Sympy Math

SymPy Mathematics Skill

Symbolic mathematics: algebra, calculus, equation solving, and LaTeX output.

When to Use

• "Solve this equation symbolically"
• "Differentiate/integrate this expression"
• "Simplify this algebraic expression"
• "Convert to LaTeX"
• Symbolic matrix operations
• Solving ODEs/PDEs symbolically

When NOT to Use

• Numerical computation (use scipy-analysis)
• Statistical analysis (use statsmodels-stats)
• Data visualization (use matplotlib-viz)

Setup

uv pip install sympy

Common Commands

Algebra

python3 -c "
from sympy import *
x, y = symbols('x y')
print('Expanded:', expand((x + y)**3))
print('Factored:', factor(x**3 - 1))
print('Simplified:', simplify((x**2 - 1)/(x - 1)))
"

Calculus

python3 -c "
from sympy import *
x = symbols('x')
f = sin(x) * exp(-x)
print('Derivative:', diff(f, x))
print('Integral:', integrate(f, x))
print('Definite:', integrate(f, (x, 0, oo)))
print('Limit:', limit(sin(x)/x, x, 0))
print('Series:', series(exp(x), x, 0, 5))
"

Equation Solving

python3 -c "
from sympy import *
x, y = symbols('x y')
print(solve(x**2 - 5*x + 6, x))
print(solve([x + y - 5, x - y - 1], [x, y]))
y = Function('y')
t = symbols('t')
print(dsolve(y(t).diff(t, 2) + y(t), y(t)))
"

Linear Algebra

python3 -c "
from sympy import *
M = Matrix([[1, 2], [3, 4]])
print('Det:', M.det())
print('Inverse:', M.inv())
print('Eigenvals:', M.eigenvals())
print('RREF:', M.rref())
"

LaTeX Output

python3 -c "
from sympy import *
x = symbols('x')
expr = Integral(exp(-x**2), (x, -oo, oo))
print(latex(expr))
print(latex(expr.doit()))
"

Notes

• Operates symbolically, not numerically
• Use N(expr) or expr.evalf() for numerical evaluation
• Supports assumptions: x = symbols('x', positive=True)
• For numerical work, use scipy/numpy instead