Aaron Fenyes
c933e07312
Switch to Ganja.js basis ordering
2024-06-26 11:39:34 -07:00
Aaron Fenyes
2b6c4f4720
Avoid naming conflict with identity transformation
2024-06-26 11:28:47 -07:00
Aaron Fenyes
5aadfecf6c
Merge branch 'ganja' into gram
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Visualize low-rank factorization results.
2024-06-26 11:12:24 -07:00
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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
