 Canonical orientation of the orientation double cover (source code)

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= Canonical orientation of the orientation double cover

At $(p,o)$ in the <orientation double cover>, use the derivative of the covering projection to transport the chosen <orientation> $o$ to the tangent space of the cover. In local oriented sheets this prescription is smooth, so it defines a global <orientation>. The involution $(p,o)\mapsto(p,-o)$ reverses it.

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