Math2.0: A Symbolic Math Engine

Math2.0 is a robust, modular C++ mathematical expression engine. It parses, evaluates, and symbolically manipulates complex mathematical expressions, correctly handling operator precedence, variables, and user-defined functions.

The project is built around a clean AST (Abstract Syntax Tree) and features a hybrid evaluation system: it first attempts numerical evaluation, and if it fails (e.g., due to undefined variables), it falls back to symbolic manipulation.

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Core Components

The engine is divided into five main modules:

• Lexer: A token generator that converts raw string input into a stream of tokens (Numbers, Symbols, Words, etc.).
• Parser: A recursive-descent parser that consumes tokens and builds an Abstract Syntax Tree (AST), correctly handling operator precedence, associativity, prefix/postfix operators, and implicit multiplication.
• Evaluator: A tree-walking evaluator that recursively calculates the numerical result of an AST.
• Simplifier: An algebraic simplifier that applies rules to an AST to reduce complexity (e.g., constant folding, x + x -> 2*x, x^0 -> 1).
• SymbolicEvaluator: Expands user-defined functions and variables within the AST, creating a new, expanded tree for further simplification or evaluation.

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Key Features

• Full Operator Support: Correctly handles precedence and associativity for +, -, *, /, ^ (power), and ! (factorial).
• Prefix/Postfix: Handles unary operators like -x and postfix operators like x!.
• Implicit Multiplication: Automatically detects and inserts multiplication (e.g., 2x, 2(x+y), (x+1)(y+2)).
• Variables: Supports variable assignment (x = 10) and built-in constants (pi, e).
• User-Defined Functions: Define and call your own functions (e.g., f(x) = x^2, g(x, y) = f(x) + f(y)).
• Hybrid Evaluation: The engine intelligently switches between numerical and symbolic processing.
• Detailed Error Reporting: Provides clear, user-friendly error messages that pinpoint the exact location and nature of any syntax error.

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Examples

The system can process a wide variety of inputs.

Mathematical Expression	Generated AST (Lisp Format)
2 + 3 * 4	14
(2 + 3) * 4	20
2x^3	(* 2 (^ x 3))
-sin(x+1)!	(- (! (sin (+ x 1))))
f(x) = x^2	(f (^ x 2))
g(y) = f(y) + 1	(g (+ (f y) 1))

Error Handling

When the parser encounters an invalid expression, it provides a detailed message:

Input: sin()

Error:

An expression was expected inside parentheses, but none was found.
--> at line 1:
    sin()
       ^-- Expected an expression after this parenthesis

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Build Instructions

The project uses a standard CMake setup.

# 1. Clone the repository
git clone [https://github.com/erhantrk/Math2.0](https://github.com/erhantrk/Math2.0)
cd math2.0

# 2. Create a build directory and enter it
mkdir build
cd build

# 3. Generate build files with CMake
cmake ..

# 4. Build the project
make

# 5. Run the main program or tests
./Math2.0

You can modify the sample expression in main.cpp to run your own tests.

Roadmap & Future Improvements

• Interactive Console (REPL): Provide a command‑line interface where users can enter expressions interactively.