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🧮 Interactive Algebraic Structures Demo
Change any input - see results update in real-time!
1️⃣ SO(2) Equivariance (G-Modules)
Rotation Angle θ:
45°
Layer Angle α:
30°
Input Vector x:
,
Test Equivariance
Click "Test Equivariance" to see results...
2️⃣ Tensor Products (Attention Mechanism)
Query Dimension:
Key Dimension:
Query Vector v:
Key Vector w:
Compute Tensor Product
Click "Compute Tensor Product" to see results...
4️⃣ Betti Numbers (Homology)
Shape:
Triangle (3 vertices, 3 edges)
Square (4 vertices, 4 edges)
Filled Triangle (3 vertices, 3 edges, 1 face)
Circle (8 vertices, 8 edges)
Compute Betti Numbers
Click "Compute Betti Numbers" to see results...
5️⃣ XOR Polynomial (Algebraic Varieties)
Custom Weights:
Reset to XOR Solution
w₀:
w₁:
w₂:
w₃:
w₄:
w₅:
Test Point (x₁, x₂):
,
Test Point
Click "Test Point" or modify weights to see results...