This program is the second version of a program I made a few years ago during covid. I am going back and redoing the script with better programming practices. The program is split up into the following sections:
The inp7ut string is taken within the main function and passed to tokenize.cpp. This parses the input string into tokens defined by token.hpp. It also uses a multi-way trie to lookup functions in a defined lookup table
The parsed output is passed in a token container and passed to postfix.cpp, where I have implemented a shunting yard algorithm that I have adapted to take in functions and variables.
The postfixed expression is then formed into a binary expression tree (expression_tree.cpp) of expression nodes (expression_nodes.cpp). This makes the expression easier to traverse and modify.
The derivative is taken from the expression tree, using an automatic differentiation algorithm. If steps are requested, we use derivative rules taught in calc 1 as well as a generalized power rule to create a new tree.