Let's produce a simple document with LaTeX that incorporates typeset equations and graphics. This is a suitable starting point for a report, journal article, or homework assignment. First, let's make a plot of the Bessel function of the first kind for three values of n.
from matplotlib import pyplot as plt
import numpy
def J_n_numerical(n, x):
integrand(n1, x1, t) = cos(n1 * t - x1 * sin(t))
J_n = numpy.zeros(len(x))
for j in range(len(x)):
J_n[j] = 1 / pi.n() * integrand(n1=n, x1=x[j]).nintegrate(t, 0, pi)[0]
return J_n
n_values = [0, 1, 2]
x = numpy.arange(0.0, 10.0, 0.1)
plt.figure()
for n in n_values:
plt.plot(x, J_n_numerical(n, x), label='n=' + str(n))
plt.xlabel('x')
plt.ylabel('J(x)')
plt.legend(loc='upper right')
plt.savefig('J_n.pdf')
plt.close()The plot will be saved as a PDF file in the SAGE_TEMP directory, so you won't see the plot in your browser. Instead, you will see a link to the file. Click this link...