#### vela

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It's not too bad, actually. In terms of your variables, LCKurtz's ##u## and ##v## areI guess the two forms must be equivalent, but that is far from obvious.

\begin{align*}

u &= X + Y \\

v &= -X + Y

\end{align*} which we can interpret as a rotation by ##45^\circ## and a rescaling by ##\sqrt 2##. Interpreting the terms in the two solutions geometrically, it makes sense that the two are equivalent.