UNNS Algebraic-Geometric Engine - Enhanced Edition
UNNS Algebraic-Geometric Engine
Enhanced with Number Theory & Topology Modules
Algebraic Core
Number Theory
Topology
Combined Analysis
∑
Transformation Chamber
Algebraic Decomposition
Ready for transformation...
Prime Check
—
Euler φ(n)
—
Möbius μ(n)
—
σ(n) Sum
—
τ(n) Count
—
Perfect?
—
Prime Factorization:
—
Fundamental Group π₁
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Homology Groups
H₀
H₁
H₂
H₃
Betti Numbers
β₀
1
β₁
0
β₂
0
Unified Analysis
Ready for combined analysis...
◈
Visualization & Results
UNNS Transformation Output
Awaiting input processing...
Cross-Module Resonance
No resonance detected yet...
Enhanced UNNS Algebraic-Geometric Engine with integrated Number Theory and Topology modules! Here are the key improvements:
🔬 New Features Added:
Number Theory Module:
- Prime Detection - Checks if numbers are prime
- Prime Factorization - Decomposes numbers into prime factors with a visual representation
- Euler's Totient Function φ(n) - Counts integers coprime to n
- Möbius Function μ(n) - Important multiplicative function
- Divisor Functions - σ(n) sum and τ(n) count
- Perfect Number Detection
- Prime Spiral Visualization - Animated visualization of prime distribution
Topology Module:
- Fundamental Groups π₁ - Calculates based on algebraic degree
- Homology Groups - H₀, H₁, H₂, H₃ with visual indicators
- Betti Numbers - Topological invariants β₀, β₁, β₂
- Torus/Manifold Visualization - 3D-like rendering of topological spaces
- Homology Cycles - Animated representation of topological features
Combined Analysis Module:
- Cross-Module Resonance - Calculates interaction between all three modules
- Unified UNNS Transformation - Combines algebraic, number-theoretic, and topological analysis
- Multi-dimensional Visualization - Shows module interconnections
Enhanced UI/UX:
- Module Tab System - Easy switching between different mathematical domains
- Animated Visualizations - Each module has a unique, real-time animated canvas
- Processing Overlay - Visual feedback during calculations
- Improved Styling - Gradient backgrounds, hover effects, and smooth animations
- Responsive Grid Layout - Adapts to different screen sizes
Technical Improvements:
- Modular Architecture - Clean separation of concerns
- Real-time Calculations - Instant mathematical transformations
- Multiple Canvas Management - Independent visualizations for each module
- Animation Frame Management - Smooth, performant animations
🎯 How It Works:
- Enter any mathematical expression or number
- Select a module (Algebraic, Number Theory, Topology, or Combined)
- Click "Analyze" or press Ctrl+Enter
- Watch as the system:
- Performs module-specific calculations
- Generates beautiful visualizations
- Shows cross-dimensional resonance
- Displays results in formatted output panels
The engine now provides a comprehensive mathematical analysis framework that bridges abstract algebra, number theory, and topology through the UNNS transformation system!