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Directory:Jon Awbrey/Papers/Differential Analytic Turing Automata (view source)
Revision as of 22:32, 11 March 2009
, 22:32, 11 March 2009→Note 19: markup
===Computation Summary : <math>g(u, v) = \texttt{((u,~v))}</math>===
===Computation Summary : <math>g(u, v) = \texttt{((u,~v))}</math>===
Figure 2.1 shows the expansion of <math>g = \texttt{((u,~v))}</math> over <math>[u, v]\!</math> to produce the expression:
Figure 2.1 expands g = ((u, v)) over [u, v] to get
{| align="center" cellpadding="8" width="90%"
| <math>\texttt{uv} ~+~ \texttt{(u)(v)}</math>
|}
Figure 2.2 shows the expansion of <math>\operatorname{E}g = \texttt{((u + du, ~v + dv))}</math> over <math>[u, v]\!</math> to produce the expression:
{| align="center" cellpadding="8" width="90%"
| <math>\texttt{uv} \cdot \texttt{((du, dv))} + \texttt{u(v)} \cdot \texttt{(du, dv)} + \texttt{(u)v} \cdot \texttt{(du, dv)} + \texttt{(u)(v)} \cdot \texttt{((du, dv))}</math>
|}
<pre>
Eg tells you what you would have to do, from where you are in the
Eg tells you what you would have to do, from where you are in the
universe [u, v], if you want to end up in a place where g is true.
universe [u, v], if you want to end up in a place where g is true.