math-solver

# Math Solver Skill A comprehensive skill for solving math problems from images with formula extraction, rendering, and guided learning. ## Quick Start ### Use Case 1: Image to Solution ``` User: "I have a math problem photo. Can you help me solve it?" Flow: Image → OCR → LaTeX extraction → Formula PNG → Guided hints → Solution ``` ### Use Case 2: LaTeX to PNG ``` User: "Render this LaTeX formula beautifully" Flow: LaTeX code → math-images skill → PNG with custom styling ``` ### Use Case 3: Problem Batch Processing ``` User: "Extract all formulas from my homework photos" Flow: Multiple images → OCR all → Extract LaTeX → Render PNG grid ``` --- ## Core Workflow ### 1. Image Recognition & OCR When user uploads math problem image(s): - Use PaddleOCR Document Parsing skill to extract text and formulas - Identify mathematical expressions, layout, and problem structure - Output structured markdown with extracted content **Supported formats:** JPG, PNG, BMP, TIFF, PDF ### 2. LaTeX Extraction & Normalization - Convert recognized formulas to proper LaTeX syntax - Handle common variations (fractions, exponents, subscripts, Greek letters) - Validate LaTeX syntax before rendering - Preserve mathematical meaning and formatting **Examples of auto-corrected formats:** ``` Input: "a/b + c/d" → LaTeX: \frac{a}{b} + \frac{c}{d} Input: "x^2 + 2x + 1" → LaTeX: x^{2} + 2x + 1 Input: "sqrt(2) + pi" → LaTeX: \sqrt{2} + \pi Input: "∑(i=1 to n)" → LaTeX: \sum_{i=1}^{n} ``` ### 3. Formula Rendering to PNG Use `math-images` skill to convert LaTeX to high-quality PNG: - Support multiple themes (light, dark, sepia, chalk) - Configurable text sizes and colors - Batch rendering for multiple formulas - DPI optimization for different use cases **Output file naming:** `formula_<problem_number>_<formula_id>.png` ### 4. Guided Solution Modes #### Mode A: Socratic (Exploratory Learning) Strategy: Ask guiding questions, don't reveal answers directly Process: 1. **Problem Analysis** - "What does this problem ask you to find?" 2. **Concept Check** - "Which mathematical concept applies here?" 3. **Method Hint** - "What approach would you use?" 4. **Progress Check** - "Show me your work so far. What's the next step?" 5. **Verification** - "Does your answer make sense?" **When to use:** Student wants to learn, not just get answers #### Mode B: Detailed Explanation Strategy: Full step-by-step solution with reasoning Process: 1. **Problem Understanding** - Restate the problem in clear terms 2. **Formula Extraction** - Identify relevant mathematical formulas 3. **Step-by-Step Solution** - Each step with LaTeX rendering and explanation 4. **Verification** - Check answer validity 5. **Alternative Methods** - Show other approaches if applicable **When to use:** Student wants complete understanding #### Mode C: Quick Answer (Minimum Guidance) Just the answer with brief verification --- ## Configuration Options ### Visual Themes ```yaml themes: light: background: white text: black accent: blue dark: background: "#1e1e1e" text: white accent: cyan sepia: background: "#f4f1de" text: "#2d2d2d" accent: "#d4a574" chalk: background: "#2c2c2c" text: "#e0e0e0" accent: "#ffeb3b" ``` ### Rendering Options ```yaml formula_size: "medium" # small, medium, large dpi: 300 # 150 (fast), 300 (quality), 600 (print) background_transparent: false include_explanation: true # Show formula explanation below ``` --- ## Supported Mathematical Domains ### Algebra - Linear equations: `ax + b = c` - Quadratic equations: `ax^2 + bx + c = 0` - Polynomial operations - Rational expressions - Systems of equations ### Geometry - Area and perimeter formulas - Trigonometric relationships - Vector operations - 3D transformations ### Calculus - Limits and continuity - Derivatives and integrals - Series and sequences - Differential equations ### Statistics - Mean, variance, standard deviation - Probability distributions - Hypothesis testing - Regression analysis ### Linear Algebra - Matrix operations - Eigenvalues and eigenvectors - Linear transformations - Determinants --- ## Input & Output Examples ### Example 1: Simple Fraction Problem **Input Image:** Photo of "Simplify: (1/2) + (1/3)" **Output:** ```markdown ## Problem Extracted Simplify: (1/2) + (1/3) ## LaTeX Formula \frac{1}{2} + \frac{1}{3} ## Rendered Formula [PNG image with formula] ## Solution Guidance (Socratic Mode) 1. What do we need to do to add fractions? → We need a common denominator 2. What's the LCD of 2 and 3? → 6 3. Rewrite each fraction with denominator 6... ``` ### Example 2: Complex Expression **Input:** Handwritten quadratic equation image **LaTeX Extraction:** ```latex \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ``` **Themed Renderings:** - Light theme PNG - Dark theme PNG - Chalk board theme PNG --- ## API Integration ### Internal Integrations - **PaddleOCR Document Parsing** - Image to text/formula extraction - **math-images** - LaTeX to PNG rendering - **Claude API** - Problem analysis and guidance generation ### External Support - **Mathpix API** (optional) - High-accuracy formula recognition - **Wolfram Alpha API** (optional) - Answer verification --- ## Limitations & Edge Cases ### Known Limitations 1. **Handwriting Quality** - Works best with clear, print-like handwriting 2. **Complex Diagrams** - May struggle with embedded geometry diagrams 3. **Incomplete Problems** - Needs full problem statement in image 4. **Multiple Languages** - Optimized for English/Chinese; others may vary ### Error Handling - If OCR confidence < 70%, ask user to retake clearer photo - If LaTeX syntax invalid, suggest manual correction - If problem type unsupported, suggest alternative approaches --- ## User Preferences When user specifies preferences, save and apply consistently: ```yaml user_preferences: solution_mode: "detailed" # or "socratic" or "quick" theme: "dark" language: "en" # or "zh" for Chinese include_diagrams: true step_detail_level: "medium" # high, medium, low ``` --- ## Troubleshooting ### "OCR failed to recognize formula" - Request clearer image - Try different angle/lighting - Manually paste LaTeX if available ### "PNG rendering looks wrong" - Check LaTeX syntax validity - Try different theme/size settings - Use math-images skill directly for advanced options ### "I don't understand the guidance" - Switch to Detailed Explanation mode - Ask for more specific hints - Request step-by-step walkthrough --- ## Next Steps 1. **Quick Demo?** Upload a math problem image to test 2. **Configure Preferences?** Choose solution style and theme 3. **Batch Processing?** Upload multiple problem images 4. **Custom Styling?** Specify color/size/format preferences