12,089
edits
Changes
Directory:Jon Awbrey/Papers/Differential Analytic Turing Automata (view source)
Revision as of 21:44, 11 March 2009
, 21:44, 11 March 2009→Computation Summary : <math>f(u, v) = \texttt{((u)(v))}</math>: alignment
{| align="center" cellpadding="8" width="90%"
{| align="center" cellpadding="8" width="90%"
|
|
<math>\begin{matrix}
<math>\begin{array}{lrrrrrrrr}
\operatorname{d}f
\operatorname{d}f
& = & \texttt{uv} \cdot \texttt{0} & + & \texttt{u(v)} \cdot \texttt{du} & + & \texttt{(u)v} \cdot \texttt{dv} & + & \texttt{(u)(v)} \cdot \texttt{(du, dv)}
& = & \texttt{uv} \cdot \texttt{0} & + & \texttt{u(v)} \cdot \texttt{du} & + & \texttt{(u)v} \cdot \texttt{dv} & + & \texttt{(u)(v)} \cdot \texttt{(du, dv)}
\\ \\
\\ \\
& = & & & \texttt{u(v)} \cdot \texttt{du} & + & \texttt{(u)v} \cdot \texttt{dv} & + & \texttt{(u)(v)} \cdot \texttt{(du, dv)}
& = & & & \texttt{u(v)} \cdot \texttt{du} & + & \texttt{(u)v} \cdot \texttt{dv} & + & \texttt{(u)(v)} \cdot \texttt{(du, dv)}
\end{matrix}</math>
\end{array}</math>
|}
|}
{| align="center" cellpadding="8" width="90%"
{| align="center" cellpadding="8" width="90%"
|
|
<math>\begin{matrix}
<math>\begin{array}{lrrrrrrrr}
\operatorname{r}f
\operatorname{r}f
& = & \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}
& = & \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}
\\ \\
\\ \\
& = & \texttt{du~dv}
& = & \texttt{du~dv}
\end{matrix}</math>
\end{array}</math>
|}
|}