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| In the current example, we already know in advance the program that generates the state transitions, and it is a rule of the following equivalent and easily derivable forms: | | In the current example, we already know in advance the program that generates the state transitions, and it is a rule of the following equivalent and easily derivable forms: |
| | | |
− | <pre>
| + | {| align="center" cellpadding="8" width="90%" |
− | 2.1. F : B^2 -> B^2 such that F : <u, v> ~> <((u)(v)), ((u, v))> | + | | 2.1. || <math>F : \mathbb{B}^2 \to \mathbb{B}^2</math> such that <math>F : (u, v) \mapsto ( ~\underline{((}~ u ~\underline{)(}~ v ~\underline{))}~ , ~\underline{((}~ u ~,~ v ~\underline{))}~ )</math> |
| + | |- |
| + | | 2.2. || <math>u' ~=~ \underline{((}~ u ~\underline{)(}~ v ~\underline{))}~, \quad v' ~=~ ~\underline{((}~ u ~,~ v ~\underline{))}</math> |
| + | |- |
| + | | 2.3. || <math>u ~:=~ \underline{((}~ u ~\underline{)(}~ v ~\underline{))}~, \quad v := ~\underline{((}~ u ~,~ v ~\underline{))}</math> |
| + | |- |
| + | | 2.4. || ??? |
| + | |} |
| | | |
− | 2.2. u' = ((u)(v)), v' = ((u, v))
| + | Well, the last one is not such a fall off the log, but that is exactly the purpose for which we have been developing all of the foregoing machinations. |
| | | |
− | 2.3. u := ((u)(v)), v := ((u, v))
| + | Here is what I got when I just went ahead and calculated the finite differences willy-nilly: |
− | | |
− | 2.4. ???
| |
− | | |
− | Well, the last one is not such a fall off the log,
| |
− | but that is exactly the purpose for which we have
| |
− | been developing all of the foregoing machinations.
| |
− | | |
− | Here is what I got when I just went ahead and | |
− | calculated the finite differences willy-nilly: | |
| | | |
| + | <pre> |
| Incipit 1. <u, v> = <0, 0> | | Incipit 1. <u, v> = <0, 0> |
| o-----o-----o-----o-----o-----o-----o | | o-----o-----o-----o-----o-----o-----o |