Math Tools Agent Skill

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.

8k tokens

context cost

the whole folder, loaded on every use

files

ships runnable scripts

copies elsewhere

how many repositories repackaged it

2583

stars on the repo

on the repository, not the skill itself

Install

one command, takes just this skill from the repository

npx skills add https://github.com/foryourhealth111-pixel/Vibe-Skills --skill math-tools

What comes with it

25 518 bytes besides the instruction

references/api_reference.md

scripts/math_calculator.py

The instruction itself

15 sections, as written by the author

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

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How to use it

Copy the folder

Take foryourhealth111-pixel/math-tools from the repository into ~/.claude/skills for personal use, or into .claude/skills inside a project.

Check the name does not clash

The agent identifies a skill by the name field in its header. Two skills with the same name cannot sit side by side — one of them will be ignored.

Install what it needs

The instructions reference pip. Without those the skill loads but fails at the first command.