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| − | ===Wiki TeX Tables===  | + | ===Wiki TeX Tables : PQ===  | 
|   | + |    | 
|   | + | <br>  | 
|   | + |    | 
|   | + | {| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; text-align:center; width:90%"  | 
|   | + | |+ <math>\text{Table A1.}~~\text{Propositional Forms on Two Variables}</math>  | 
|   | + | |- style="background:#f0f0ff"  | 
|   | + | | width="15%" |  | 
|   | + | <p><math>\mathcal{L}_1</math></p>  | 
|   | + | <p><math>\text{Decimal}</math></p>  | 
|   | + | | width="15%" |  | 
|   | + | <p><math>\mathcal{L}_2</math></p>  | 
|   | + | <p><math>\text{Binary}</math></p>  | 
|   | + | | width="15%" |  | 
|   | + | <p><math>\mathcal{L}_3</math></p>  | 
|   | + | <p><math>\text{Vector}</math></p>  | 
|   | + | | width="15%" |  | 
|   | + | <p><math>\mathcal{L}_4</math></p>  | 
|   | + | <p><math>\text{Cactus}</math></p>  | 
|   | + | | width="25%" |  | 
|   | + | <p><math>\mathcal{L}_5</math></p>  | 
|   | + | <p><math>\text{English}</math></p>  | 
|   | + | | width="15%" |  | 
|   | + | <p><math>\mathcal{L}_6</math></p>  | 
|   | + | <p><math>\text{Ordinary}</math></p>  | 
|   | + | |- style="background:#f0f0ff"  | 
|   | + | |    | 
|   | + | | align="right" | <math>p\colon\!</math>  | 
|   | + | | <math>1~1~0~0\!</math>  | 
|   | + | |    | 
|   | + | |    | 
|   | + | |    | 
|   | + | |- style="background:#f0f0ff"  | 
|   | + | |    | 
|   | + | | align="right" | <math>q\colon\!</math>  | 
|   | + | | <math>1~0~1~0\!</math>  | 
|   | + | |    | 
|   | + | |    | 
|   | + | |    | 
|   | + | |-  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | f_0  | 
|   | + | \\[4pt]  | 
|   | + | f_1  | 
|   | + | \\[4pt]  | 
|   | + | f_2  | 
|   | + | \\[4pt]  | 
|   | + | f_3  | 
|   | + | \\[4pt]  | 
|   | + | f_4  | 
|   | + | \\[4pt]  | 
|   | + | f_5  | 
|   | + | \\[4pt]  | 
|   | + | f_6  | 
|   | + | \\[4pt]  | 
|   | + | f_7  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | f_{0000}  | 
|   | + | \\[4pt]  | 
|   | + | f_{0001}  | 
|   | + | \\[4pt]  | 
|   | + | f_{0010}  | 
|   | + | \\[4pt]  | 
|   | + | f_{0011}  | 
|   | + | \\[4pt]  | 
|   | + | f_{0100}  | 
|   | + | \\[4pt]  | 
|   | + | f_{0101}  | 
|   | + | \\[4pt]  | 
|   | + | f_{0110}  | 
|   | + | \\[4pt]  | 
|   | + | f_{0111}  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | 0~0~0~0  | 
|   | + | \\[4pt]  | 
|   | + | 0~0~0~1  | 
|   | + | \\[4pt]  | 
|   | + | 0~0~1~0  | 
|   | + | \\[4pt]  | 
|   | + | 0~0~1~1  | 
|   | + | \\[4pt]  | 
|   | + | 0~1~0~0  | 
|   | + | \\[4pt]  | 
|   | + | 0~1~0~1  | 
|   | + | \\[4pt]  | 
|   | + | 0~1~1~0  | 
|   | + | \\[4pt]  | 
|   | + | 0~1~1~1  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (~)  | 
|   | + | \\[4pt]  | 
|   | + | (p)(q)  | 
|   | + | \\[4pt]  | 
|   | + | (p)~q~  | 
|   | + | \\[4pt]  | 
|   | + | (p)~~~  | 
|   | + | \\[4pt]  | 
|   | + | ~p~(q)  | 
|   | + | \\[4pt]  | 
|   | + | ~~~(q)  | 
|   | + | \\[4pt]  | 
|   | + | (p,~q)  | 
|   | + | \\[4pt]  | 
|   | + | (p~~q)  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | \text{false}  | 
|   | + | \\[4pt]  | 
|   | + | \text{neither}~ p ~\text{nor}~ q  | 
|   | + | \\[4pt]  | 
|   | + | q ~\text{without}~ p  | 
|   | + | \\[4pt]  | 
|   | + | \text{not}~ p  | 
|   | + | \\[4pt]  | 
|   | + | p ~\text{without}~ q  | 
|   | + | \\[4pt]  | 
|   | + | \text{not}~ q  | 
|   | + | \\[4pt]  | 
|   | + | p ~\text{not equal to}~ q  | 
|   | + | \\[4pt]  | 
|   | + | \text{not both}~ p ~\text{and}~ q  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | 0  | 
|   | + | \\[4pt]  | 
|   | + | \lnot p \land \lnot q  | 
|   | + | \\[4pt]  | 
|   | + | \lnot p \land q  | 
|   | + | \\[4pt]  | 
|   | + | \lnot p  | 
|   | + | \\[4pt]  | 
|   | + | p \land \lnot q  | 
|   | + | \\[4pt]  | 
|   | + | \lnot q  | 
|   | + | \\[4pt]  | 
|   | + | p \ne q  | 
|   | + | \\[4pt]  | 
|   | + | \lnot p \lor \lnot q  | 
|   | + | \end{matrix}</math>  | 
|   | + | |-  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | f_8  | 
|   | + | \\[4pt]  | 
|   | + | f_9  | 
|   | + | \\[4pt]  | 
|   | + | f_{10}  | 
|   | + | \\[4pt]  | 
|   | + | f_{11}  | 
|   | + | \\[4pt]  | 
|   | + | f_{12}  | 
|   | + | \\[4pt]  | 
|   | + | f_{13}  | 
|   | + | \\[4pt]  | 
|   | + | f_{14}  | 
|   | + | \\[4pt]  | 
|   | + | f_{15}  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | f_{1000}  | 
|   | + | \\[4pt]  | 
|   | + | f_{1001}  | 
|   | + | \\[4pt]  | 
|   | + | f_{1010}  | 
|   | + | \\[4pt]  | 
|   | + | f_{1011}  | 
|   | + | \\[4pt]  | 
|   | + | f_{1100}  | 
|   | + | \\[4pt]  | 
|   | + | f_{1101}  | 
|   | + | \\[4pt]  | 
|   | + | f_{1110}  | 
|   | + | \\[4pt]  | 
|   | + | f_{1111}  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | 1~0~0~0  | 
|   | + | \\[4pt]  | 
|   | + | 1~0~0~1  | 
|   | + | \\[4pt]  | 
|   | + | 1~0~1~0  | 
|   | + | \\[4pt]  | 
