| Line 4,063: |
Line 4,063: |
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| − | ==Propositional Forms on Two Variables== | + | ==Detail of Calculation for the Difference Map== |
| | | | |
| − | ===Table 1===
| + | {| align="center" border="1" cellpadding="4" cellspacing="0" style="font-weight:bold; text-align:center; width:96%" |
| − | | + | |+ '''Orbit Table Template''' |
| − | {| align="center" border="1" cellpadding="0" cellspacing="0" style="font-weight:bold; text-align:center; width:96%" | |
| − | |+ '''Table 1. Propositional Forms on Two Variables''' | |
| | |- style="background:ghostwhite; height:36px" | | |- style="background:ghostwhite; height:36px" |
| − | | <math>\mathcal{L}_1</math>
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| − | | <math>\mathcal{L}_2</math>
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| − | | <math>\mathcal{L}_3</math>
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| − | | <math>\mathcal{L}_4</math>
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| − | | <math>\mathcal{L}_5</math>
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| − | | <math>\mathcal{L}_6</math>
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| − | |- style="background:ghostwhite; height:48px"
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| − | |
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| − | {| align="right" style="background:ghostwhite; text-align:right"
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| − | |-
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| − | | <math>x\!</math> :
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| − | |-
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| − | | <math>y\!</math> :
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| − | |}
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| − | {| align="center" style="background:ghostwhite"
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| − | | 1 1 0 0
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| − | | 1 0 1 0
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| − | |}
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| − | |-
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| − | {| align="center"
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| − | |-
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| − | | height="36px" | <p><math>f_{0}\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>f_{1}\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>f_{2}\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>f_{3}\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>f_{4}\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>f_{5}\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>f_{6}\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>f_{7}\!</math></p>
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| − | |}
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| − | |
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| − | {| align="center"
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| − | |-
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| − | | height="36px" | <p><math>f_{0000}\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>f_{0001}\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>f_{0010}\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>f_{0011}\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>f_{0100}\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>f_{0101}\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>f_{0110}\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>f_{0111}\!</math></p>
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| − | |}
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| − | |
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| − | {| align="center"
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| − | |-
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| − | | height="36px" | 0 0 0 0
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| − | | height="36px" | 0 0 0 1
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| − | | height="36px" | 0 0 1 0
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| − | | height="36px" | 0 0 1 1
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| − | | height="36px" | 0 1 0 0
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| − | | height="36px" | 0 1 0 1
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| − | | height="36px" | 0 1 1 0
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| − | | height="36px" | 0 1 1 1
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| − | |}
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| − | |
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| − | {| align="center"
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| − | |-
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| − | | height="36px" | <p><math>(~)\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>(x)(y)\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>(x)\ y\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>(x)\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>x\ (y)\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>(y)\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>(x,\ y)\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>(x\ y)\!</math></p>
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| − | |}
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| − | |
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| − | {| align="center"
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| − | |-
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| − | | height="36px" | <p><math>\operatorname{false}</math></p>
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| − | |-
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| − | | height="36px" | <p><math>\operatorname{neither}\ x\ \operatorname{nor}\ y</math></p>
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| − | |-
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| − | | height="36px" | <p><math>y\ \operatorname{without}\ x</math></p>
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| − | |-
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| − | | height="36px" | <p><math>\operatorname{not}\ x</math></p>
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| − | |-
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| − | | height="36px" | <p><math>x\ \operatorname{without}\ y</math></p>
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| − | |-
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| − | | height="36px" | <p><math>\operatorname{not}\ y</math></p>
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| − | |-
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| − | | height="36px" | <p><math>x\ \operatorname{not~equal~to}\ y</math></p>
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| − | |-
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| − | | height="36px" | <p><math>\operatorname{not~both}\ x\ \operatorname{and}\ y</math></p>
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| − | |}
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| − | |
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| − | {| align="center"
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| − | |-
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| − | | height="36px" | <p><math>0\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>\lnot x \land \lnot y</math></p>
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| − | |-
