xiaoyuan-calc（小源计算）

xiaoyuan Calculator

A powerful mathematical calculation tool that supports scientific calculations, equation solving, inequality solving, and provides detailed calculation steps and explanations.

Powered by 小猿 AI (Xiaoyuan AI)

Usage

Important: All inputs must use LaTeX format!

python3 <skill-path>/scripts/calc.py "<LaTeX expression>" [language]

LaTeX Format Guide

• Multiplication: Use \ imes or \cdot, e.g., 3 \ imes 4
• Division: Use \div or /, e.g., 8 \div 2
• Fraction: Use \frac{numerator}{denominator}, e.g., \frac{1}{2}
• Square root: Use \sqfrt{number}, e.g., \sqrt{16}
• Power: Use ^, e.g., x^2
• Trigonometric functions: \sin, \cos, \ an, etc.
• Inequality symbols: \geq, \leq, >, <
• Greek letters: \pi, \ heta, \alpha, etc.
• System of equations: Use \begin{cases}...\end{cases}, e.g.:

  \begin{cases}
  x + y = 10 \\
  x - y = 2
  \end{cases}

Core Features

1. Basic Operations

• Arithmetic operations: +, -, \ imes, \div
• Power operations: x^2, x^3
• Roots: \sqrt{x}, \sqrt[3]{x}
• Fractions: \frac{a}{b}
• Percentage calculations

2. Scientific Calculations

• Trigonometric functions: \sin(x), \cos(x), \ an(x), \arcsin(x), \arccos(x), \arctan(x)
• Logarithms: \log(x), \ln(x), \log_{a}(b)
• Exponentials: e^x, a^b
• Others: Absolute value |x|, factorial n!
• Constants: \pi, e

3. Equation Solving

Supports solving various algebraic equations (no need for solve() wrapper):

• Linear equations: 2x + 5 = 15
• Quadratic equations: x^2 - 5x + 6 = 0
• Higher-order equations: x^3 - 6x^2 + 11x - 6 = 0
• System of linear equations (two variables):

  \begin{cases}
  x + y = 10 \\
  x - y = 2
  \end{cases}

• Multi-variable systems:

  \begin{cases}
  x + y + z = 6 \\
  2x - y + z = 3 \\
  x + 2y - z = 2
  \end{cases}

4. Inequality Solving

Supports solving various inequalities (no need for solve() wrapper):

• Single-variable inequalities: 2x + 5 > 15
• Quadratic inequalities: x^2 - 4 \geq 0
• Inequality systems: x + 2 > 5, x - 3 < 10

5. Step-by-Step Solutions

Automatically returns detailed calculation process, for example:

Input: x^2 - 5x + 6 = 0
Step 1: Identified as a quadratic equation
Step 2: Using factorization method (x-2)(x-3) = 0
Step 3: Solutions found: x = 2 or x = 3
Result: x = 2, x = 3

Usage Examples

# Basic calculations (LaTeX format)
python3 scripts/calc.py "2 + 3 \	imes 4"                    # 14
python3 scripts/calc.py "(2 + 3) \	imes 4"                  # 20
python3 scripts/calc.py "\sqrt{144}"                        # 12
python3 scripts/calc.py "2^8"                               # 256
python3 scripts/calc.py "\frac{10}{2}"                      # 5

# Scientific calculations
python3 scripts/calc.py "\sin(\frac{\pi}{2})"               # 1.0
python3 scripts/calc.py "\log(1000)"                        # 3.0
python3 scripts/calc.py "5!"                                # 120

# Equation solving (direct input, no solve wrapper needed)
python3 scripts/calc.py "2x + 5 = 15"                       # Linear equation: x = 5
python3 scripts/calc.py "x^2 - 4 = 0"                       # Quadratic equation: x = -2, x = 2

# System of linear equations (two variables)
python3 scripts/calc.py "\\begin{cases} x + y = 10 \\\\ x - y = 2 \\end{cases}"              # x = 6, y = 4
python3 scripts/calc.py "\\begin{cases} 2x + 3y = 12 \\\\ x - y = 1 \\end{cases}"            # x = 3, y = 2

# System of linear equations (three variables)
python3 scripts/calc.py "\\begin{cases} x + y + z = 6 \\\\ 2x - y + z = 3 \\\\ x + 2y - z = 2 \\end{cases}"

# Inequality solving
python3 scripts/calc.py "2x + 5 > 15"                       # x > 5
python3 scripts/calc.py "x^2 - 4 \geq 0"                    # x ≤ -2 or x ≥ 2

# Specify language
python3 scripts/calc.py "2 + 3" zh
python3 scripts/calc.py "2 + 3" en

Features

• Supports complete LaTeX mathematical expressions
• Automatically records and displays calculation steps
• High-precision numerical calculations
• User-friendly error messages
• Multi-language output support

Notes

• LaTeX format input is required
• Equations and inequalities should be input directly, no solve() wrapper needed
• Trigonometric functions use radians by default
• Default variable for equation solving is x
• Inequality solutions are represented in interval notation