|   | + | 1~0~1~1  | 
|   | + | \\[4pt]  | 
|   | + | 1~1~0~0  | 
|   | + | \\[4pt]  | 
|   | + | 1~1~0~1  | 
|   | + | \\[4pt]  | 
|   | + | 1~1~1~0  | 
|   | + | \\[4pt]  | 
|   | + | 1~1~1~1  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ~~p~~q~~  | 
|   | + | \\[4pt]  | 
|   | + | ((p,~q))  | 
|   | + | \\[4pt]  | 
|   | + | ~~~~~q~~  | 
|   | + | \\[4pt]  | 
|   | + | ~(p~(q))  | 
|   | + | \\[4pt]  | 
|   | + | ~~p~~~~~  | 
|   | + | \\[4pt]  | 
|   | + | ((p)~q)~  | 
|   | + | \\[4pt]  | 
|   | + | ((p)(q))  | 
|   | + | \\[4pt]  | 
|   | + | ((~))  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | p ~\text{and}~ q  | 
|   | + | \\[4pt]  | 
|   | + | p ~\text{equal to}~ q  | 
|   | + | \\[4pt]  | 
|   | + | q  | 
|   | + | \\[4pt]  | 
|   | + | \text{not}~ p ~\text{without}~ q  | 
|   | + | \\[4pt]  | 
|   | + | p  | 
|   | + | \\[4pt]  | 
|   | + | \text{not}~ q ~\text{without}~ p  | 
|   | + | \\[4pt]  | 
|   | + | p ~\text{or}~ q  | 
|   | + | \\[4pt]  | 
|   | + | \text{true}  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | p \land q  | 
|   | + | \\[4pt]  | 
|   | + | p = q  | 
|   | + | \\[4pt]  | 
|   | + | q  | 
|   | + | \\[4pt]  | 
|   | + | p \Rightarrow q  | 
|   | + | \\[4pt]  | 
|   | + | p  | 
|   | + | \\[4pt]  | 
|   | + | p \Leftarrow q  | 
|   | + | \\[4pt]  | 
|   | + | p \lor q  | 
|   | + | \\[4pt]  | 
|   | + | 1  | 
|   | + | \end{matrix}</math>  | 
|   | + | |}  | 
|   | + |    | 
|   | + | <br>  | 
|   | + |    | 
|   | + | {| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; text-align:center; width:90%"  | 
|   | + | |+ <math>\text{Table A2.}~~\text{Propositional Forms on Two Variables}</math>  | 
|   | + | |- style="background:#f0f0ff"  | 
|   | + | | width="15%" |  | 
|   | + | <p><math>\mathcal{L}_1</math></p>  | 
|   | + | <p><math>\text{Decimal}</math></p>  | 
|   | + | | width="15%" |  | 
|   | + | <p><math>\mathcal{L}_2</math></p>  | 
|   | + | <p><math>\text{Binary}</math></p>  | 
|   | + | | width="15%" |  | 
|   | + | <p><math>\mathcal{L}_3</math></p>  | 
|   | + | <p><math>\text{Vector}</math></p>  | 
|   | + | | width="15%" |  | 
|   | + | <p><math>\mathcal{L}_4</math></p>  | 
|   | + | <p><math>\text{Cactus}</math></p>  | 
|   | + | | width="25%" |  | 
|   | + | <p><math>\mathcal{L}_5</math></p>  | 
|   | + | <p><math>\text{English}</math></p>  | 
|   | + | | width="15%" |  | 
|   | + | <p><math>\mathcal{L}_6</math></p>  | 
|   | + | <p><math>\text{Ordinary}</math></p>  | 
|   | + | |- style="background:#f0f0ff"  | 
|   | + | |    | 
|   | + | | align="right" | <math>p\colon\!</math>  | 
|   | + | | <math>1~1~0~0\!</math>  | 
|   | + | |    | 
|   | + | |    | 
|   | + | |    | 
|   | + | |- style="background:#f0f0ff"  | 
|   | + | |    | 
|   | + | | align="right" | <math>q\colon\!</math>  | 
|   | + | | <math>1~0~1~0\!</math>  | 
|   | + | |    | 
|   | + | |    | 
|   | + | |    | 
|   | + | |-  | 
|   | + | | <math>f_0\!</math>  | 
|   | + | | <math>f_{0000}\!</math>  | 
|   | + | | <math>0~0~0~0</math>  | 
|   | + | | <math>(~)</math>  | 
|   | + | | <math>\text{false}\!</math>  | 
|   | + | | <math>0\!</math>  | 
|   | + | |-  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | f_1  | 
|   | + | \\[4pt]  | 
|   | + | f_2  | 
|   | + | \\[4pt]  | 
|   | + | f_4  | 
|   | + | \\[4pt]  | 
|   | + | f_8  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | f_{0001}  | 
|   | + | \\[4pt]  | 
|   | + | f_{0010}  | 
|   | + | \\[4pt]  | 
|   | + | f_{0100}  | 
|   | + | \\[4pt]  | 
|   | + | f_{1000}  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | 0~0~0~1  | 
|   | + | \\[4pt]  | 
|   | + | 0~0~1~0  | 
|   | + | \\[4pt]  | 
|   | + | 0~1~0~0  | 
|   | + | \\[4pt]  | 
|   | + | 1~0~0~0  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (p)(q)  | 
|   | + | \\[4pt]  | 
|   | + | (p)~q~  | 
|   | + | \\[4pt]  | 
|   | + | ~p~(q)  | 
|   | + | \\[4pt]  | 
|   | + | ~p~~q~  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | \text{neither}~ p ~\text{nor}~ q  | 
|   | + | \\[4pt]  | 
|   | + | q ~\text{without}~ p  | 
|   | + | \\[4pt]  | 
|   | + | p ~\text{without}~ q  | 
|   | + | \\[4pt]  | 
|   | + | p ~\text{and}~ q  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | \lnot p \land \lnot q  | 
|   | + | \\[4pt]  | 
|   | + | \lnot p \land q  | 
|   | + | \\[4pt]  | 
|   | + | p \land \lnot q  | 
|   | + | \\[4pt]  | 
|   | + | p \land q  | 
|   | + | \end{matrix}</math>  | 
|   | + | |-  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | f_3  | 
|   | + | \\[4pt]  | 
|   | + | f_{12}  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | f_{0011}  | 
|   | + | \\[4pt]  | 
|   | + | f_{1100}  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | 0~0~1~1  | 
|   | + | \\[4pt]  | 
|   | + | 1~1~0~0  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (p)  | 
|   | + | \\[4pt]  | 
