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 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

# 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

xiaoyuan-calc

Installation