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| − | | height="36px" | <p><math>\lnot x \land y</math></p>
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| − | |-
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| − | | height="36px" | <p><math>\lnot x</math></p>
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| − | |-
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| − | | height="36px" | <p><math>x \land \lnot y</math></p>
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| − | |-
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| − | | height="36px" | <p><math>\lnot y</math></p>
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| − | |-
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| − | | height="36px" | <p><math>x \ne y</math></p>
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| − | |-
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| − | | height="36px" | <p><math>\lnot x \lor \lnot y</math></p>
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| − | |}
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| − | |-
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| − | |
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| − | {| align="center"
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| − | | height="36px" | <p><math>f_{8}\!</math></p>
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| − | | height="36px" | <p><math>f_{9}\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>f_{10}\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>f_{11}\!</math></p>
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| − | | height="36px" | <p><math>f_{12}\!</math></p>
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| − | | height="36px" | <p><math>f_{13}\!</math></p>
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| − | | height="36px" | <p><math>f_{14}\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>f_{15}\!</math></p>
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| − | |}
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| − | |
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| − | {| align="center"
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| − | |-
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| − | | height="36px" | <p><math>f_{1000}\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>f_{1001}\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>f_{1010}\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>f_{1011}\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>f_{1100}\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>f_{1101}\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>f_{1110}\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>f_{1111}\!</math></p>
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| − | |}
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| − | |
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| − | {| align="center"
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| − | |-
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| − | | height="36px" | 1 0 0 0
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| − | | height="36px" | 1 0 0 1
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| − | | height="36px" | 1 0 1 0
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| − | |-
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| − | | height="36px" | 1 0 1 1
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| − | |-
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| − | | height="36px" | 1 1 0 0
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| − | |-
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| − | | height="36px" | 1 1 0 1
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| − | |-
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| − | | height="36px" | 1 1 1 0
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| − | |-
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| − | | height="36px" | 1 1 1 1
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| − | |}
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| − | |
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| − | {| align="center"
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| − | |-
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| − | | height="36px" | <p><math>x\ y\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>((x,\ y))\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>y\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>(x\ (y))\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>x\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>((x)\ y)\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>((x)(y))\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>((~))\!</math></p>
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| − | |}
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| − | |
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| − | {| align="center"
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| − | |-
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| − | | height="36px" | <p><math>x\ \operatorname{and}\ y</math></p>
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| − | |-
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| − | | height="36px" | <p><math>x\ \operatorname{equal~to}\ y</math></p>
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| − | |-
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| − | | height="36px" | <p><math>y\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>\operatorname{not}\ x\ \operatorname{without}\ y</math></p>
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| − | |-
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| − | | height="36px" | <p><math>x\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>\operatorname{not}\ y\ \operatorname{without}\ x</math></p>
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| − | |-
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| − | | height="36px" | <p><math>x\ \operatorname{or}\ y</math></p>
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| − | |-
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| − | | height="36px" | <p><math>\operatorname{true}</math></p>
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| − | |}
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| − | |
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| − | {| align="center"
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| − | |-
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| − | | height="36px" | <p><math>x \land y</math></p>
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| − | |-
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| − | | height="36px" | <p><math>x = y\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>y\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>x \Rightarrow y</math></p>
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| − | |-
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| − | | height="36px" | <p><math>x\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>x \Leftarrow y</math></p>
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| − | |-
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| − | | height="36px" | <p><math>x \lor y</math></p>
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| − | |-
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| − | | height="36px" | <p><math>1\!</math></p>
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| − | |}
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| − | |}
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| − | <br>
