math-tools

Files (3)

• SKILL.md
• api_reference.md · references/
• math_calculator.py · scripts/

SKILL.md (first lines)

# Math Tools

Deterministic mathematical computation engine using SymPy. All calculations use symbolic math - no LLM estimation.

## When to Use

Use this skill whenever mathematical accuracy matters:
- Arithmetic involving fractions, roots, or large numbers
- Algebraic simplification, expansion, factoring
- Solving equations (polynomial, transcendental, systems)
- Calculus (derivatives, integrals, limits, series)
- Linear algebra (matrices, eigenvalues, determinants)
- Number theory (primes, factorization, GCD/LCM)
- Statistical calculations

## Quick Start

Run the calculator script with operation and arguments:

```bash
python scripts/math_calculator.py <operation> <args...>
```

All results return JSON with `result`, `latex`, and `numeric` fields.

## Core Operations

### Arithmetic
```bash
python scripts/math_calculator.py add 5 3 2          # 10
python scripts/math_calculator.py multiply 2 3 4    # 24
python scripts/math_calculator.py divide 10 4       # 5/2 (exact)
python scripts/math_calculator.py sqrt 8            # 2*sqrt(2)
python scripts/math_calculator.py factorial 10      # 3628800
```

### Algebra
```bash
# Simplify
python scripts/math_calculator.py simplify "(x**2 - 1)/(x - 1)"
# → x + 1

# Expand
python scripts/math_calculator.py expand "(x + 1)**3"
# → x**3 + 3*x**2 + 3*x + 1

# Factor
python scripts/math_calculator.py factor "x**3 - 8"
# → (x - 2)*(x**2 + 2*x + 4)

# Solve equations
python scripts/math_calculator.py solve "x**2 - 5*x + 6" x
# → [2, 3]

python scripts/math_calculator.py solve "2*x + 3 = 7" x
# → [2]
```

### Calculus
```bash
# Derivative
python scripts/math_calculator.py derivative "x**3 + sin(x)" x
# → 3*x**2 + cos(x)

# Second derivative
python scripts/math_calculator.py derivative "x**4" x 2
# → 12*x**2

# Indefinite integral
python scripts/math_calculator.py integrate "x**2" x
# → x**3/3

# Definite integral
python scripts/math_calculator.py integrate "x**2" x 0 1
# → 1/3

# Limit
python scripts/math_calculator.py limit "sin(x)/x" x 0
# → 1

# Limit at infinity
python scripts/math_calculator.py limit "(x**2 + 1)/(x**2 - 1)" x oo
# → 1

# Taylor series
python scripts/math_calculator.py series "exp(x)" x 0 5
# → 1 + x + x**2/2 + x**3/6 + x**4/24 + O(x**5)
```

### Linear Algebra
```bash
# Determinant
python scripts/math_calculator.py det '[[1,2],[3,4]]'
# → -2

# Inverse
python scripts/math_calculator.py inverse '[[1,2],[3,4]]'

# Eigenvalues
python scripts/math_calculator.py eigenvalues '[[4,2],[1,3]]'
# → {5: 1, 2: 1}

# RREF
python scripts/math_calculator.py rref '[[1,2,3],[4,5,6]]'
```

### Number Theory
```bash
python scripts/math_calculator.py gcd 24 36 48       # 12
python scripts/math_calculator.py lcm 4 6 8         # 24
python scripts/math_calculator.py prime_factors 360  # 2^3 × 3^2 × 5
python scripts/math_calculator.py is_prime 17       # true
python scripts/math_calculator.py nth_prime 100     # 541
python scripts/math_calculator.py binomial 10 3     # 120
```

### Statistics
```bash
python scripts/math_calculator.py mean '[1,2,3,4,5]'      # 3

From foryourhealth111-pixel/Vibe-Skills, Apache-2.0.

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