|   | + | ~p~  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | \text{not}~ p  | 
|   | + | \\[4pt]  | 
|   | + | p  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | \lnot p  | 
|   | + | \\[4pt]  | 
|   | + | p  | 
|   | + | \end{matrix}</math>  | 
|   | + | |-  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | f_6  | 
|   | + | \\[4pt]  | 
|   | + | f_9  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | f_{0110}  | 
|   | + | \\[4pt]  | 
|   | + | f_{1001}  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | 0~1~1~0  | 
|   | + | \\[4pt]  | 
|   | + | 1~0~0~1  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ~(p,~q)~  | 
|   | + | \\[4pt]  | 
|   | + | ((p,~q))  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | p ~\text{not equal to}~ q  | 
|   | + | \\[4pt]  | 
|   | + | p ~\text{equal to}~ q  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | p \ne q  | 
|   | + | \\[4pt]  | 
|   | + | p = q  | 
|   | + | \end{matrix}</math>  | 
|   | + | |-  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | f_5  | 
|   | + | \\[4pt]  | 
|   | + | f_{10}  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | f_{0101}  | 
|   | + | \\[4pt]  | 
|   | + | f_{1010}  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | 0~1~0~1  | 
|   | + | \\[4pt]  | 
|   | + | 1~0~1~0  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (q)  | 
|   | + | \\[4pt]  | 
|   | + | ~q~  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | \text{not}~ q  | 
|   | + | \\[4pt]  | 
|   | + | q  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | \lnot q  | 
|   | + | \\[4pt]  | 
|   | + | q  | 
|   | + | \end{matrix}</math>  | 
|   | + | |-  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | f_7  | 
|   | + | \\[4pt]  | 
|   | + | f_{11}  | 
|   | + | \\[4pt]  | 
|   | + | f_{13}  | 
|   | + | \\[4pt]  | 
|   | + | f_{14}  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | f_{0111}  | 
|   | + | \\[4pt]  | 
|   | + | f_{1011}  | 
|   | + | \\[4pt]  | 
|   | + | f_{1101}  | 
|   | + | \\[4pt]  | 
|   | + | f_{1110}  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | 0~1~1~1  | 
|   | + | \\[4pt]  | 
|   | + | 1~0~1~1  | 
|   | + | \\[4pt]  | 
|   | + | 1~1~0~1  | 
|   | + | \\[4pt]  | 
|   | + | 1~1~1~0  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ~(p~~q)~  | 
|   | + | \\[4pt]  | 
|   | + | ~(p~(q))  | 
|   | + | \\[4pt]  | 
|   | + | ((p)~q)~  | 
|   | + | \\[4pt]  | 
|   | + | ((p)(q))  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | \text{not both}~ p ~\text{and}~ q  | 
|   | + | \\[4pt]  | 
|   | + | \text{not}~ p ~\text{without}~ q  | 
|   | + | \\[4pt]  | 
|   | + | \text{not}~ q ~\text{without}~ p  | 
|   | + | \\[4pt]  | 
|   | + | p ~\text{or}~ q  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | \lnot p \lor \lnot q  | 
|   | + | \\[4pt]  | 
|   | + | p \Rightarrow q  | 
|   | + | \\[4pt]  | 
|   | + | p \Leftarrow q  | 
|   | + | \\[4pt]  | 
|   | + | p \lor q  | 
|   | + | \end{matrix}</math>  | 
|   | + | |-  | 
|   | + | | <math>f_{15}\!</math>  | 
|   | + | | <math>f_{1111}\!</math>  | 
|   | + | | <math>1~1~1~1</math>  | 
|   | + | | <math>((~))</math>  | 
|   | + | | <math>\text{true}\!</math>  | 
|   | + | | <math>1\!</math>  | 
|   | + | |}  | 
|   | + |    | 
|   | + | <br>  | 
|   | + |    | 
|   | + | {| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; text-align:center; width:90%"  | 
|   | + | |+ <math>\text{Table A3.}~~\operatorname{E}f ~\text{Expanded Over Differential Features}~ \{ \operatorname{d}p, \operatorname{d}q \}</math>  | 
|   | + | |- style="background:#f0f0ff"  | 
|   | + | | width="10%" |    | 
|   | + | | width="18%" | <math>f\!</math>  | 
|   | + | | width="18%" |   | 
|   | + | <p><math>\operatorname{T}_{11} f</math></p>  | 
|   | + | <p><math>\operatorname{E}f|_{\operatorname{d}p~\operatorname{d}q}</math></p>  | 
|   | + | | width="18%" |  | 
|   | + | <p><math>\operatorname{T}_{10} f</math></p>  | 
|   | + | <p><math>\operatorname{E}f|_{\operatorname{d}p(\operatorname{d}q)}</math></p>  | 
|   | + | | width="18%" |  | 
|   | + | <p><math>\operatorname{T}_{01} f</math></p>  | 
|   | + | <p><math>\operatorname{E}f|_{(\operatorname{d}p)\operatorname{d}q}</math></p>  | 
|   | + | | width="18%" |  | 
|   | + | <p><math>\operatorname{T}_{00} f</math></p>  | 
|   | + | <p><math>\operatorname{E}f|_{(\operatorname{d}p)(\operatorname{d}q)}</math></p>  | 
|   | + | |-  | 
|   | + | | <math>f_0\!</math>  | 
|   | + | | <math>(~)</math>  | 
|   | + | | <math>(~)</math>  | 
|   | + | | <math>(~)</math>  | 
|   | + | | <math>(~)</math>  | 
|   | + | | <math>(~)</math>  | 
|   | + | |-  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | f_1  | 
|   | + | \\[4pt]  | 
|   | + | f_2  | 
|   | + | \\[4pt]  | 
|   | + | f_4  | 
|   | + | \\[4pt]  | 
|   | + | f_8  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (p)(q)  | 
|   | + | \\[4pt]  | 
|   | + | (p)~q~  | 
