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Directory:Jon Awbrey/Papers/Differential Analytic Turing Automata (view source)
Revision as of 14:12, 10 March 2009
, 14:12, 10 March 2009→Computation Summary : <math>g(u, v) = \texttt{((u,~v))}</math>
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Figure 2.2 expands Eg = ((u + du, v + dv)) over [u, v] to give:
Figure 2.2 expands <math>\operatorname{E}g = \texttt{((u + du,~v + dv))}</math> over <math>[u, v]\!</math> to give:
uv.((du, dv)) + u(v).(du, dv) + (u)v.(du, dv) + (u)(v).((du, dv))
{| align="center" cellpadding="8" width="90%"
| <math>\texttt{uv~((du,~dv)) ~+~ u(v)~(du,~dv) ~+~ (u)v~(du,~dv) ~+~ (u)(v)~((du,~dv))}</math>
|}
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Figure 2.3 expands Dg = g + Eg over [u, v] to yield the form:
Figure 2.3 expands <math>\operatorname{D}g = g + \operatorname{E}g</math> over <math>[u, v]\!</math> to yield the form:
uv.(du, dv) + u(v).(du, dv) + (u)v.(du, dv) + (u)(v).(du, dv)
{| align="center" cellpadding="8" width="90%"
| <math>\texttt{uv~(du,~dv) ~+~ u(v)~(du,~dv) ~+~ (u)v~(du,~dv) ~+~ (u)(v)~(du,~dv)}</math>
|}
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