In Chapter 3, we learned how to define a mathematical function as a callable symbolic expression. Since we'll be working with callable symbolic expressions extensively in this chapter, let's learn a little more about how to use them. Enter the following code into an input cell in a worksheet, and evaluate the cell:
var('a, b, c, x')
f(x) = a * x^2 + b * x + c # A callable symbolic expression
print("f(x):")
f.show()
print("Variables in f: {0} Arguments in f: {1}".format(
f.variables(), f.arguments()))
print("Type of f: {0}".format(type(f)))
g(x) = f.derivative(x)
print("g(x):")
g.show()
print("Variables in g: {0} Arguments in g: {1}".format(
g.variables(), g.arguments()))
g_plot = plot(g(a=1, b=-1), (-1, 1))
g_plot.axes_labels(['x', 'g(x)'])
show(g_plot, figsize=(3,3), aspect_ratio=1.0)The output is shown below:
