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Describe test suite

Vectornaut 2024-02-04 23:46:59 +00:00
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Engine-prototype.md

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## 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.
### Best order
The size of the Gröbner basis depends a lot on the variable order. For the examples below, 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: $r_\text{s1}, r_\text{p1}, r_\text{p2}$
* Within each coordinate, put spheres before points: $r_\text{s1}, r_\text{p1}, r_\text{p2}$
### Test suite
* One point on a sphere
* Two points on a sphere
* Three mutually tangent spheres