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

Use Case 2: LaTeX to PNG

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

• - 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:
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3. Formula Rendering to 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: INLINECODE1

4. Guided Solution Modes

Mode A: Socratic (Exploratory Learning)

Process:

1. 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

Process:

1. 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)

Configuration Options

Visual Themes

Rendering Options

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: INLINECODE2
• Quadratic equations: INLINECODE3
• 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

Output:
CODEBLOCK6

Example 2: Complex Expression

LaTeX Extraction:
CODEBLOCK7

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. 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:

CODEBLOCK8

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. 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