Symbolic Math DSL with C++20

A compile-time symbolic algebra library implemented in modern C++20 using template metaprogramming. This project provides a zero-overhead symbolic math DSL that models algebraic expressions with full compile-time evaluation, formatting, and simplification support. Designed with extensibility and clarity in mind, it is inspired by expression template techniques in libraries like Eigen.

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🚀 Features

• Compile-Time Evaluation: Symbolic expressions are evaluated entirely at compile time using constexpr techniques.
• Expression Simplification: Includes simplification rules such as: (Have to be implemented)
  • x + x → 2 * x
  • a * x + b * x → (a + b) * x (already implemented)
• CRTP-Based Expression Hierarchy: All expressions inherit from ExpressionBase<Derived> for zero-cost polymorphism.
• Uniform Representation: All expressions normalized as Scaled<Coeff, Expr> to simplify folding, evaluation, and transformation.
• Algebraic Operators: Natural support for +, -, *, variadic Add, and Multiplication with correct operator precedence.
• Tuple-Based Internal Storage: Variadic expressions internally stored in std::tuple and manipulated via std::apply.
• Fully Header-Only: Just include the headers and use the DSL in your project.

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📂 Directory Structure

Symbolic_Math_DSL_with_Cpp20/
├── include/
│   ├── expressions.hpp   # Core DSL types and operators
│   ├── concepts.hpp      # Concepts for constraining symbolic types
│   └── utility.hpp       # Formatting and type utilities
├── tests/
│   └── test.cpp          # Catch2 unit tests
├── CMakeLists.txt        # Build file for tests (Catch2)
└── README.md             # This file

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🔧 Example Usage

#include "expressions.hpp"
using namespace math_dsl;

constexpr Variable<'x'> x;
constexpr Variable<'y'> y;
constexpr Scalar<2> two;

constexpr auto expr = x * (y + two);
static_assert(expr.eval(Input<InputPair<'x', 3>, InputPair<'y', 5>>{}) == 21);

std::cout << expr.expr(); // prints: (x*y + 2x)

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🧪 Building and Testing

This project uses Catch2 for unit testing.

git clone https://github.com/basava70/Symbolic_Math_DSL_with_Cpp20.git
cd Symbolic_Math_DSL_with_Cpp20
mkdir build && cd build
cmake ..
make
./check.sh
./run.sh

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✅ Planned Features

• Division operator / support
• Exponentiation (e.g., x^n)
• Symbolic logarithms (e.g., log(x))
• Symbolic differentiation (d/dx support)

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📜 License

This project is licensed under the MIT License. See the LICENSE file for details.

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