|   | + | \\[4pt]  | 
|   | + | ~p~(q)  | 
|   | + | \\[4pt]  | 
|   | + | ~p~~q~  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ~p~~q~  | 
|   | + | \\[4pt]  | 
|   | + | ~p~(q)  | 
|   | + | \\[4pt]  | 
|   | + | (p)~q~  | 
|   | + | \\[4pt]  | 
|   | + | (p)(q)  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ~p~(q)  | 
|   | + | \\[4pt]  | 
|   | + | ~p~~q~  | 
|   | + | \\[4pt]  | 
|   | + | (p)(q)  | 
|   | + | \\[4pt]  | 
|   | + | (p)~q~  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (p)~q~  | 
|   | + | \\[4pt]  | 
|   | + | (p)(q)  | 
|   | + | \\[4pt]  | 
|   | + | ~p~~q~  | 
|   | + | \\[4pt]  | 
|   | + | ~p~(q)  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (p)(q)  | 
|   | + | \\[4pt]  | 
|   | + | (p)~q~  | 
|   | + | \\[4pt]  | 
|   | + | ~p~(q)  | 
|   | + | \\[4pt]  | 
|   | + | ~p~~q~  | 
|   | + | \end{matrix}</math>  | 
|   | + | |-  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | f_3  | 
|   | + | \\[4pt]  | 
|   | + | f_{12}  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (p)  | 
|   | + | \\[4pt]  | 
|   | + | ~p~  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ~p~  | 
|   | + | \\[4pt]  | 
|   | + | (p)  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ~p~  | 
|   | + | \\[4pt]  | 
|   | + | (p)  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (p)  | 
|   | + | \\[4pt]  | 
|   | + | ~p~  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (p)  | 
|   | + | \\[4pt]  | 
|   | + | ~p~  | 
|   | + | \end{matrix}</math>  | 
|   | + | |-  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | f_6  | 
|   | + | \\[4pt]  | 
|   | + | f_9  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ~(p,~q)~  | 
|   | + | \\[4pt]  | 
|   | + | ((p,~q))  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ~(p,~q)~  | 
|   | + | \\[4pt]  | 
|   | + | ((p,~q))  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ((p,~q))  | 
|   | + | \\[4pt]  | 
|   | + | ~(p,~q)~  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ((p,~q))  | 
|   | + | \\[4pt]  | 
|   | + | ~(p,~q)~  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ~(p,~q)~  | 
|   | + | \\[4pt]  | 
|   | + | ((p,~q))  | 
|   | + | \end{matrix}</math>  | 
|   | + | |-  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | f_5  | 
|   | + | \\[4pt]  | 
|   | + | f_{10}  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (q)  | 
|   | + | \\[4pt]  | 
|   | + | ~q~  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ~q~  | 
|   | + | \\[4pt]  | 
|   | + | (q)  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (q)  | 
|   | + | \\[4pt]  | 
|   | + | ~q~  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ~q~  | 
|   | + | \\[4pt]  | 
|   | + | (q)  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (q)  | 
|   | + | \\[4pt]  | 
|   | + | ~q~  | 
|   | + | \end{matrix}</math>  | 
|   | + | |-  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | f_7  | 
|   | + | \\[4pt]  | 
|   | + | f_{11}  | 
|   | + | \\[4pt]  | 
|   | + | f_{13}  | 
|   | + | \\[4pt]  | 
|   | + | f_{14}  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (~p~~q~)  | 
|   | + | \\[4pt]  | 
|   | + | (~p~(q))  | 
|   | + | \\[4pt]  | 
|   | + | ((p)~q~)  | 
|   | + | \\[4pt]  | 
|   | + | ((p)(q))  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ((p)(q))  | 
|   | + | \\[4pt]  | 
|   | + | ((p)~q~)  | 
|   | + | \\[4pt]  | 
|   | + | (~p~(q))  | 
|   | + | \\[4pt]  | 
|   | + | (~p~~q~)  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ((p)~q~)  | 
|   | + | \\[4pt]  | 
|   | + | ((p)(q))  | 
|   | + | \\[4pt]  | 
|   | + | (~p~~q~)  | 
|   | + | \\[4pt]  | 
|   | + | (~p~(q))  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (~p~(q))  | 
|   | + | \\[4pt]  | 
|   | + | (~p~~q~)  | 
|   | + | \\[4pt]  | 
|   | + | ((p)(q))  | 
|   | + | \\[4pt]  | 
|   | + | ((p)~q~)  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (~p~~q~)  | 
|   | + | \\[4pt]  | 
|   | + | (~p~(q))  | 
|   | + | \\[4pt]  | 
|   | + | ((p)~q~)  | 
|   | + | \\[4pt]  | 
|   | + | ((p)(q))  | 
|   | + | \end{matrix}</math>  | 
|   | + | |-  | 
|   | + | | <math>f_{15}\!</math>  | 
|   | + | | <math>((~))</math>  | 
|   | + | | <math>((~))</math>  | 
|   | + | | <math>((~))</math>  | 
|   | + | | <math>((~))</math>  | 
|   | + | | <math>((~))</math>  | 
|   | + | |- style="background:#f0f0ff"  | 
|   | + | | colspan="2" | <math>\text{Fixed Point Total}\!</math>  | 
|   | + | | <math>4\!</math>  | 
|   | + | | <math>4\!</math>  | 
|   | + | | <math>4\!</math>  | 
|   | + | | <math>16\!</math>  | 
|   | + | |}  | 
|   | + |    | 
|   | + | <br>  | 
|   | + |    | 
|   | + | {| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; text-align:center; width:90%"  | 
|   | + | |+ <math>\text{Table A4.}~~\operatorname{D}f ~\text{Expanded Over Differential Features}~ \{ \operatorname{d}p, \operatorname{d}q \}</math>  | 
