt{((} q \texttt{,} r \texttt{))} ~ p  & \cdot &  \texttt{~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~(} \mathrm{d}p \texttt{)}  \\[4pt]  + &  \texttt{(} p \texttt{)(} q \texttt{)(} r \texttt{)}  & \cdot &  \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~}  \end{array}

Version 2

\begin{array}{*{4}{c}}  \multicolumn{4}{l}{\mathrm{D}f(p, q, r, \mathrm{d}p, \mathrm{d}q, \mathrm{d}r) =}  \\[10pt]  &  \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)}  & \cdot &  q \texttt{~} r  \\[4pt]  + &  \texttt{~} \mathrm{d}q \texttt{~(} \mathrm{d}p \texttt{)(} \mathrm{d}r \texttt{)}  & \cdot &  p \texttt{~} r  \\[4pt]  + &  \texttt{~} \mathrm{d}r \texttt{~(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)}  & \cdot &  p \texttt{~} q  \\[4pt]  + &  \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)}  & \cdot &  \texttt{((} p \texttt{,} q \texttt{))} ~ r  \\[4pt]  + &  \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}r \texttt{~(} \mathrm{d}q \texttt{)}  & \cdot &  \texttt{((} p \texttt{,} r \texttt{))} ~ q  \\[4pt]  + &  \texttt{~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~(} \mathrm{d}p \texttt{)}  & \cdot &  \texttt{((} q \texttt{,} r \texttt{))} ~ p  \\[4pt]  + &  \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~}  & \cdot &  p \texttt{~} q \texttt{~} r  \\[4pt]  + &  \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~}  & \cdot &  \texttt{(} p \texttt{)(} q \texttt{)(} r \texttt{)}  \end{array}

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