Using Sympy Equations for Plotting

Question

What is the best way to create a Sympy equation, do something like take the derivative, and then plot the results of that equation?

I have my symbolic equation, but can't figure out how to make an array of values for plotting. Here's my code:

from sympy import symbols
import matplotlib.pyplot as mpl

t = symbols('t')
x = 0.05*t + 0.2/((t - 5)**2 + 2)

nums = []
for i in range(1000):
    nums.append(t)
    t += 0.02

plotted = [x for t in nums]

mpl.plot(plotted)
mpl.ylabel("Speed")
mpl.show()

In my case I just calculated the derivative of that equation, and now I want to plot the speed x, so this is fairly simplified.

Solution 1

You can use numpy.linspace() to create the values of the x axis (x_vals in the code below) and lambdify().

from sympy import symbols
from numpy import linspace
from sympy import lambdify
import matplotlib.pyplot as mpl

t = symbols('t')
x = 0.05*t + 0.2/((t - 5)**2 + 2)
lam_x = lambdify(t, x, modules=['numpy'])

x_vals = linspace(0, 10, 100)
y_vals = lam_x(x_vals)

mpl.plot(x_vals, y_vals)
mpl.ylabel("Speed")
mpl.show()

_{(improvements suggested by asmeurer and MaxNoe)}

Alternatively, you can use sympy's plot():

from sympy import symbols
from sympy import plot

t = symbols('t')
x = 0.05*t + 0.2/((t - 5)**2 + 2)

plot(x, (t, 0, 10), ylabel='Speed')

Solution 2

Using SymPy

You can use directly the plotting functions of SymPy:

from sympy import symbols
from sympy.plotting import plot as symplot

t = symbols('t')
x = 0.05*t + 0.2/((t - 5)**2 + 2)
symplot(x)

Most of the time it uses matplotlib as a backend.