|   | + | |- style="background:#f0f0ff"  | 
|   | + | | width="10%" |    | 
|   | + | | width="18%" | <math>f\!</math>  | 
|   | + | | width="18%" |  | 
|   | + | <math>\operatorname{D}f|_{\operatorname{d}p~\operatorname{d}q}</math>  | 
|   | + | | width="18%" |  | 
|   | + | <math>\operatorname{D}f|_{\operatorname{d}p(\operatorname{d}q)}</math>  | 
|   | + | | width="18%" |  | 
|   | + | <math>\operatorname{D}f|_{(\operatorname{d}p)\operatorname{d}q}</math>  | 
|   | + | | width="18%" |  | 
|   | + | <math>\operatorname{D}f|_{(\operatorname{d}p)(\operatorname{d}q)}</math>  | 
|   | + | |-  | 
|   | + | | <math>f_0\!</math>  | 
|   | + | | <math>(~)</math>  | 
|   | + | | <math>(~)</math>  | 
|   | + | | <math>(~)</math>  | 
|   | + | | <math>(~)</math>  | 
|   | + | | <math>(~)</math>  | 
|   | + | |-  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | f_1  | 
|   | + | \\[4pt]  | 
|   | + | f_2  | 
|   | + | \\[4pt]  | 
|   | + | f_4  | 
|   | + | \\[4pt]  | 
|   | + | f_8  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (p)(q)  | 
|   | + | \\[4pt]  | 
|   | + | (p)~q~  | 
|   | + | \\[4pt]  | 
|   | + | ~p~(q)  | 
|   | + | \\[4pt]  | 
|   | + | ~p~~q~  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ((p,~q))  | 
|   | + | \\[4pt]  | 
|   | + | ~(p,~q)~  | 
|   | + | \\[4pt]  | 
|   | + | ~(p,~q)~  | 
|   | + | \\[4pt]  | 
|   | + | ((p,~q))  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (q)  | 
|   | + | \\[4pt]  | 
|   | + | ~q~  | 
|   | + | \\[4pt]  | 
|   | + | (q)  | 
|   | + | \\[4pt]  | 
|   | + | ~q~  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (p)  | 
|   | + | \\[4pt]  | 
|   | + | (p)  | 
|   | + | \\[4pt]  | 
|   | + | ~p~  | 
|   | + | \\[4pt]  | 
|   | + | ~p~  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (~)  | 
|   | + | \\[4pt]  | 
|   | + | (~)  | 
|   | + | \\[4pt]  | 
|   | + | (~)  | 
|   | + | \\[4pt]  | 
|   | + | (~)  | 
|   | + | \end{matrix}</math>  | 
|   | + | |-  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | f_3  | 
|   | + | \\[4pt]  | 
|   | + | f_{12}  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (p)  | 
|   | + | \\[4pt]  | 
|   | + | ~p~  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ((~))  | 
|   | + | \\[4pt]  | 
|   | + | ((~))  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ((~))  | 
|   | + | \\[4pt]  | 
|   | + | ((~))  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (~)  | 
|   | + | \\[4pt]  | 
|   | + | (~)  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (~)  | 
|   | + | \\[4pt]  | 
|   | + | (~)  | 
|   | + | \end{matrix}</math>  | 
|   | + | |-  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | f_6  | 
|   | + | \\[4pt]  | 
|   | + | f_9  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ~(p,~q)~  | 
|   | + | \\[4pt]  | 
|   | + | ((p,~q))  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (~)  | 
|   | + | \\[4pt]  | 
|   | + | (~)  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ((~))  | 
|   | + | \\[4pt]  | 
|   | + | ((~))  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ((~))  | 
|   | + | \\[4pt]  | 
|   | + | ((~))  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (~)  | 
|   | + | \\[4pt]  | 
|   | + | (~)  | 
|   | + | \end{matrix}</math>  | 
|   | + | |-  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | f_5  | 
|   | + | \\[4pt]  | 
|   | + | f_{10}  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (q)  | 
|   | + | \\[4pt]  | 
|   | + | ~q~  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ((~))  | 
|   | + | \\[4pt]  | 
|   | + | ((~))  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (~)  | 
|   | + | \\[4pt]  | 
|   | + | (~)  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ((~))  | 
|   | + | \\[4pt]  | 
|   | + | ((~))  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (~)  | 
|   | + | \\[4pt]  | 
|   | + | (~)  | 
|   | + | \end{matrix}</math>  | 
|   | + | |-  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | f_7  | 
|   | + | \\[4pt]  | 
|   | + | f_{11}  | 
|   | + | \\[4pt]  | 
|   | + | f_{13}  | 
|   | + | \\[4pt]  | 
|   | + | f_{14}  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ~(p~~q)~  | 
|   | + | \\[4pt]  | 
|   | + | ~(p~(q))  | 
|   | + | \\[4pt]  | 
|   | + | ((p)~q)~  | 
|   | + | \\[4pt]  | 
|   | + | ((p)(q))  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ((p,~q))  | 
|   | + | \\[4pt]  | 
|   | + | ~(p,~q)~  | 
|   | + | \\[4pt]  | 
|   | + | ~(p,~q)~  | 
|   | + | \\[4pt]  | 
|   | + | ((p,~q))  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ~q~  | 
|   | + | \\[4pt]  | 
|   | + | (q)  | 
|   | + | \\[4pt]  | 
|   | + | ~q~  | 
|   | + | \\[4pt]  | 
|   | + | (q)  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ~p~  | 
|   | + | \\[4pt]  | 
|   | + | ~p~  | 
|   | + | \\[4pt]  | 
|   | + | (p)  | 
|   | + | \\[4pt]  | 
|   | + | (p)  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (~)  | 
