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Line 4,278:
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<pre>
Reading the arrows off the map produces the following data:
Reading the arrows off the map produces the following data:
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<pre>
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{| align="center" cellspacing="10" style="text-align:center"
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r[pq]
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|
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<math>\begin{array}{rcccccc}
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=
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\operatorname{r}(pq)
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& = & p & \cdot & q & \cdot &
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p q . dp dq
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\operatorname{d}p ~ \operatorname{d}q
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\\[4pt]
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+
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& + & p & \cdot & \texttt{(} q \texttt{)} & \cdot &
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\operatorname{d}p ~ \operatorname{d}q
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p (q) . dp dq
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\\[4pt]
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& + & \texttt{(} p \texttt{)} & \cdot & q & \cdot &
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+
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\operatorname{d}p ~ \operatorname{d}q
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\\[4pt]
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(p) q . dp dq
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& + & \texttt{(} p \texttt{)} & \cdot & \texttt{(}q \texttt{)} & \cdot &
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\operatorname{d}p ~ \operatorname{d}q
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\end{array}</math>
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|}
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(p)(q) . dp dq
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</pre>
In short, <math>\operatorname{r}(pq)</math> is a constant field, having the value <math>\operatorname{d}p~\operatorname{d}q</math> at each cell.
In short, <math>\operatorname{r}(pq)</math> is a constant field, having the value <math>\operatorname{d}p~\operatorname{d}q</math> at each cell.
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A more detailed presentation of Differential Logic can be found here:
A more detailed presentation of Differential Logic can be found here:
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* DLOG D. http://stderr.org/pipermail/inquiry/2003-May/thread.html#478
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* [[Directory:Jon_Awbrey/Papers/Differential_Logic_and_Dynamic_Systems_2.0|Differential Logic and Dynamic Systems]]
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* DLOG D. http://stderr.org/pipermail/inquiry/2003-June/thread.html#553
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* DLOG D. http://stderr.org/pipermail/inquiry/2003-June/thread.html#571
==Document History==
==Document History==