Today's Challenge

Manipulating expressions in SymPy at an advanced level necessitates familiarity with how these expressions are internally structured, specifically in the form of expression trees. Visualizing this structure can be extremely beneficial. Today, we will create a specific SymPy expression and illustrate its internal representation as a graph.

To begin, let's define the expression:

Next, we will visualize how this expression is represented internally.

Solution Steps

Creating the expression itself is relatively straightforward. We start by defining the necessary symbols and then construct the expression:

We can also represent the internal structure of the expression as a string using SymPy’s srepr function:

As you can see, the internal representation can appear quite complex. This is where visualization becomes useful. We will create a graph to make this representation clearer. To achieve this, we will write a function that extracts the nodes, and then utilize the networkx package to generate the graph. If you haven't installed networkx, you can do so by running pip install networkx.

Once you have the function code ready, you can implement it as shown here:

The majority of the plot_graph function consists of organizational elements. We define several helper classes for node representation, but the crux of the function is the _walk method, which traverses the expression recursively, creating nodes and establishing connections between them. This data is stored in JSON format, which networkx can interpret, allowing us to use its Graphviz layout function to depict the graph as a tree structure.

If you're not particularly interested in the intricacies of the code, that's perfectly fine. However, having a visualization function like this in your programming toolkit can be incredibly advantageous, so I recommend saving the code for your future use.