Correct align
environment in notes
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@ -47,11 +47,13 @@ One conceivable way to canonicalize lines is to use the *perpendicular* plane th
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The coordinate conventions used in the engine are different from the ones used in these notes. Marking the engine vectors and coordinates with $'$, we have
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$$I' = (x', y', z', b', c'),$$
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where
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$$\begin{align*}
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$$
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\begin{align*}
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x' & = x & b' & = b/2 \\
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y' & = y & c' & = c/2. \\
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z' & = z
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\end{align*}$$
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\end{align*}
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$$
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The engine uses the quadratic form $Q' = -Q$, which is expressed in engine coordinates as
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$$Q'(I'_1, I'_2) = x'_1 x'_2 + y'_1 y'_2 + z'_1 z'_2 - 2(b'_1c'_2 + c'_1 b'_2).$$
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In the `engine` module, the matrix of $Q'$ is encoded in the lazy static variable `Q`.
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