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Start notes on engine prototype, with basis optimization as the first topic

Vectornaut 2024-02-04 23:44:28 +00:00
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# Engine prototype
## Basis optimization
The size of the Gröbner basis depends a lot on the variable order. So far, I've gotten the best performance with the degree › reverse lexicographic monomial order and the following variable order.
* First, sort by coordinate: $r$, $s$, $x$, $y$, $z$
* Within each coordinate, put spheres before points: $r_\text{s1}, r_\text{p1}, r_\text{p2}$