Mathematical Expression Evaluation and Differentiation Using LR Parser

This project implements a system for evaluating mathematical expressions and computing their derivatives. It leverages a custom-built LR parser to process expressions, and it supports a wide range of mathematical operations, including basic arithmetic, trigonometric functions, exponentiation, and logarithms.

Features

• Evaluation: The program evaluates mathematical expressions given as strings, including support for variables (e.g., X).
• Differentiation: It computes the derivative of the expression by constructing and traversing an operation tree.
• Python and Haskell Implementations: The project is implemented in both Python and Haskell, demonstrating flexibility across programming languages.
• Tree Visualization: In the Python version, the operation tree used for differentiation can be visualized using Graphviz.

Grammar

The LR parser is built using the following context-free grammar:

E  -> E + T
    | E - T
    | T

T  -> T * F
    | T / F
    | F

F  -> G ^ F
    | G

G  -> ( E )
    | - G
    | Func ( E )
    | NUMBER
    | X

Func -> sin
     | cos
     | tg
     | arcsin
     | arccos
     | arctg
     | exp
     | ln

This grammar allows the parser to recognize and process a wide variety of mathematical expressions.

Usage

Python

1. Evaluation and Differentiation:

   • The main functionality is encapsulated in the Eval and Diff using LR Parser.py file.
   • The script evaluates the expression and computes its derivative, printing the results to the console.

2. Tree Visualization:

   • The tree_vizualize_functions.py file contains functions to convert the operation tree into a .png file using Graphviz.
   • you will need to add them in order to work.

Haskell

• The Haskell implementation is available in the Eval_and_Diff_using_LR_Parser.hs file.
• It provides similar functionality for evaluating expressions and computing derivatives.

Example

Given the expression:

X^7 + sin(X) - ln(X^2)

The program will:

1. Evaluate the expression for a given value of X.
2. Compute and display the derivative of the expression.
3. (Python) Visualize the operation tree for the expression.

Comparison with Existing Solutions

The Python implementation includes a comparison against traditional evaluation and differentiation methods (e.g., using Python's eval and SymPy).

Acknowledgments

• Graphviz for tree visualization.
• SymPy for symbolic computation in Python.