|   | + | \\[4pt]  | 
|   | + | (~)  | 
|   | + | \\[4pt]  | 
|   | + | (~)  | 
|   | + | \\[4pt]  | 
|   | + | (~)  | 
|   | + | \end{matrix}</math>  | 
|   | + | |-  | 
|   | + | | <math>f_{15}\!</math>  | 
|   | + | | <math>((~))</math>  | 
|   | + | | <math>(~)</math>  | 
|   | + | | <math>(~)</math>  | 
|   | + | | <math>(~)</math>  | 
|   | + | | <math>(~)</math>  | 
|   | + | |}  | 
|   | + |    | 
|   | + | <br>  | 
|   | + |    | 
|   | + | {| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; text-align:center; width:90%"  | 
|   | + | |+ <math>\text{Table A5.}~~\operatorname{E}f ~\text{Expanded Over Ordinary Features}~ \{ p, q \}</math>  | 
|   | + | |- style="background:#f0f0ff"  | 
|   | + | | width="10%" |    | 
|   | + | | width="18%" | <math>f\!</math>  | 
|   | + | | width="18%" | <math>\operatorname{E}f|_{xy}</math>  | 
|   | + | | width="18%" | <math>\operatorname{E}f|_{p(q)}</math>  | 
|   | + | | width="18%" | <math>\operatorname{E}f|_{(p)q}</math>  | 
|   | + | | width="18%" | <math>\operatorname{E}f|_{(p)(q)}</math>  | 
|   | + | |-  | 
|   | + | | <math>f_0\!</math>  | 
|   | + | | <math>(~)</math>  | 
|   | + | | <math>(~)</math>  | 
|   | + | | <math>(~)</math>  | 
|   | + | | <math>(~)</math>  | 
|   | + | | <math>(~)</math>  | 
|   | + | |-  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | f_1  | 
|   | + | \\[4pt]  | 
|   | + | f_2  | 
|   | + | \\[4pt]  | 
|   | + | f_4  | 
|   | + | \\[4pt]  | 
|   | + | f_8  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (p)(q)  | 
|   | + | \\[4pt]  | 
|   | + | (p)~q~  | 
|   | + | \\[4pt]  | 
|   | + | ~p~(q)  | 
|   | + | \\[4pt]  | 
|   | + | ~p~~q~  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ~\operatorname{d}p~~\operatorname{d}q~  | 
|   | + | \\[4pt]  | 
|   | + | ~\operatorname{d}p~(\operatorname{d}q)  | 
|   | + | \\[4pt]  | 
|   | + | (\operatorname{d}p)~\operatorname{d}q~  | 
|   | + | \\[4pt]  | 
|   | + | (\operatorname{d}p)(\operatorname{d}q)  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ~\operatorname{d}p~(\operatorname{d}q)  | 
|   | + | \\[4pt]  | 
|   | + | ~\operatorname{d}p~~\operatorname{d}q~  | 
|   | + | \\[4pt]  | 
|   | + | (\operatorname{d}p)(\operatorname{d}q)  | 
|   | + | \\[4pt]  | 
|   | + | (\operatorname{d}p)~\operatorname{d}q~  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (\operatorname{d}p)~\operatorname{d}q~  | 
|   | + | \\[4pt]  | 
|   | + | (\operatorname{d}p)(\operatorname{d}q)  | 
|   | + | \\[4pt]  | 
|   | + | ~\operatorname{d}p~~\operatorname{d}q~  | 
|   | + | \\[4pt]  | 
|   | + | ~\operatorname{d}p~(\operatorname{d}q)  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (\operatorname{d}p)(\operatorname{d}q)  | 
|   | + | \\[4pt]  | 
|   | + | (\operatorname{d}p)~\operatorname{d}q~  | 
|   | + | \\[4pt]  | 
|   | + | ~\operatorname{d}p~(\operatorname{d}q)  | 
|   | + | \\[4pt]  | 
|   | + | ~\operatorname{d}p~~\operatorname{d}q~  | 
|   | + | \end{matrix}</math>  | 
|   | + | |-  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | f_3  | 
|   | + | \\[4pt]  | 
|   | + | f_{12}  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (p)  | 
|   | + | \\[4pt]  | 
|   | + | ~p~  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ~\operatorname{d}p~  | 
|   | + | \\[4pt]  | 
|   | + | (\operatorname{d}p)  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ~\operatorname{d}p~  | 
|   | + | \\[4pt]  | 
|   | + | (\operatorname{d}p)  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (\operatorname{d}p)  | 
|   | + | \\[4pt]  | 
|   | + | ~\operatorname{d}p~  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (\operatorname{d}p)  | 
|   | + | \\[4pt]  | 
|   | + | ~\operatorname{d}p~  | 
|   | + | \end{matrix}</math>  | 
|   | + | |-  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | f_6  | 
|   | + | \\[4pt]  | 
|   | + | f_9  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ~(p,~q)~  | 
|   | + | \\[4pt]  | 
|   | + | ((p,~q))  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ~(\operatorname{d}p,~\operatorname{d}q)~  | 
|   | + | \\[4pt]  | 
|   | + | ((\operatorname{d}p,~\operatorname{d}q))  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ((\operatorname{d}p,~\operatorname{d}q))  | 
|   | + | \\[4pt]  | 
|   | + | ~(\operatorname{d}p,~\operatorname{d}q)~  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ((\operatorname{d}p,~\operatorname{d}q))  | 
|   | + | \\[4pt]  | 
|   | + | ~(\operatorname{d}p,~\operatorname{d}q)~  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ~(\operatorname{d}p,~\operatorname{d}q)~  | 
|   | + | \\[4pt]  | 
|   | + | ((\operatorname{d}p,~\operatorname{d}q))  | 
|   | + | \end{matrix}</math>  | 
|   | + | |-  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | f_5  | 
|   | + | \\[4pt]  | 
|   | + | f_{10}  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (q)  | 
|   | + | \\[4pt]  | 
