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118 Commits 14 Branches 2 Tags 1.6 MiB
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Author SHA1 Message Date
Aaron Fenyes
4a28a47520 Update namespace of AbstractAlgebra.Rationals 2024-06-26 01:06:27 -07:00
Aaron Fenyes
a3b1f4920c Build construction viewer module 2024-06-26 00:41:21 -07:00
Aaron Fenyes
665cb30ce0 Correct indentation of CSS 2024-06-25 23:31:00 -07:00
Aaron Fenyes
182b5bb9f6 Generate palette automatically 2024-06-25 17:57:16 -07:00
Aaron Fenyes
b7b5b9386b Load elements from Julia into Ganja.js 2024-06-25 16:30:19 -07:00
Aaron Fenyes
06a9dda5bb Play with reflections 
Try configuration of five tangent spheres.
 2024-06-25 13:40:40 -07:00
Aaron Fenyes
69a9baa8ee Add live updates to Ganja.js visualization 2024-06-25 03:11:50 -07:00
Aaron Fenyes
3b10c95d5f Clean up examples 
Declare JavaScript variables. Revise Julia comments to match new code.
 2024-06-25 02:58:39 -07:00
Aaron Fenyes
3c34481519 Get familiar with Ganja.js inline syntax 2024-06-25 01:54:01 -07:00
Aaron Fenyes
d1ce91d2aa Get a Ganja.js visualization running in Blink 2024-06-24 19:37:57 -07:00
Aaron Fenyes
58a5c38e62 Try numerical low-rank factorization 
The best technique I've found so far is the homemade gradient descent
routine in `descent-test.jl`.
 2024-05-30 00:36:03 -07:00
Aaron Fenyes
ef33b8ee10 Correct signature 2024-03-01 13:26:20 -05:00
Aaron Fenyes
717e5a6200 Extend Gram matrix automatically 
The signature of the Minkowski form on the subspace spanned by the Gram
matrix should tell us what the big Gram matrix has to look like
 2024-02-21 03:00:06 -05:00
Aaron Fenyes
16826cf07c Try out the Gram matrix approach 2024-02-20 22:35:24 -05:00
Aaron Fenyes
3170a933e4 Clean up example of three mutually tangent spheres 2024-02-15 17:16:37 -08:00
Aaron Fenyes
f2000e5731 Test different sign patterns for cosines 
It seems like there are real solutions if and only if the product of the
cosines is positive.
 2024-02-15 16:25:09 -08:00
Aaron Fenyes
ba365174d3 Find real solutions for three mutually tangent spheres 
I'm not sure why the solver wasn't working before. It might've been just
an unlucky random number draw.
 2024-02-15 16:16:06 -08:00
Aaron Fenyes
ae5db0f9ea Make results reproducible 2024-02-15 16:00:46 -08:00
Aaron Fenyes
8d8bc9162c Store elements in arrays to keep order stable 
This seems to restore reproducibility.
 2024-02-15 15:42:26 -08:00
Aaron Fenyes
291d5c8ff6 Study mutually tangent spheres with two fixed 2024-02-15 13:28:01 -08:00
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 
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
Aaron Fenyes
4e02ee16fc Find dimension of solution variety 2024-01-30 02:45:14 -05:00
Aaron Fenyes
6349f298ae Extend AbstractAlgebra ideals to rational coefficients 
The extension should also let us work over finite fields of prime order,
although we don't need to do that.
 2024-01-29 19:11:21 -05:00
Aaron Fenyes
0731c7aac1 Correct relation equations 2024-01-29 12:41:07 -05:00
Aaron Fenyes
59a527af43 Correct Minkowski product; build chain of three spheres 2024-01-29 12:28:57 -05:00
Aaron Fenyes
c29000d912 Write a simple solver for the hitting set problem 
I think we need this to find the dimension of the solution variety.
 2024-01-28 01:34:13 -05:00
Aaron Fenyes
86dbd9ea45 Order variables by coordinate and then element 
In other words, order coordinates like
  (rₛ₁, rₛ₂, sₛ₁, sₛ₂, xₛ₁, xₛ₂, xₚ₃, yₛ₁, yₛ₂, yₚ₃, zₛ₁, zₛ₂, zₚ₃)
instead of like
  (rₛ₁, sₛ₁, xₛ₁, yₛ₁, zₛ₁, rₛ₂, sₛ₂, xₛ₂, yₛ₂, zₛ₂, xₚ₃, yₚ₃, zₚ₃).

In the test cases, this really cuts down the size of the Gröbner basis.
 2024-01-27 14:21:03 -05:00
Aaron Fenyes
463a3b21e1 Realize relations as equations 2024-01-27 12:28:29 -05:00
Aaron Fenyes
4d5aa3b327 Realize geometric elements as symbolic vectors 2024-01-26 11:14:32 -05:00
Aaron Fenyes
b864cf7866 Start drafting engine prototype 2024-01-24 11:16:24 -05:00
Glen Whitney
c48d685ad6 doc: Extend comments on coordinatization; add a theory.md notes file 2023-11-07 17:06:19 -08:00