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| − |
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| − | ===Table 2===
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| − |
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| − | {| align="center" border="1" cellpadding="0" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
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| − | |+ '''Table 2. Propositional Forms on Two Variables'''
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| − | |- style="background:ghostwhite; height:36px"
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| − | | <math>\mathcal{L}_1</math>
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| − | | <math>\mathcal{L}_2</math>
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| − | | <math>\mathcal{L}_3</math>
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| − | | <math>\mathcal{L}_4</math>
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| − | | <math>\mathcal{L}_5</math>
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| − | | <math>\mathcal{L}_6</math>
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| − | |- style="background:ghostwhite; height:48px"
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| − | |
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| − | |
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| − | {| align="right" style="background:ghostwhite; text-align:right"
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| − | |-
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| − | | <math>x\!</math> :
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| − | |-
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| − | | <math>y\!</math> :
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| − | |}
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| − | |
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| − | {| align="center" style="background:ghostwhite"
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| − | |-
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| − | | 1 1 0 0
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| − | |-
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| − | | 1 0 1 0
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| − | |}
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| − | |
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| − | |
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| − | |
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| − | |- style="height:36px"
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| − | | <p><math>f_{0}\!</math></p>
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| − | | <p><math>f_{0000}\!</math></p>
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| − | | <p>0 0 0 0</p>
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| − | | <p><math>(~)\!</math></p>
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| − | | <p><math>\operatorname{false}</math></p>
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| − | | <p><math>1\!</math></p>
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| − | |-
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| − | |
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| − | {| align="center"
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| − | |-
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| − | | height="36px" | <p><math>f_{1}\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>f_{2}\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>f_{4}\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>f_{8}\!</math></p>
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| − | |}
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| − | |
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| − | {| align="center"
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| − | |-
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| − | | height="36px" | <p><math>f_{0001}\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>f_{0010}\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>f_{0100}\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>f_{1000}\!</math></p>
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| − | |}
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| − | |
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| − | {| align="center"
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| − | |-
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| − | | height="36px" | <p>0 0 0 1</p>
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| − | |-
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| − | | height="36px" | <p>0 0 1 0</p>
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| − | |-
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| − | | height="36px" | <p>0 1 0 0</p>
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| − | |-
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| − | | height="36px" | <p>1 0 0 0</p>
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| − | |}
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| − | |
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| − | {| align="center"
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| − | |-
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| − | | height="36px" | <p><math>(x)(y)\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>(x)\ y\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>x\ (y)\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>x\ y\!</math></p>
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| − | |}
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| − | |
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| − | {| align="center"
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| − | |-
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| − | | height="36px" | <p><math>\operatorname{neither}\ x\ \operatorname{nor}\ y</math></p>
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| − | |-
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| − | | height="36px" | <p><math>y\ \operatorname{without}\ x</math></p>
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| − | |-
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| − | | height="36px" | <p><math>x\ \operatorname{without}\ y</math></p>
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| − | |-
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| − | | height="36px" | <p><math>x\ \operatorname{and}\ y</math></p>
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| − | |}
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| − | |
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| − | {| align="center"
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| − | |-
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| − | | height="36px" | <p><math>\lnot x \land \lnot y</math></p>
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| − | |-
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| − | | height="36px" | <p><math>\lnot x \land y</math></p>
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| − | |-
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| − | | height="36px" | <p><math>x \land \lnot y</math></p>
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| − | |-
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| − | | height="36px" | <p><math>x \land y</math></p>
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| − | |}
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| − | |-
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| − | |
