The Math Tools skill is a high-performance deterministic computation engine powered by SymPy, designed to provide 100% mathematical accuracy. By leveraging symbolic computation instead of LLM estimation, it enables Claude to solve complex algebraic equations, perform advanced calculus, and handle linear algebra with verified precision, making it an essential tool for scientific research and technical analysis.

When should I use math-tools?

math-tools is useful in the following scenarios: • 1. Advanced Symbolic Calculus: Perform exact derivatives, integrals, limits, and Taylor series expansions for academic research and physics modeling. • 2. Complex Algebraic Manipulation: Simplify, expand, and factor intricate algebraic expressions or solve systems of equations without rounding errors. • 3. Linear Algebra & Matrix Operations: Calculate determinants, eigenvalues, and inverses for high-dimensional matrices used in data science and engineering. • 4. Number Theory & Cryptography: Conduct primality testing, prime factorization, and GCD/LCM calculations for cryptographic verification and mathematical proofs. • 5. Verified Statistical Reporting: Compute precise mean, variance, and standard deviation for datasets, ensuring results are mathematically sound for formal reports.

name	math-tools
description	Deterministic mathematical computation using SymPy. Use for ANY math operation requiring exact/verified results - basic arithmetic, algebra (simplify, expand, factor, solve equations), calculus (derivatives, integrals, limits, series), linear algebra (matrices, determinants, eigenvalues), trigonometry, number theory (primes, GCD/LCM, factorization), and statistics. Ensures mathematical accuracy by using symbolic computation rather than LLM estimation.

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:

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

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

Core Operations

Arithmetic

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

# 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

# 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

# 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

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

python scripts/math_calculator.py mean '[1,2,3,4,5]'      # 3
python scripts/math_calculator.py variance '[1,2,3,4,5]'  # 2
python scripts/math_calculator.py std_dev '[1,2,3,4,5]'   # sqrt(2)

Utilities

# Numerical evaluation with precision
python scripts/math_calculator.py evaluate "pi" 50

# LaTeX output
python scripts/math_calculator.py latex "x**2 + 1/x"
# → x^{2} + \frac{1}{x}

# Compare expressions
python scripts/math_calculator.py compare "(x+1)**2" "x**2 + 2*x + 1"
# → equal: true

Expression Syntax

Powers: x**2 or x^2
Multiplication: 2*x or 2x (implicit)
Functions: sin(x), cos(x), exp(x), log(x), sqrt(x)
Constants: pi, E, I (imaginary), oo (infinity)

Complex Operations (JSON Input)

For operations requiring structured input:

# Solve system of equations
python scripts/math_calculator.py solve_system \
  '{"equations": ["x + y = 10", "x - y = 2"], "variables": ["x", "y"]}'

# Substitute values
python scripts/math_calculator.py substitute \
  '{"expr_str": "x**2 + y", "substitutions": {"x": 3, "y": 2}}'

# Matrix multiplication
python scripts/math_calculator.py matrix_mult \
  '{"matrix_a": [[1,2],[3,4]], "matrix_b": [[5,6],[7,8]]}'

Full API Reference

See references/api_reference.md for complete documentation of all operations, including:

All operation names and aliases
Detailed parameter descriptions
Output format specifications
Additional examples

Dependencies

Requires SymPy:

pip install sympy

math-tools

When & Why to Use This Skill

Use Cases