sympy

When to use it

Use this skill when:

• Solving equations symbolically (algebraic, differential, systems of equations)
• Performing calculus operations (derivatives, integrals, limits, series)
• Manipulating and simplifying algebraic expressions
• Working with matrices and linear algebra symbolically
• Doing physics calculations (mechanics, quantum mechanics, vector analysis)
• Number theory computations (primes, factorization, modular arithmetic)
• Geometric calculations (2D/3D geometry, analytic geometry)
• Converting mathematical expressions to executable code (Python, C, Fortran)
• Generating LaTeX or other formatted mathematical output
• Needing exact mathematical results (e.g., sqrt(2) not 1.414...)

Mistakes to avoid

1. "NameError: name 'x' is not defined"

• Solution: Always define symbols using symbols() before use

1. Unexpected numerical results

• Issue: Using floating-point numbers like 0.5 instead of Rational(1, 2)
• Solution: Use Rational() or S() for exact arithmetic

1. Slow performance in loops

• Issue: Using subs() and evalf() repeatedly
• Solution: Use lambdify() to create a fast numerical function

1. "Can't solve this equation"

• Try different solvers: solve, solveset, nsolve (numerical)
• Check if the equation is solvable algebraically
• Use numerical methods if no closed-form solution exists

1. Simplification not working as expected

• Try different simplification functions: simplify, factor, expand, trigsimp
• Add assumptions to symbols (e.g., positive=True)
• Use simplify(expr, force=True) for aggressive simplification