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| − | {| align="center"
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| − | |-
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| − | | height="36px" | <p><math>f_{3}\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>f_{12}\!</math></p>
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| − | |}
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| − | |
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| − | {| align="center"
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| − | |-
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| − | | height="36px" | <p><math>f_{0011}\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>f_{1100}\!</math></p>
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| − | |}
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| − | |
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| − | {| align="center"
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| − | |-
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| − | | height="36px" | <p>0 0 1 1</p>
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| − | |-
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| − | | height="36px" | <p>1 1 0 0</p>
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| − | |}
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| − | |
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| − | {| align="center"
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| − | |-
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| − | | height="36px" | <p><math>(x)\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>x\!</math></p>
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| − | |}
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| − | |
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| − | {| align="center"
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| − | |-
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| − | | height="36px" | <p><math>\operatorname{not}\ x</math></p>
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| − | |-
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| − | | height="36px" | <p><math>x\!</math></p>
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| − | |}
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| − | |
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| − | {| align="center"
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| − | |-
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| − | | height="36px" | <p><math>\lnot x</math></p>
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| − | |-
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| − | | height="36px" | <p><math>x\!</math></p>
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| − | |}
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| − | |-
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| − | |
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| − | {| align="center"
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| − | |-
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| − | | height="36px" | <p><math>f_{6}\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>f_{9}\!</math></p>
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| − | |}
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| − | |
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| − | {| align="center"
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| − | |-
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| − | | height="36px" | <p><math>f_{0110}\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>f_{1001}\!</math></p>
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| − | |}
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| − | |
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| − | {| align="center"
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| − | |-
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| − | | height="36px" | <p>0 1 1 0</p>
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| − | |-
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| − | | height="36px" | <p>1 0 0 1</p>
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| − | |}
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| − | |
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| − | {| align="center"
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| − | |-
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| − | | height="36px" | <p><math>(x,\ y)\!</math></p>
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| − | |-
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| − | | height="36px" | <p><math>((x,\ y))\!</math></p>
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| − | |}
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| − | |
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| − | {| align="center"
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| − | |-
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| − | | height="36px" | <p><math>x\ \operatorname{not~equal~to}\ y</math></p>
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| − | |-
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| − | | height="36px" | <p><math>x\ \operatorname{equal~to}\ y</math></p>
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| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <p><math>x \ne y</math></p>
| |
| − | |-
| |
| − | | height="36px" | <p><math>x = y\!</math></p>
| |
| − | |}
| |
| − | |-
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <p><math>f_{5}\!</math></p>
| |
| − | |-
| |
| − | | height="36px" | <p><math>f_{10}\!</math></p>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <p><math>f_{0101}\!</math></p>
| |
| − | |-
| |
| − | | height="36px" | <p><math>f_{1010}\!</math></p>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <p>0 1 0 1</p>
| |
| − | |-
| |
| − | | height="36px" | <p>1 0 1 0</p>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <p><math>(y)\!</math></p>
| |
| − | |-
| |
| − | | height="36px" | <p><math>y\!</math></p>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <p><math>\operatorname{not}\ y</math></p>
| |
| − | |-
| |
| − | | height="36px" | <p><math>y\!</math></p>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <p><math>\lnot y</math></p>
| |
| − | |-
| |
| − | | height="36px" | <p><math>y\!</math></p>
| |
| − | |}
| |
| − | |-
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <p><math>f_{7}\!</math></p>
| |
| − | |-
| |
| − | | height="36px" | <p><math>f_{11}\!</math></p>
| |
| − | |-
| |
| − | | height="36px" | <p><math>f_{13}\!</math></p>
| |
| − | |-
| |
| − | | height="36px" | <p><math>f_{14}\!</math></p>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <p><math>f_{0111}\!</math></p>
| |
| − | |-
| |
| − | | height="36px" | <p><math>f_{1011}\!</math></p>
| |
| − | |-
| |
| − | | height="36px" | <p><math>f_{1101}\!</math></p>
| |
| − | |-
| |
| − | | height="36px" | <p><math>f_{1110}\!</math></p>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <p>0 1 1 1</p>
| |
| − | |-
| |
| − | | height="36px" | <p>1 0 1 1</p>
| |
| − | |-
| |
| − | | height="36px" | <p>1 1 0 1</p>
| |
| − | |-
| |
| − | | height="36px" | <p>1 1 1 0</p>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <p><math>(x\ y)\!</math></p>
| |
| − | |-
| |
| − | | height="36px" | <p><math>(x\ (y))\!</math></p>
| |
| − | |-
| |
| − | | height="36px" | <p><math>((x)\ y)\!</math></p>
| |
| − | |-
| |
| − | | height="36px" | <p><math>((x)(y))\!</math></p>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <p><math>\operatorname{not~both}\ x\ \operatorname{and}\ y</math></p>
