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| Here is what I got when I just went ahead and calculated the finite differences willy-nilly: | | Here is what I got when I just went ahead and calculated the finite differences willy-nilly: |
| + | |
| + | {| align="center" cellpadding="8" style="text-align:center" |
| + | |- |
| + | | <math>\text{Incipit 1.}\ (u, v) = (0, 0)</math> |
| + | |- |
| + | | |
| + | <math>\begin{array}{c|cc|cc|cc|cc|cc|c} |
| + | t & u & v & du & dv & d^2 u & d^2 v & d^3 u & d^3 v & d^4 u & d^4 v & \ldots \\ |
| + | \\ |
| + | 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & \ldots \\ |
| + | 1 & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & \ldots \\ |
| + | 2 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \ldots \\ |
| + | 3 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \ldots \\ |
| + | 4 & '' & '' & '' & '' & '' & '' & '' & '' & '' & '' & \ldots \\ |
| + | \end{array}</math> |
| + | |- |
| + | | <math>\text{Incipit 2.}\ (u, v) = (1, 1)</math> |
| + | |- |
| + | | |
| + | <math>\begin{array}{c|cc} |
| + | t & u & v \\ |
| + | \\ |
| + | 0 & 1 & 1 \\ |
| + | 1 & 1 & 1 \\ |
| + | 2 & '' & '' \\ |
| + | \end{array}</math> |
| + | |} |
| | | |
| <pre> | | <pre> |
− | Incipit 1. <u, v> = <0, 0>
| |
− | o-----o-----o-----o-----o-----o-----o
| |
− | | d d | d d | d d | d d | d d | ... |
| |
− | | 0 0 | 1 1 | 2 2 | 3 3 | 4 4 | ... |
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− | | u v | u v | u v | u v | u v | ... |
| |
− | o-----o-----o-----o-----o-----o-----o
| |
− | | 0 0 | 0 1 | 1 0 | 0 1 | 1 0 | ... |
| |
− | | 0 1 | 1 1 | 1 1 | 1 1 | 1 1 | ... |
| |
− | | 1 0 | 0 0 | 0 0 | 0 0 | 0 0 | ... |
| |
− | | 1 0 | 0 0 | 0 0 | 0 0 | 0 0 | ... |
| |
− | | " " | " " | " " | " " | " " | """ |
| |
− | o-----o-----o-----o-----o-----o-----o
| |
− |
| |
| Incipit 2. <u, v> = <1, 1> | | Incipit 2. <u, v> = <1, 1> |
| o-----o-----o-----o-----o | | o-----o-----o-----o-----o |