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Record hyperplane cut results

Vectornaut 2024-02-10 18:50:27 +00:00
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Engine-prototype.md

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## Witness sets
* Cutting along a hyperplane with real coefficients and offset has been doing a good job of finding real solutions.
* Hyperplanes that go through the origin has been performing better than hyperplanes with other offsets.
* Ones that go through the trivial solution seem the worst.
* In tests based on commit 8e33987, hyperplanes through the origin tend to hit around 1.5 times as many real solutions as ones through the trivial solution.
## Rational points
One strategy for exploring a positive-dimensional solution variety is to enumerate rational points. When the user drags the display, we move numerically along the solution variety, snapping to the nearest known rational point when the drag ends.