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"

→ x3 + 3x2 + 3x + 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 "(x2 + 1)/(x2 - 1)" x oo

→ 1

Taylor series

python scripts/math_calculator.py series "exp(x)" x 0 5

→ 1 + x + x2/2 + x3/6 + x4/24 + O(x5)

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" "x2 + 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