Let's now define the expression for the function we want to compute by running the following code in a Jupyter cell:

r, theta = symbols('r, theta')
x = r * cos(theta)
y = r * sin(theta)
x, y

In the first line in this code, we define the symbols r and theta. A symbol in sympy is used to represent the name of a mathematical variable.

Next, with the x = r * cos(theta) and y = r * sin(theta) assignments, we define two sympy expressions, x and y.

The last line in the cell, x,y, will print the x and y expressions in pretty format, according to the usual rules for typesetting mathematics.

The reader may have noticed that the preceding expressions compute the Cartesian coordinates for a point expressed in polar coordinates.

One weakness of symbolic code is that it tends to produce slow code, but sympy has a neat solution to this problem. We can create a NumPy ufunc from a set of sympy expressions, as follows:

polar_to_rectangular = lambdify((r, theta), (x, y), modules='numpy')