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Intelligent Patterning
or
Why I've been doing computer science

Brief overview of where I'm headed:

General problem solving

Pattern recognition

Pattern recognition examples

Symbols and signs

Intelligent patterning

Some history

We have the map $ b_n: \Sigma^2U(n) \rightarrow SU(n+1) $
given by


where i(g) is the inclusion, $\left[g, h\right] = ghg^{-1}h^{-1}$
and

vn(r,s) =



where




We have the map
	$ b_n: \Sigma^2U(n) \rightarrow SU(n+1) $ \newline
given by
	\[ b_n(g, r, s) = \left[ i(g), v_n(r, s) \right] \]
where $i(g)$ is the inclusion,
	$\left[g, h\right] = ghg^{-1}h^{-1}$ \newline
and

$ v_n(r,s) = $

\[
\left[ \begin{array}{cccccc}
	\alpha & 0 & 0 & \cdots & 0 & \beta (-\overline{\alpha})^0 \\
	\beta (-\overline{\alpha})^0\overline{\beta} &
	   \alpha  &  0  & \cdots & 0 &
	   \beta (-\overline{\alpha})^1 \\
	\beta (-\overline{\alpha})^1\overline{\beta} &
	   \beta (-\overline{\alpha})^0\overline{\beta} &
	   \alpha & \cdots & 0 & \beta (-\overline{\alpha})^2 \\
	\vdots & \vdots & \vdots &  & \vdots & \vdots \\
	\vdots & \vdots & \vdots & \ddots & \vdots & \vdots \\
	\vdots & \vdots & \vdots &  & \vdots & \vdots \\
	\beta (-\overline{\alpha})^{n-1}\overline{\beta} &
	   \beta (-\overline{\alpha})^{n-2}\overline{\beta} &
	   \cdots &  \cdots & \alpha &
	   \beta (-\overline{\alpha})^n \\
	-(-\overline{\alpha})^n\overline{\beta} &
	   -(-\overline{\alpha})^{n-1}\overline{\beta} &
	   \cdots &  \cdots & -(-\overline{\alpha})^0 
	   \overline{\beta} & -(-\overline{\alpha})^n \\
	\end{array} \right]
\]
where
\[ \alpha = \alpha(r,s) =
	\cos(\pi r) + i \sin(\pi r)\cos(\pi s) \]
\[ \beta = \beta(r,s) = i \sin(\pi r)\sin(\pi s) \]

What's wrong in computing today

The intelligent mathematical assistant



 
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Tom Carter
1999-04-21