12,080
edits
Changes
Directory:Jon Awbrey/Papers/Differential Analytic Turing Automata (view source)
Revision as of 02:42, 11 March 2009
, 02:42, 11 March 2009→Computation Summary : <math>f(u, v) = \texttt{((u)(v))}</math>: markup
===Computation Summary : <math>f(u, v) = \texttt{((u)(v))}</math>===
===Computation Summary : <math>f(u, v) = \texttt{((u)(v))}</math>===
Figure 1.1 shows the expansion of <math>f = \texttt{((u)(v))}</math> over <math>[u, v]\!</math> to produce the expression:
Figure 1.1 expands f = ((u)(v)) over [u, v] to produce
{| align="center" cellpadding="8" width="90%"
| <math>\texttt{uv ~+~ u(v) ~+~ (u)v}</math>
|}
Figure 1.2 shows the expansion of <math>\operatorname{E}f = \texttt{((u + du)(v + dv))}</math> over <math>[u, v]\!</math> to produce the expression:
{| align="center" cellpadding="8" width="90%"
| <math>\texttt{uv~(du~dv) ~+~ u(v)~(du (dv)) ~+~ (u)v~((du) dv) ~+~ (u)(v)~((du)(dv))}</math>
|}
<pre>
Ef tells you what you would have to do, from where you are in the
Ef 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 f is true.
universe [u, v], if you want to end up in a place where f is true.