math-guide-solver

Complete mathematical problem solving workflow with OCR, LaTeX formula extraction, PNG rendering, and guided solutions. Use this skill when users want to: - Upload math problem images and automatically extract formulas as clean LaTeX - Convert LaTeX formulas to beautifully rendered PNG images with customizable themes - Get guided step-by-step problem-solving hints (Socratic method) - View detailed solutions with mathematical reasoning Handles single images, batches of images, and markdown files with embedded LaTeX. Supports multiple visual styles and provides both exploratory and detailed explanation modes.

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

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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

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User: "Render this LaTeX formula beautifully"
Flow: LaTeX code → math-images skill → PNG with custom styling

Use Case 3: Problem Batch Processing

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User: "Extract all formulas from my homework photos"
Flow: Multiple images → OCR all → Extract LaTeX → Render PNG grid

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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:

text

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

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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

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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

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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

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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

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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

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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

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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

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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