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
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

bash

# 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:

bash

# 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:

bash

pip install sympy