MyWikiBiz, Author Your Legacy — Friday November 22, 2024
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| ==Work Area== | | ==Work Area== |
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− | {| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:90%"
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− | |+ <math>\text{Table A3.}~~\mathrm{E}f ~\text{Expanded over Differential Features}~ \{ \mathrm{d}p, \mathrm{d}q \}\!</math>
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− | |- style="background:#f0f0ff"
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− | | width="10%" |
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− | | width="18%" | <math>f\!</math>
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− | | width="18%" |
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− | <p><math>\mathrm{T}_{11} f\!</math></p>
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− | <p><math>\mathrm{E}f|_{\mathrm{d}p~\mathrm{d}q}\!</math></p>
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− | | width="18%" |
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− | <p><math>\mathrm{T}_{10} f\!</math></p>
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− | <p><math>\mathrm{E}f|_{\mathrm{d}p(\mathrm{d}q)}\!</math></p>
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− | | width="18%" |
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− | <p><math>\mathrm{T}_{01} f\!</math></p>
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− | <p><math>\mathrm{E}f|_{(\mathrm{d}p)\mathrm{d}q}\!</math></p>
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− | | width="18%" |
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− | <p><math>\mathrm{T}_{00} f\!</math></p>
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− | <p><math>\mathrm{E}f|_{(\mathrm{d}p)(\mathrm{d}q)}\!</math></p>
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− | |-
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− | | <math>f_0\!</math>
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− | | <math>(~)\!</math>
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− | | <math>(~)\!</math>
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− | | <math>(~)\!</math>
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− | | <math>(~)\!</math>
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− | | <math>(~)\!</math>
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− | <math>\begin{matrix}
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− | f_1
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− | \\[4pt]
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− | f_2
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− | \\[4pt]
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− | f_4
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− | \\[4pt]
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− | f_8
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− | \end{matrix}\!</math>
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− | <math>\begin{matrix}
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− | (p)(q)
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− | \\[4pt]
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− | (p)~q~
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− | \\[4pt]
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− | ~p~(q)
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− | \\[4pt]
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− | ~p~~q~
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− | \end{matrix}\!</math>
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− | <math>\begin{matrix}
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− | ~p~~q~
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− | \\[4pt]
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− | ~p~(q)
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− | \\[4pt]
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− | (p)~q~
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− | \\[4pt]
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− | (p)(q)
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− | \end{matrix}\!</math>
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− | <math>\begin{matrix}
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− | ~p~(q)
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− | \\[4pt]
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− | ~p~~q~
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− | \\[4pt]
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− | (p)(q)
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− | \\[4pt]
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− | (p)~q~
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− | \end{matrix}\!</math>
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− | <math>\begin{matrix}
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− | (p)~q~
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− | \\[4pt]
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− | (p)(q)
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− | \\[4pt]
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− | ~p~~q~
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− | \\[4pt]
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− | ~p~(q)
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− | \end{matrix}\!</math>
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− | <math>\begin{matrix}
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− | (p)(q)
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− | \\[4pt]
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− | (p)~q~
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− | \\[4pt]
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− | ~p~(q)
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− | \\[4pt]
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− | ~p~~q~
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− | \end{matrix}\!</math>
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− | <math>\begin{matrix}
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− | f_3
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− | \\[4pt]
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− | f_{12}
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− | \end{matrix}\!</math>
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− | <math>\begin{matrix}
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− | (p)
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− | \\[4pt]
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− | ~p~
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− | \end{matrix}\!</math>
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− | <math>\begin{matrix}
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− | ~p~
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− | \\[4pt]
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− | (p)
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− | \end{matrix}\!</math>
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− | <math>\begin{matrix}
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− | ~p~
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− | \\[4pt]
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− | (p)
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− | \end{matrix}\!</math>
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− | <math>\begin{matrix}
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− | (p)
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− | \\[4pt]
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− | ~p~
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− | \end{matrix}\!</math>
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− | <math>\begin{matrix}
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− | (p)
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− | \\[4pt]
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− | ~p~
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− | \end{matrix}\!</math>
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− | <math>\begin{matrix}
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− | f_6
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− | \\[4pt]
