What are some examples of using SymPy for symbolic mathematics?

Can you show me some examples of using SymPy for symbolic mathematics?

Sure! SymPy is a powerful library for symbolic mathematics in Python. What specific examples are you interested in?

I'd like to see how to solve equations and simplify expressions.

Great! To solve an equation, you can use sympy.solve(). For example, to solve x**2 - 4 = 0, you would do:

from sympy import symbols, solve
x = symbols('x')
equation = x**2 - 4
solution = solve(equation, x)
print(solution)

This will give you the solutions for x.

What about simplifying expressions?

To simplify an expression, you can use sympy.simplify(). For instance:

from sympy import simplify
expr = (x**2 - 4)/(x - 2)
simplified_expr = simplify(expr)
print(simplified_expr)

This will simplify the expression to x + 2.

Can you explain how to differentiate functions using SymPy?

Absolutely! You can differentiate functions using sympy.diff(). For example:

from sympy import diff
f = x**2 + 3*x + 2
derivative = diff(f, x)
print(derivative)

This will give you the derivative of the function.