From 627d05eb4beb9bf48b5aabcd86044522127e28bf Mon Sep 17 00:00:00 2001 From: Vectornaut Date: Sun, 4 Feb 2024 23:44:28 +0000 Subject: [PATCH] Start notes on engine prototype, with basis optimization as the first topic --- Engine-prototype.md | 8 ++++++++ 1 file changed, 8 insertions(+) create mode 100644 Engine-prototype.md diff --git a/Engine-prototype.md b/Engine-prototype.md new file mode 100644 index 0000000..35cc5ee --- /dev/null +++ b/Engine-prototype.md @@ -0,0 +1,8 @@ +# 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: $r_\text{s1}, r_\text{p1}, r_\text{p2}$ \ No newline at end of file