math-guide-solver

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name: math-solver description: | 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.

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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

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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:

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__.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

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

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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:

## 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

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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:

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

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

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"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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