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Discuss hyperplane hit rate with and without scale constraint

Vectornaut 2024-02-10 19:23:31 +00:00
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Engine-prototype.md

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* Cutting along a hyperplane with real coefficients and offset has been doing a good job of finding real solutions. * 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. * 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. * 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. * In tests with no scale constraint (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.
* In tests with a scale constraint (based on commit af1d31f), the hit ratio drops to 1.0 to 1.2, and becomes more variable.
## Rational points ## Rational points