| |
| − | |-
| |
| − | | height="36px" | <p><math>\operatorname{not}\ x\ \operatorname{without}\ y</math></p>
| |
| − | |-
| |
| − | | height="36px" | <p><math>\operatorname{not}\ y\ \operatorname{without}\ x</math></p>
| |
| − | |-
| |
| − | | height="36px" | <p><math>x\ \operatorname{or}\ y</math></p>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <p><math>\lnot x \lor \lnot y</math></p>
| |
| − | |-
| |
| − | | height="36px" | <p><math>x \Rightarrow y</math></p>
| |
| − | |-
| |
| − | | height="36px" | <p><math>x \Leftarrow y</math></p>
| |
| − | |-
| |
| − | | height="36px" | <p><math>x \lor y</math></p>
| |
| − | |}
| |
| − | |- style="height:36px"
| |
| − | | <p><math>f_{15}\!</math></p>
| |
| − | | <p><math>f_{1111}\!</math></p>
| |
| − | | <p>1 1 1 1</p>
| |
| − | | <p><math>((~))\!</math></p>
| |
| − | | <p><math>\operatorname{true}</math></p>
| |
| − | | <p><math>1\!</math></p>
| |
| − | |}
| |
| − | <br>
| |
| − |
| |
| − | ===Table 3===
| |
| − |
| |
| − | {| align="center" border="1" cellpadding="4" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
| |
| − | |+ '''Table 3. <math>\operatorname{E}f</math> Expanded Over Differential Features <math>\{ \operatorname{d}x, \operatorname{d}y \}</math>'''
| |
| − | |- style="background:ghostwhite; height:48px"
| |
| | | | | | |
| | | <math>f\!</math> | | | <math>f\!</math> |
| − | |
| + | | <math>\operatorname{F}f|_{xy}</math> |
| − | {| align="center"
| + | | <math>\operatorname{F}f|_{x(y)}</math> |
| − | |-
| + | | <math>\operatorname{F}f|_{(x)y}</math> |
| − | | <math>\operatorname{T}_{11}f</math>
| + | | <math>\operatorname{F}f|_{(x)(y)}</math> |
| − | |-
| |
| − | | <math>\operatorname{E}f|_{\operatorname{d}x\ \operatorname{d}y}</math> | |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | <math>\operatorname{T}_{10}f</math>
| |
| − | |-
| |
| − | | <math>\operatorname{E}f|_{\operatorname{d}x(\operatorname{d}y)}</math> | |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | <math>\operatorname{T}_{01}f</math>
| |
| − | |-
| |
| − | | <math>\operatorname{E}f|_{(\operatorname{d}x)\operatorname{d}y}</math> | |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | <math>\operatorname{T}_{00}f</math> | |
| − | |-
| |
| − | | <math>\operatorname{E}f|_{(\operatorname{d}x)(\operatorname{d}y)}</math>
| |
| − | |}
| |
| | |- style="height:36px" | | |- style="height:36px" |
| | | <math>f_{0}\!</math> | | | <math>f_{0}\!</math> |
| Line 4,706: |
Line 4,107: |
| | {| align="center" | | {| align="center" |
| | |- | | |- |
| − | | height="36px" | <math>x\ y\!</math> | + | | height="36px" | |
| | |- | | |- |
| − | | height="36px" | <math>x\ (y)\!</math> | + | | height="36px" | |
| | |- | | |- |
| − | | height="36px" | <math>(x)\ y\!</math> | + | | height="36px" | |
| | |- | | |- |
| − | | height="36px" | <math>(x)(y)\!</math> | + | | height="36px" | |
| | |} | | |} |
| | | | | | |
| | {| align="center" | | {| align="center" |
| | |- | | |- |
| − | | height="36px" | <math>x\ (y)\!</math> | + | | height="36px" | |
| | |- | | |- |
| − | | height="36px" | <math>x\ y\!</math> | + | | height="36px" | |
| | |- | | |- |
| − | | height="36px" | <math>(x)(y)\!</math> | + | | height="36px" | |
| | |- | | |- |
| − | | height="36px" | <math>(x)\ y\!</math> | + | | height="36px" | |
| | |} | | |} |
| | | | | | |
| | {| align="center" | | {| align="center" |
| | |- | | |- |
| − | | height="36px" | <math>(x)\ y\!</math> | + | | height="36px" | |
| | |- | | |- |
| − | | height="36px" | <math>(x)(y)\!</math> | + | | height="36px" | |
| | |- | | |- |
| − | | height="36px" | <math>x\ y\!</math> | + | | height="36px" | |
| | |- | | |- |
| − | | height="36px" | <math>x\ (y)\!</math> | + | | height="36px" | |
| | |} | | |} |
| | | | | | |
| | {| align="center" | | {| align="center" |
| | |- | | |- |
| − | | height="36px" | <math>(x)(y)\!</math> | + | | height="36px" | |
| | |- | | |- |
| − | | height="36px" | <math>(x)\ y\!</math> | + | | height="36px" | |
| | |- | | |- |
| − | | height="36px" | <math>x\ (y)\!</math> | + | | height="36px" | |
| | |- | | |- |
| − | | height="36px" | <math>x\ y\!</math> | + | | height="36px" | |
| | |} | | |} |
| | |- | | |- |
| Line 4,765: |
Line 4,166: |
| | {| align="center" | | {| align="center" |
| | |- | | |- |
| − | | height="36px" | <math>x\!</math> | + | | height="36px" | |
| | |- | | |- |
| − | | height="36px" | <math>(x)\!</math> | + | | height="36px" | |
| | |} | | |} |
| | | | | | |
| | {| align="center" | | {| align="center" |
| | |- | | |- |
| − | | height="36px" | <math>x\!</math> | + | | height="36px" | |
| | |- | | |- |
| − | | height="36px" | <math>(x)\!</math> | + | | height="36px" | |
| | |} | | |} |
| | | | | | |
| | {| align="center" | | {| align="center" |
| | |- | | |- |
| − | | height="36px" | <math>(x)\!</math> | + | | height="36px" | |
| | |- | | |- |
| − | | height="36px" | <math>x\!</math> | + | | height="36px" | |
| | |} | | |} |
| | | | | | |
| | {| align="center" | | {| align="center" |
| | |- | | |- |
| − | | height="36px" | <math>(x)\!</math> | + | | height="36px" | |
| | |- | | |- |
| − | | height="36px" | <math>x\!</math> | + | | height="36px" | |
| | |} | | |} |
| | |- | | |- |
| Line 4,808: |
Line 4,209: |
| | {| align="center" | | {| align="center" |
| | |- | | |- |
| − | | height="36px" | <math>(x,\ y)\!</math> | + | | height="36px" | |
| | |- | | |- |
| − | | height="36px" | <math>((x,\ y))\!</math> | + | | height="36px" | |
| | |} | | |} |
| | | | | | |
| | {| align="center" | | {| align="center" |
| | |- | | |- |
| − | | height="36px" | <math>((x,\ y))\!</math> | + | | height="36px" | |
| | |- | | |- |
| − | | height="36px" | <math>(x,\ y)\!</math> | + | | height="36px" | |
| | |} | | |} |
| | | | | | |
| | {| align="center" | | {| align="center" |
| | |- | | |- |
| − | | height="36px" | <math>((x,\ y))\!</math> | + | | height="36px" | |
| | |- | | |- |
| − | | height="36px" | <math>(x,\ y)\!</math> | + | | height="36px" | |
| | |} | | |} |
| | | | | | |
| | {| align="center" | | {| align="center" |
| | |- | | |- |
| − | | height="36px" | <math>(x,\ y)\!</math> | + | | height="36px" | |
| | |- | | |- |
| − | | height="36px" | <math>((x,\ y))\!</math> | + | | height="36px" | |
| | |} | | |} |
| | |- | | |- |
| Line 4,851: |
Line 4,252: |
| | {| align="center" | | {| align="center" |
| | |- | | |- |
| − | | height="36px" | <math>y\!</math> | + | | height="36px" | |
| | |- | | |- |
| − | | height="36px" | <math>(y)\!</math> | + | | height="36px" | |
| | |} | | |} |
| | | | | | |
| | {| align="center" | | {| align="center" |
| | |- | | |- |
| − | | height="36px" | <math>(y)\!</math> | + | | height="36px" | |
| | |- | | |- |
| − | | height="36px" | <math>y\!</math> | + | | height="36px" | |
| | |} | | |} |
| | | | | | |
| | {| align="center" | | {| align="center" |
| | |- | | |- |
| − | | height="36px" | <math>y\!</math> | + | | height="36px" | |
| | |- | | |- |
| − | | height="36px" | <math>(y)\!</math> | + | | height="36px" | |
| | |} | | |} |
| | | | | | |
| | {| align="center" | | {| align="center" |
| | |- | | |- |
| − | | height="36px" | <math>(y)\!</math> | + | | height="36px" | |
| | |- | | |- |
| − | | height="36px" | <math>y\!</math> | + | | height="36px" | |
| | |} | | |} |
| | |- | | |- |
| Line 4,902: |
Line 4,303: |
| | {| align="center" | | {| align="center" |
| | |- | | |- |
| − | | height="36px" | <math>((x)(y))\!</math> | + | | height="36px" | |
| | |- | | |- |
| − | | height="36px" | <math>((x)\ y)\!</math> | + | | height="36px" | |
| | |- | | |- |
| − | | height="36px" | <math>(x\ (y))\!</math> | + | | height="36px" | |
