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