Aaron Fenyes
e41bcc7e13
Explore the performance wall
...
Three points on two spheres is too much.
2024-02-13 04:02:14 -05:00
Aaron Fenyes
31d5e7e864
Play with two points on two spheres
...
Guess conditions that make the scaling constraint impossible to satisfy.
2024-02-12 22:48:16 -05:00
Aaron Fenyes
a450f701fb
Try displaying a chain of spheres
...
For three mutually tangent spheres, I couldn't find real solutions.
2024-02-12 21:14:07 -05:00
Aaron Fenyes
6cf07dc6a1
Evaluate and display elements
2024-02-12 20:34:12 -05:00
Aaron Fenyes
1f173708eb
Move random cut routine into engine
2024-02-10 17:39:26 -05:00
Aaron Fenyes
6f18d4efcc
Test lots of uniformly distributed hyperplanes
2024-02-10 15:10:48 -05:00
Aaron Fenyes
621c4c5776
Try uniformly distributed hyperplane orientations
...
Unit normals are uniformly distributed over the sphere.
2024-02-10 15:02:26 -05:00
Aaron Fenyes
b3b7c2026d
Separate the algebraic and numerical parts of the engine
2024-02-10 14:50:50 -05:00
Aaron Fenyes
af1d31f6e6
Test a scale constraint
...
In all but a few cases (for example, a single point on a plane), we
should be able to us the radius-coradius boost symmetry to make the
average co-radius—representing the "overall scale"—roughly one.
2024-02-10 14:21:52 -05:00
Aaron Fenyes
8e33987f59
Systematically try out different cut planes
2024-02-10 13:46:01 -05:00
Aaron Fenyes
06872a04af
Say how many sample solutions we found
2024-02-10 01:06:06 -05:00
Aaron Fenyes
becefe0c47
Try switching to compiled system
2024-02-10 00:59:50 -05:00
Aaron Fenyes
34358a8728
Find witnesses on random rational hyperplanes
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Choose hyperplanes that go through the trivial solution.
2024-02-09 23:44:10 -05:00
Aaron Fenyes
95c0ff14b2
Show explicitly that all coefficients are 1 in first cut equation
2024-02-09 17:09:43 -05:00
Aaron Fenyes
f97090c997
Try a cut that goes through the trivial solution
...
The previous cut was supposed to do this, but I was missing some parentheses.
2024-02-08 01:58:12 -05:00
Aaron Fenyes
45aaaafc8f
Seek sample solutions by cutting with a hyperplane
...
The example hyperplane yields a single solution, with multiplicity six. You can
find it analytically by hand, and homotopy continuation finds it numerically.
2024-02-08 01:53:55 -05:00
Aaron Fenyes
43cbf8a3a0
Add relations to center and orient the construction
2024-02-05 00:10:13 -05:00
Aaron Fenyes
21f09c4a4d
Switch element abbreviation from "elem" to "elt"
2024-02-04 16:08:13 -05:00
Aaron Fenyes
a3f3f6a31b
Order spheres before points within each coordinate block
...
In the cases I've tried so far, this leads to substantially smaller
Gröbner bases.
2024-02-01 16:13:22 -05:00
Aaron Fenyes
65d23fb667
Use module names as filenames
...
You're right: this naming convention seems to be standard for Julia
modules now.
2024-01-30 02:49:33 -05:00