| | |- | | |- |
| − | | height="36px" | <math>(x\ y)\!</math> | + | | height="36px" | |
| | |} | | |} |
| | | | | | |
| | {| align="center" | | {| align="center" |
| | |- | | |- |
| − | | height="36px" | <math>((x)\ y)\!</math> | + | | height="36px" | |
| | |- | | |- |
| − | | height="36px" | <math>((x)(y))\!</math> | + | | height="36px" | |
| | |- | | |- |
| − | | height="36px" | <math>(x\ y)\!</math> | + | | height="36px" | |
| | |- | | |- |
| − | | height="36px" | <math>(x\ (y))\!</math> | + | | height="36px" | |
| | |} | | |} |
| | | | | | |
| | {| align="center" | | {| align="center" |
| | |- | | |- |
| − | | height="36px" | <math>(x\ (y))\!</math> | + | | height="36px" | |
| | |- | | |- |
| − | | height="36px" | <math>(x\ y)\!</math> | + | | height="36px" | |
| | |- | | |- |
| − | | height="36px" | <math>((x)(y))\!</math> | + | | height="36px" | |
| | |- | | |- |
| − | | height="36px" | <math>((x)\ y)\!</math> | + | | height="36px" | |
| | |} | | |} |
| | | | | | |
| | {| align="center" | | {| align="center" |
| | |- | | |- |
| − | | height="36px" | <math>(x\ y)\!</math> | + | | height="36px" | |
| | |- | | |- |
| − | | height="36px" | <math>(x\ (y))\!</math> | + | | height="36px" | |
| | |- | | |- |
| − | | height="36px" | <math>((x)\ y)\!</math> | + | | height="36px" | |
| | |- | | |- |
| − | | height="36px" | <math>((x)(y))\!</math> | + | | height="36px" | |
| | |} | | |} |
| | |- style="height:36px" | | |- style="height:36px" |
| | | <math>f_{15}\!</math> | | | <math>f_{15}\!</math> |
| | | <math>((~))\!</math> | | | <math>((~))\!</math> |
| − | | <math>((~))\!</math>
| |
| − | | <math>((~))\!</math>
| |
| − | | <math>((~))\!</math>
| |
| − | | <math>((~))\!</math>
| |
| − | |- style="background:ghostwhite; height:36px"
| |
| − | | colspan="2" | Fixed Point Total :
| |
| − | | <math>4\!</math>
| |
| − | | <math>4\!</math>
| |
| − | | <math>4\!</math>
| |
| − | | <math>16\!</math>
| |
| − | |}
| |
| − | <br>
| |
| − |
| |
| − | ===Table 4===
| |
| − |
| |
| − | {| align="center" border="1" cellpadding="4" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
| |
| − | |+ '''Table 4. <math>\operatorname{D}f</math> Expanded Over Differential Features <math>\{ \operatorname{d}x, \operatorname{d}y \}</math>'''
| |
| − | |- style="background:ghostwhite; height:36px"
| |
| | | | | | |
| − | | <math>f\!</math>
| |
| − | | <math>\operatorname{D}f|_{\operatorname{d}x\ \operatorname{d}y}</math>
| |
| − | | <math>\operatorname{D}f|_{\operatorname{d}x(\operatorname{d}y)}</math>
| |
| − | | <math>\operatorname{D}f|_{(\operatorname{d}x)\operatorname{d}y}</math>
| |
| − | | <math>\operatorname{D}f|_{(\operatorname{d}x)(\operatorname{d}y)}</math>
| |
| − | |- style="height:36px"
| |
| − | | <math>f_{0}\!</math>
| |
| − | | <math>(~)\!</math>
| |
| − | | <math>(~)\!</math>
| |
| − | | <math>(~)\!</math>
| |
| − | | <math>(~)\!</math>
| |
| − | | <math>(~)\!</math>
| |
| − | |-
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>f_{1}\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>f_{2}\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>f_{4}\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>f_{8}\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>(x)(y)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(x)\ y\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>x\ (y)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>x\ y\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>((x,\ y))\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(x,\ y)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(x,\ y)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>((x,\ y))\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>(y)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>y\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(y)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>y\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>(x)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(x)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>x\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>x\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>(~)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(~)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(~)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(~)\!</math>
| |
| − | |}
| |
| − | |-
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>f_{3}\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>f_{12}\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>(x)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>x\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>((~))\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>((~))\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>((~))\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>((~))\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>(~)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(~)\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>(~)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(~)\!</math>
| |
| − | |}
| |
| − | |-
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>f_{6}\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>f_{9}\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>(x,\ y)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>((x,\ y))\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>(~)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(~)\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>((~))\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>((~))\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>((~))\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>((~))\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>(~)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(~)\!</math>
| |
| − | |}
| |
| − | |-
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>f_{5}\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>f_{10}\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>(y)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>y\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>((~))\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>((~))\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>(~)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(~)\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>((~))\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>((~))\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>(~)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(~)\!</math>
| |
| − | |}
| |
| − | |-
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>f_{7}\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>f_{11}\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>f_{13}\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>f_{14}\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>(x\ y)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(x\ (y))\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>((x)\ y)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>((x)(y))\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>((x,\ y))\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(x,\ y)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(x,\ y)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>((x,\ y))\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>y\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(y)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>y\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(y)\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>x\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>x\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(x)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(x)\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>(~)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(~)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(~)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(~)\!</math>