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− | f_9
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− | \end{matrix}\!</math>
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− | <math>\begin{matrix}
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− | ~(p,~q)~
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− | \\[4pt]
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− | ((p,~q))
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− | \end{matrix}\!</math>
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− | <math>\begin{matrix}
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− | ~(p,~q)~
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− | \\[4pt]
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− | ((p,~q))
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− | \end{matrix}\!</math>
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− | <math>\begin{matrix}
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− | ((p,~q))
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− | \\[4pt]
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− | ~(p,~q)~
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− | \end{matrix}\!</math>
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− | <math>\begin{matrix}
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− | ((p,~q))
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− | \\[4pt]
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− | ~(p,~q)~
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− | <math>\begin{matrix}
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− | <math>\begin{matrix}
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− | f_5
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− | \\[4pt]
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− | f_{10}
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− | \end{matrix}\!</math>
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− | <math>\begin{matrix}
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− | (q)
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− | \\[4pt]
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− | \end{matrix}\!</math>
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− | <math>\begin{matrix}
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− | ~q~
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− | \end{matrix}\!</math>
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− | <math>\begin{matrix}
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− | (q)
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− | \\[4pt]
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− | ~q~
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− | \end{matrix}\!</math>
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− | <math>\begin{matrix}
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− | \\[4pt]
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− | \end{matrix}\!</math>
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− | <math>\begin{matrix}
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− | (q)
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− | \\[4pt]
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− | ~q~
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− | \end{matrix}\!</math>
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− | <math>\begin{matrix}
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− | f_7
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− | \\[4pt]
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− | f_{11}
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− | f_{13}
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− | f_{14}
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− | \end{matrix}\!</math>
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− | <math>\begin{matrix}
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− | (~p~~q~)
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− | \\[4pt]
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− | (~p~(q))
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− | \\[4pt]
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− | ((p)~q~)
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− | \\[4pt]
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− | ((p)(q))
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− | \end{matrix}\!</math>
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− | <math>\begin{matrix}
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− | ((p)(q))
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− | \\[4pt]
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− | ((p)~q~)
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− | \\[4pt]
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− | (~p~(q))
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− | \\[4pt]
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− | (~p~~q~)
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− | \end{matrix}\!</math>
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− | <math>\begin{matrix}
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− | ((p)~q~)
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− | \\[4pt]
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− | ((p)(q))
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− | \\[4pt]
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− | (~p~~q~)
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− | \\[4pt]
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− | (~p~(q))
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− | \end{matrix}\!</math>
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− | <math>\begin{matrix}
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− | (~p~(q))
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− | \\[4pt]
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− | (~p~~q~)
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− | \\[4pt]
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− | ((p)(q))
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− | \\[4pt]
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− | ((p)~q~)
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− | \end{matrix}\!</math>
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− | <math>\begin{matrix}
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− | (~p~~q~)
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− | \\[4pt]
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− | (~p~(q))
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− | \\[4pt]
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− | ((p)~q~)
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− | \\[4pt]
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− | ((p)(q))
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− | \end{matrix}\!</math>
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− | |-
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− | | <math>f_{15}\!</math>
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− | | <math>((~))\!</math>
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− | | <math>((~))\!</math>
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− | | <math>((~))\!</math>
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− | | <math>((~))\!</math>
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− | | <math>((~))\!</math>
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− | |- style="background:#f0f0ff"
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− | | colspan="2" | <math>\text{Fixed Point Total}\!</math>
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− | | <math>4\!</math>
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− | | <math>4\!</math>
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− | | <math>4\!</math>
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− | | <math>16\!</math>
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− | |}
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− | <br>
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− | <math>\text{Number of orbits}~ = (4 + 4 + 4 + 16) \div 4 = 7.\!</math> Amazing!
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| ==Operational Representation== | | ==Operational Representation== |