Math-To-Manim: Скилл для создания анимаций математики

--- name: Math-To-Manim description: This skill should be used when the user asks to "create a math animation", "animate a mathematical concept", "generate Manim code", "visualize [topic] with animation", "explain [concept] visually", "create an educational video", "build a Manim scene", or mentions "reverse knowledge tree", "prerequisite discovery", or "verbose prompt generation". Provides a complete six-agent workflow for transforming any concept into professional Manim animations through recursive prerequisite discovery. version: 1.0.0 --- # Math-To-Manim: Reverse Knowledge Tree Animation Pipeline Transform any concept into professional mathematical animations using a six-agent workflow that requires NO training data - only pure LLM reasoning. ## Core Innovation: Reverse Knowledge Tree Instead of training on example animations, this system recursively asks: **"What must I understand BEFORE this concept?"** This builds pedagogically sound animations that flow naturally from foundation concepts to advanced topics. ## When to Use This Skill Invoke this workflow when: - Creating mathematical or scientific animations - Building educational visualizations with Manim - Generating code from conceptual explanations - Needing pedagogically structured content progression ## The Six-Agent Pipeline ### Agent 1: ConceptAnalyzer Parse user intent to extract: - **Core concept** (specific topic name) - **Domain** (physics, math, CS, etc.) - **Level** (beginner/intermediate/advanced) - **Goal** (learning objective) ### Agent 2: PrerequisiteExplorer (Key Innovation) Recursively build knowledge tree: 1. Ask: "What are the prerequisites for [concept]?" 2. For each prerequisite, recursively ask the same question 3. Stop when hitting foundation concepts (high school level) 4. Build DAG structure with depth tracking **Foundation detection criteria**: Would a high school graduate understand this without further explanation? ### Agent 3: MathematicalEnricher For each node in the tree, add: - LaTeX equations (2-5 key formulas) - Variable definitions and interpretations - Worked examples with typical values - Complexity-appropriate rigor ### Agent 4: VisualDesigner For each node, design: - Visual elements (graphs, 3D objects, diagrams) - Color scheme (maintain consistency) - Animation sequences (FadeIn, Transform, etc.) - Camera movements and transitions - Duration and pacing ### Agent 5: NarrativeComposer Walk tree from foundation to target: 1. Topologically sort nodes 2. Generate 200-300 word segment per concept 3. Include exact LaTeX, colors, animations 4. Stitch into 2000+ token verbose prompt ### Agent 6: CodeGenerator Generate working Manim code: - Use Manim Community Edition - Handle LaTeX with raw strings: `r"$frac{a}{b}$"` - Implement all visual specifications - Produce runnable Python file ## Workflow Execution To execute this workflow for a user request: ### Step 1: Analyze the Concept ```python # Extract intent analysis = { "core_concept": "quantum tunneling", "domain": "physics/quantum mechanics", "level": "intermediate", "goal": "Understand barrier penetration" } ``` ### Step 2: Build Knowledge Tree Recursively discover prerequisites with max depth of 3-4 levels: ``` Target: quantum tunneling ├─ wave-particle duality │ ├─ de Broglie wavelength [FOUNDATION] │ └─ Heisenberg uncertainty ├─ Schrödinger equation │ ├─ wave function │ └─ probability density └─ potential barriers [FOUNDATION] ``` ### Step 3: Enrich with Mathematics Add to each node: - Primary equations in LaTeX - Variable definitions - Physical interpretations ### Step 4: Design Visuals Specify for each concept: - Elements: `['wave_function', 'potential_barrier']` - Colors: `{'wave': 'BLUE', 'barrier': 'RED'}` - Animations: `['FadeIn', 'Create', 'Transform']` - Duration: 15-30 seconds per concept ### Step 5: Compose Narrative Generate verbose prompt with: - Scene-by-scene instructions - Exact LaTeX formulas - Specific animation timings - Color and position details ### Step 6: Generate Code Produce complete Python file: ```python from manim import * class ConceptAnimation(ThreeDScene): def construct(self): # Implementation following verbose prompt ... ``` ## Critical Implementation Details ### LaTeX Handling Always use raw strings for LaTeX: ```python equation = MathTex(r"E = mc^2") ``` ### Color Consistency Define color palette at scene start and reuse throughout. ### Transition Pattern Connect concepts with smooth animations: - Previous concept fades - New concept builds from prior elements - Use `Transform` or `ReplacementTransform` ### Verbose Prompt Format Structure prompts with: 1. Overview section with concept count and duration 2. Scene-by-scene instructions 3. Exact specifications (no ambiguity) See `references/verbose-prompt-format.md` for complete template. ## Output Files The pipeline generates: - `{concept}_prompt.txt` - Verbose prompt - `{concept}_tree.json` - Knowledge tree structure - `{concept}_animation.py` - Manim Python code - `{concept}_result.json` - Complete metadata ## Additional Resources ### Reference Files - **`references/reverse-knowledge-tree.md`** - Detailed algorithm explanation - **`references/agent-system-prompts.md`** - All six agent prompts - **`references/verbose-prompt-format.md`** - Complete prompt template - **`references/manim-code-patterns.md`** - Code generation patterns ### Example Files - **`examples/pythagorean-theorem/`** - Complete workflow example ## Quick Start For immediate use, follow this simplified pattern: 1. **Parse**: Extract the core concept from user input 2. **Discover**: Build prerequisite tree (depth 3-4) 3. **Enrich**: Add math and visual specs to each node 4. **Compose**: Generate verbose prompt (2000+ tokens) 5. **Generate**: Produce working Manim code The key insight: verbose, specific prompts with exact LaTeX and visual specifications produce dramatically better code than vague descriptions.