| |
| − | |}
| |
| − | |- style="height:36px"
| |
| − | | <math>f_{15}\!</math>
| |
| − | | <math>((~))\!</math>
| |
| − | | <math>(~)\!</math>
| |
| − | | <math>(~)\!</math>
| |
| − | | <math>(~)\!</math>
| |
| − | | <math>(~)\!</math>
| |
| − | |}
| |
| − | <br>
| |
| − |
| |
| − | ===Table 5===
| |
| − |
| |
| − | {| align="center" border="1" cellpadding="4" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
| |
| − | |+ '''Table 5. <math>\operatorname{E}f</math> Expanded Over Ordinary Features <math>\{ x, y \}\!</math>'''
| |
| − | |- style="background:ghostwhite; height:36px"
| |
| | | | | | |
| − | | <math>f\!</math>
| |
| − | | <math>\operatorname{E}f|_{xy}</math>
| |
| − | | <math>\operatorname{E}f|_{x(y)}</math>
| |
| − | | <math>\operatorname{E}f|_{(x)y}</math>
| |
| − | | <math>\operatorname{E}f|_{(x)(y)}</math>
| |
| − | |- style="height:36px"
| |
| − | | <math>f_{0}\!</math>
| |
| − | | <math>(~)\!</math>
| |
| − | | <math>(~)\!</math>
| |
| − | | <math>(~)\!</math>
| |
| − | | <math>(~)\!</math>
| |
| − | | <math>(~)\!</math>
| |
| − | |-
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>f_{1}\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>f_{2}\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>f_{4}\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>f_{8}\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>(x)(y)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(x)\ y\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>x\ (y)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>x\ y\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}x\ \operatorname{d}y</math>
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}x\ (\operatorname{d}y)</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}x)\ \operatorname{d}y</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}x) (\operatorname{d}y)</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}x\ (\operatorname{d}y)</math>
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}x\ \operatorname{d}y</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}x) (\operatorname{d}y)</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}x)\ \operatorname{d}y</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}x)\ \operatorname{d}y</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}x) (\operatorname{d}y)</math>
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}x\ \operatorname{d}y</math>
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}x\ (\operatorname{d}y)</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}x) (\operatorname{d}y)</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}x)\ \operatorname{d}y</math>
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}x\ (\operatorname{d}y)</math>
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}x\ \operatorname{d}y</math>
| |
| − | |}
| |
| − | |-
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>f_{3}\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>f_{12}\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>(x)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>x\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}x</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}x)</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}x</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}x)</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}x)</math>
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}x</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}x)</math>
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}x</math>
| |
| − | |}
| |
| − | |-
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>f_{6}\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>f_{9}\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>(x,\ y)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>((x,\ y))\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}x,\ \operatorname{d}y)</math>
| |
| − | |-
| |
| − | | height="36px" | <math>((\operatorname{d}x,\ \operatorname{d}y))</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>((\operatorname{d}x,\ \operatorname{d}y))</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}x,\ \operatorname{d}y)</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>((\operatorname{d}x,\ \operatorname{d}y))</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}x,\ \operatorname{d}y)</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}x,\ \operatorname{d}y)</math>
| |
| − | |-
| |
| − | | height="36px" | <math>((\operatorname{d}x,\ \operatorname{d}y))</math>
| |
| − | |}
| |
| − | |-
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>f_{5}\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>f_{10}\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>(y)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>y\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}y</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}y)</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}y)</math>
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}y</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}y</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}y)</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}y)</math>
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}y</math>
| |
| − | |}
| |
| − | |-
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>f_{7}\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>f_{11}\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>f_{13}\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>f_{14}\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>(x\ y)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(x\ (y))\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>((x)\ y)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>((x)(y))\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>((\operatorname{d}x)(\operatorname{d}y))</math>
| |
| − | |-
| |
| − | | height="36px" | <math>((\operatorname{d}x)\ \operatorname{d}y)</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}x\ (\operatorname{d}y))</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}x\ \operatorname{d}y)</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>((\operatorname{d}x)\ \operatorname{d}y)</math>
| |
| − | |-
| |
| − | | height="36px" | <math>((\operatorname{d}x)(\operatorname{d}y))</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}x\ \operatorname{d}y)</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}x\ (\operatorname{d}y))</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}x\ (\operatorname{d}y))</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}x\ \operatorname{d}y)</math>
| |
| − | |-
| |
| − | | height="36px" | <math>((\operatorname{d}x)(\operatorname{d}y))</math>
| |
| − | |-
| |
| − | | height="36px" | <math>((\operatorname{d}x)\ \operatorname{d}y)</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}x\ \operatorname{d}y)</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}x\ (\operatorname{d}y))</math>
| |
| − | |-
| |
| − | | height="36px" | <math>((\operatorname{d}x)\ \operatorname{d}y)</math>
| |
| − | |-
| |
| − | | height="36px" | <math>((\operatorname{d}x)(\operatorname{d}y))</math>
| |
| − | |}
| |
| − | |- style="height:36px"