|   | + | ~q~  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ~\operatorname{d}q~  | 
|   | + | \\[4pt]  | 
|   | + | (\operatorname{d}q)  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (\operatorname{d}q)  | 
|   | + | \\[4pt]  | 
|   | + | ~\operatorname{d}q~  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ~\operatorname{d}q~  | 
|   | + | \\[4pt]  | 
|   | + | (\operatorname{d}q)  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (\operatorname{d}q)  | 
|   | + | \\[4pt]  | 
|   | + | ~\operatorname{d}q~  | 
|   | + | \end{matrix}</math>  | 
|   | + | |-  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | f_7  | 
|   | + | \\[4pt]  | 
|   | + | f_{11}  | 
|   | + | \\[4pt]  | 
|   | + | f_{13}  | 
|   | + | \\[4pt]  | 
|   | + | f_{14}  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (~p~~q~)  | 
|   | + | \\[4pt]  | 
|   | + | (~p~(q))  | 
|   | + | \\[4pt]  | 
|   | + | ((p)~q~)  | 
|   | + | \\[4pt]  | 
|   | + | ((p)(q))  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ((\operatorname{d}p)(\operatorname{d}q))  | 
|   | + | \\[4pt]  | 
|   | + | ((\operatorname{d}p)~\operatorname{d}q~)  | 
|   | + | \\[4pt]  | 
|   | + | (~\operatorname{d}p~(\operatorname{d}q))  | 
|   | + | \\[4pt]  | 
|   | + | (~\operatorname{d}p~~\operatorname{d}q~)  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ((\operatorname{d}p)~\operatorname{d}q~)  | 
|   | + | \\[4pt]  | 
|   | + | ((\operatorname{d}p)(\operatorname{d}q))  | 
|   | + | \\[4pt]  | 
|   | + | (~\operatorname{d}p~~\operatorname{d}q~)  | 
|   | + | \\[4pt]  | 
|   | + | (~\operatorname{d}p~(\operatorname{d}q))  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (~\operatorname{d}p~(\operatorname{d}q))  | 
|   | + | \\[4pt]  | 
|   | + | (~\operatorname{d}p~~\operatorname{d}q~)  | 
|   | + | \\[4pt]  | 
|   | + | ((\operatorname{d}p)(\operatorname{d}q))  | 
|   | + | \\[4pt]  | 
|   | + | ((\operatorname{d}p)~\operatorname{d}q~)  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (~\operatorname{d}p~~\operatorname{d}q~)  | 
|   | + | \\[4pt]  | 
|   | + | (~\operatorname{d}p~(\operatorname{d}q))  | 
|   | + | \\[4pt]  | 
|   | + | ((\operatorname{d}p)~\operatorname{d}q~)  | 
|   | + | \\[4pt]  | 
|   | + | ((\operatorname{d}p)(\operatorname{d}q))  | 
|   | + | \end{matrix}</math>  | 
|   | + | |-  | 
|   | + | | <math>f_{15}\!</math>  | 
|   | + | | <math>((~))</math>  | 
|   | + | | <math>((~))</math>  | 
|   | + | | <math>((~))</math>  | 
|   | + | | <math>((~))</math>  | 
|   | + | | <math>((~))</math>  | 
|   | + | |}  | 
|   | + |    | 
|   | + | <br>  | 
|   | + |    | 
|   | + | {| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; text-align:center; width:90%"  | 
|   | + | |+ <math>\text{Table A6.}~~\operatorname{D}f ~\text{Expanded Over Ordinary Features}~ \{ p, q \}</math>  | 
|   | + | |- style="background:#f0f0ff"  | 
|   | + | | width="10%" |    | 
|   | + | | width="18%" | <math>f\!</math>  | 
|   | + | | width="18%" | <math>\operatorname{D}f|_{xy}</math>  | 
|   | + | | width="18%" | <math>\operatorname{D}f|_{p(q)}</math>  | 
|   | + | | width="18%" | <math>\operatorname{D}f|_{(p)q}</math>  | 
|   | + | | width="18%" | <math>\operatorname{D}f|_{(p)(q)}</math>  | 
|   | + | |-  | 
|   | + | | <math>f_0\!</math>  | 
|   | + | | <math>(~)</math>  | 
|   | + | | <math>(~)</math>  | 
|   | + | | <math>(~)</math>  | 
|   | + | | <math>(~)</math>  | 
|   | + | | <math>(~)</math>  | 
|   | + | |-  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | f_1  | 
|   | + | \\[4pt]  | 
|   | + | f_2  | 
|   | + | \\[4pt]  | 
|   | + | f_4  | 
|   | + | \\[4pt]  | 
|   | + | f_8  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (p)(q)  | 
|   | + | \\[4pt]  | 
|   | + | (p)~q~  | 
|   | + | \\[4pt]  | 
|   | + | ~p~(q)  | 
|   | + | \\[4pt]  | 
|   | + | ~p~~q~  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ~~\operatorname{d}p~~\operatorname{d}q~~  | 
|   | + | \\[4pt]  | 
|   | + | ~~\operatorname{d}p~(\operatorname{d}q)~  | 
|   | + | \\[4pt]  | 
|   | + | ~(\operatorname{d}p)~\operatorname{d}q~~  | 
|   | + | \\[4pt]  | 
|   | + | ((\operatorname{d}p)(\operatorname{d}q))  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ~~\operatorname{d}p~(\operatorname{d}q)~  | 
|   | + | \\[4pt]  | 
|   | + | ~~\operatorname{d}p~~\operatorname{d}q~~  | 
|   | + | \\[4pt]  | 
|   | + | ((\operatorname{d}p)(\operatorname{d}q))  | 
|   | + | \\[4pt]  | 
|   | + | ~(\operatorname{d}p)~\operatorname{d}q~~  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ~(\operatorname{d}p)~\operatorname{d}q~~  | 
|   | + | \\[4pt]  | 
|   | + | ((\operatorname{d}p)(\operatorname{d}q))  | 
|   | + | \\[4pt]  | 
|   | + | ~~\operatorname{d}p~~\operatorname{d}q~~  | 
|   | + | \\[4pt]  | 
|   | + | ~~\operatorname{d}p~(\operatorname{d}q)~  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ((\operatorname{d}p)(\operatorname{d}q))  | 
