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