Solving Equations
In this lesson, we will learn about solving different types of equations numerically and symbolically.
SymPy has equation solvers that can handle linear and non-linear algebraic equations as well as linear and non-linear multivariate equations. Depending upon the input equation, the answer returned can be symbolic or numeric. The most commonly used one is solve(). It uses the following syntax:
solve(f(x), x)
The output type of solve() varies with input, sometimes it returns a Python list and sometimes a Python dictionary. Usually, for single variable equations, it returns a list and for multivariable equations, it returns a dictionary.
Let’s explore different cases in the examples below:
Solving for a single variable
Single solution
Let’s solve the following equation that has a single solution:
from sympy import *def f(x):return 2*x + 3x = Symbol('x')sol = solve(f(x), x)print(sol)
The solve() function returns a list with the only solution.
Multiple solutions
Let’s solve the following equation, which has multiple solutions:
from sympy import *def f(x):return x**2 - x - 6x = Symbol('x')sol = solve(f(x), x)print(sol)
The solve() function returns a list with all the solutions. Let’s solve an equation with complex roots:
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