|   | + | \\[4pt]  | 
|   | + | ~(\operatorname{d}p)~\operatorname{d}q~~  | 
|   | + | \\[4pt]  | 
|   | + | ~~\operatorname{d}p~(\operatorname{d}q)~  | 
|   | + | \\[4pt]  | 
|   | + | ~~\operatorname{d}p~~\operatorname{d}q~~  | 
|   | + | \end{matrix}</math>  | 
|   | + | |-  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | f_3  | 
|   | + | \\[4pt]  | 
|   | + | f_{12}  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (p)  | 
|   | + | \\[4pt]  | 
|   | + | ~p~  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | \operatorname{d}p  | 
|   | + | \\[4pt]  | 
|   | + | \operatorname{d}p  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | \operatorname{d}p  | 
|   | + | \\[4pt]  | 
|   | + | \operatorname{d}p  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | \operatorname{d}p  | 
|   | + | \\[4pt]  | 
|   | + | \operatorname{d}p  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | \operatorname{d}p  | 
|   | + | \\[4pt]  | 
|   | + | \operatorname{d}p  | 
|   | + | \end{matrix}</math>  | 
|   | + | |-  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | f_6  | 
|   | + | \\[4pt]  | 
|   | + | f_9  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ~(p,~q)~  | 
|   | + | \\[4pt]  | 
|   | + | ((p,~q))  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (\operatorname{d}p,~\operatorname{d}q)  | 
|   | + | \\[4pt]  | 
|   | + | (\operatorname{d}p,~\operatorname{d}q)  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (\operatorname{d}p,~\operatorname{d}q)  | 
|   | + | \\[4pt]  | 
|   | + | (\operatorname{d}p,~\operatorname{d}q)  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (\operatorname{d}p,~\operatorname{d}q)  | 
|   | + | \\[4pt]  | 
|   | + | (\operatorname{d}p,~\operatorname{d}q)  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (\operatorname{d}p,~\operatorname{d}q)  | 
|   | + | \\[4pt]  | 
|   | + | (\operatorname{d}p,~\operatorname{d}q)  | 
|   | + | \end{matrix}</math>  | 
|   | + | |-  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | f_5  | 
|   | + | \\[4pt]  | 
|   | + | f_{10}  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (q)  | 
|   | + | \\[4pt]  | 
|   | + | ~q~  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | \operatorname{d}q  | 
|   | + | \\[4pt]  | 
|   | + | \operatorname{d}q  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | \operatorname{d}q  | 
|   | + | \\[4pt]  | 
|   | + | \operatorname{d}q  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | \operatorname{d}q  | 
|   | + | \\[4pt]  | 
|   | + | \operatorname{d}q  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | \operatorname{d}q  | 
|   | + | \\[4pt]  | 
|   | + | \operatorname{d}q  | 
|   | + | \end{matrix}</math>  | 
|   | + | |-  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | f_7  | 
|   | + | \\[4pt]  | 
|   | + | f_{11}  | 
|   | + | \\[4pt]  | 
|   | + | f_{13}  | 
|   | + | \\[4pt]  | 
|   | + | f_{14}  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | (~p~~q~)  | 
|   | + | \\[4pt]  | 
|   | + | (~p~(q))  | 
|   | + | \\[4pt]  | 
|   | + | ((p)~q~)  | 
|   | + | \\[4pt]  | 
|   | + | ((p)(q))  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ((\operatorname{d}p)(\operatorname{d}q))  | 
|   | + | \\[4pt]  | 
|   | + | ~(\operatorname{d}p)~\operatorname{d}q~~  | 
|   | + | \\[4pt]  | 
|   | + | ~~\operatorname{d}p~(\operatorname{d}q)~  | 
|   | + | \\[4pt]  | 
|   | + | ~~\operatorname{d}p~~\operatorname{d}q~~  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ~(\operatorname{d}p)~\operatorname{d}q~~  | 
|   | + | \\[4pt]  | 
|   | + | ((\operatorname{d}p)(\operatorname{d}q))  | 
|   | + | \\[4pt]  | 
|   | + | ~~\operatorname{d}p~~\operatorname{d}q~~  | 
|   | + | \\[4pt]  | 
|   | + | ~~\operatorname{d}p~(\operatorname{d}q)~  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ~~\operatorname{d}p~(\operatorname{d}q)~  | 
|   | + | \\[4pt]  | 
|   | + | ~~\operatorname{d}p~~\operatorname{d}q~~  | 
|   | + | \\[4pt]  | 
|   | + | ((\operatorname{d}p)(\operatorname{d}q))  | 
|   | + | \\[4pt]  | 
|   | + | ~(\operatorname{d}p)~\operatorname{d}q~~  | 
|   | + | \end{matrix}</math>  | 
|   | + | |  | 
|   | + | <math>\begin{matrix}  | 
|   | + | ~~\operatorname{d}p~~\operatorname{d}q~~  | 
|   | + | \\[4pt]  | 
|   | + | ~~\operatorname{d}p~(\operatorname{d}q)~  | 
|   | + | \\[4pt]  | 
|   | + | ~(\operatorname{d}p)~\operatorname{d}q~~  | 
|   | + | \\[4pt]  | 
|   | + | ((\operatorname{d}p)(\operatorname{d}q))  | 
|   | + | \end{matrix}</math>  | 
|   | + | |-  | 
|   | + | | <math>f_{15}\!</math>  | 
|   | + | | <math>((~))</math>  | 
|   | + | | <math>((~))</math>  | 
|   | + | | <math>((~))</math>  | 
|   | + | | <math>((~))</math>  | 
|   | + | | <math>((~))</math>  | 
|   | + | |}  | 
|   | + |    | 
|   | + | <br>  | 
|   | + |    | 
|   | + | ===Wiki TeX Tables : XY===  | 
|   |  |   |  | 
|   | <br>  |   | <br>  |