| |
| − | | <math>f_{15}\!</math>
| |
| − | | <math>((~))\!</math>
| |
| − | | <math>((~))\!</math>
| |
| − | | <math>((~))\!</math>
| |
| − | | <math>((~))\!</math>
| |
| − | | <math>((~))\!</math>
| |
| − | |}
| |
| − | <br>
| |
| − |
| |
| − | ===Table 6===
| |
| − |
| |
| − | {| align="center" border="1" cellpadding="4" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
| |
| − | |+ '''Table 6. <math>\operatorname{D}f</math> Expanded Over Ordinary Features <math>\{ x, y \}\!</math>'''
| |
| − | |- style="background:ghostwhite; height:36px"
| |
| | | | | | |
| − | | <math>f\!</math> | + | | |
| − | | <math>\operatorname{D}f|_{xy}</math>
| |
| − | | <math>\operatorname{D}f|_{x(y)}</math>
| |
| − | | <math>\operatorname{D}f|_{(x)y}</math>
| |
| − | | <math>\operatorname{D}f|_{(x)(y)}</math>
| |
| − | |- style="height:36px"
| |
| − | | <math>f_{0}\!</math>
| |
| − | | <math>(~)\!</math>
| |
| − | | <math>(~)\!</math>
| |
| − | | <math>(~)\!</math>
| |
| − | | <math>(~)\!</math>
| |
| − | | <math>(~)\!</math>
| |
| − | |-
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>f_{1}\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>f_{2}\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>f_{4}\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>f_{8}\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>(x)(y)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(x)\ y\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>x\ (y)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>x\ y\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}x\ \operatorname{d}y</math>
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}x\ (\operatorname{d}y)</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}x)\ \operatorname{d}y</math>
| |
| − | |-
| |
| − | | height="36px" | <math>((\operatorname{d}x)(\operatorname{d}y))</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}x\ (\operatorname{d}y)</math>
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}x\ \operatorname{d}y</math>
| |
| − | |-
| |
| − | | height="36px" | <math>((\operatorname{d}x)(\operatorname{d}y))</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}x)\ \operatorname{d}y</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}x)\ \operatorname{d}y</math>
| |
| − | |-
| |
| − | | height="36px" | <math>((\operatorname{d}x)(\operatorname{d}y))</math>
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}x\ \operatorname{d}y</math>
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}x\ (\operatorname{d}y)</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>((\operatorname{d}x)(\operatorname{d}y))</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}x)\ \operatorname{d}y</math>
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}x\ (\operatorname{d}y)</math>
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}x\ \operatorname{d}y</math>
| |
| − | |}
| |
| − | |-
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>f_{3}\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>f_{12}\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>(x)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>x\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}x</math>
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}x</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}x</math>
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}x</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}x</math>
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}x</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}x</math>
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}x</math>
| |
| − | |}
| |
| − | |-
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>f_{6}\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>f_{9}\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>(x,\ y)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>((x,\ y))\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}x,\ \operatorname{d}y)</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}x,\ \operatorname{d}y)</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}x,\ \operatorname{d}y)</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}x,\ \operatorname{d}y)</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}x,\ \operatorname{d}y)</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}x,\ \operatorname{d}y)</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}x,\ \operatorname{d}y)</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}x,\ \operatorname{d}y)</math>
| |
| − | |}
| |
| − | |-
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>f_{5}\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>f_{10}\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>(y)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>y\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}y</math>
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}y</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}y</math>
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}y</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}y</math>
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}y</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}y</math>
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}y</math>
| |
| − | |}
| |
| − | |-
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>f_{7}\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>f_{11}\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>f_{13}\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>f_{14}\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>(x\ y)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(x\ (y))\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>((x)\ y)\!</math>
| |
| − | |-
| |
| − | | height="36px" | <math>((x)(y))\!</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>((\operatorname{d}x)(\operatorname{d}y))</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}x)\ \operatorname{d}y</math>
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}x\ (\operatorname{d}y)</math>
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}x\ \operatorname{d}y</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}x)\ \operatorname{d}y</math>
| |
| − | |-
| |
| − | | height="36px" | <math>((\operatorname{d}x)(\operatorname{d}y))</math>
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}x\ \operatorname{d}y</math>
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}x\ (\operatorname{d}y)</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}x\ (\operatorname{d}y)</math>
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}x\ \operatorname{d}y</math>
| |
| − | |-
| |
| − | | height="36px" | <math>((\operatorname{d}x)(\operatorname{d}y))</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}x)\ \operatorname{d}y</math>
| |
| − | |}
| |
| − | |
| |
| − | {| align="center"
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}x\ \operatorname{d}y</math>
| |
| − | |-
| |
| − | | height="36px" | <math>\operatorname{d}x\ (\operatorname{d}y)</math>
| |
| − | |-
| |
| − | | height="36px" | <math>(\operatorname{d}x)\ \operatorname{d}y</math>
| |
| − | |-
| |
| − | | height="36px" | <math>((\operatorname{d}x)(\operatorname{d}y))</math>
| |
| − | |}
| |
| − | |- style="height:36px"
| |
| − | | <math>f_{15}\!</math>
| |
| − | | <math>((~))\!</math>
| |
| − | | <math>(~)\!</math>
| |
| − | | <math>(~)\!</math>
| |
| − | | <math>(~)\!</math>
| |
| − | | <math>(~)\!</math>
| |
| | |} | | |} |
| | <br> | | <br> |
| − |
| |
| − | ==Detail of Calculation for the Difference Map==
| |
| | | | |
| | =Elegant Graveyard= | | =Elegant Graveyard= |
