math-guide-solver（数学指导求解器）

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

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

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:

## 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:

\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:

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