Solving equations and inequalities

SymPy offers several ways to solve linear and nonlinear equations and systems of equations. Of course, these functions do not always succeed in finding closed-form exact solutions. In this case, we can fall back to numerical solvers and obtain approximate solutions.

How to do it...

1. Let's define a few symbols:

   >>> from sympy import *
       init_printing()
   >>> var('x y z a')

   
2. We use the solve() function to solve equations (the right-hand side is 0 by default):

   >>> solve(x**2 - a, x)

   
3. We can also solve inequalities. Here, we need to use the solve_univariate_inequality() function to solve this univariate inequality in the real domain:

   >>> x = Symbol('x')
       solve_univariate_inequality(x**2 > 4, x)

   
4. The solve() function also accepts systems of equations (here, a linear system):

   >>> solve([x + 2*y + 1, x - 3*y - 2], x, y)

   
5. Nonlinear systems are also handled:

   >>> solve([x**2 + y**2 - 1, x**2 -...