xiaoyuan-calc

# 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!** ```bash python3 <skill-path>/scripts/calc.py "<LaTeX expression>" [language] ``` ### LaTeX Format Guide - Multiplication: Use `\times` or `\cdot`, e.g., `3 \times 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`, `\tan`, etc. - Inequality symbols: `\geq`, `\leq`, `>`, `<` - Greek letters: `\pi`, `\theta`, `\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: `+`, `-`, `\times`, `\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)`, `\tan(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 ```bash # Basic calculations (LaTeX format) python3 scripts/calc.py "2 + 3 \times 4" # 14 python3 scripts/calc.py "(2 + 3) \times 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