A lightweight, comprehensive C++ implementation of a Computer Algebra System with advanced mathematical capabilities.

Features

Core Functionality

Symbolic Expression Manipulation: Variables, constants, binary operations, functions
Polynomial Arithmetic: Addition, multiplication, division, GCD, factorization
Complex Number Operations: All basic operations plus advanced functions
Matrix Operations: Determinant, inverse, eigenvalues, decompositions
Calculus: Symbolic differentiation, numerical integration, series expansions
Transforms: Laplace transforms, Fourier transforms (DFT/FFT)
Differential Equations: ODE and PDE solvers
Numerical Methods: Root finding, optimization, interpolation

Advanced Features

Taylor and Chebyshev series expansions
Multiple integration methods (Trapezoidal, Simpson's, Gaussian quadrature, Monte Carlo)
Various ODE solvers (Euler, Runge-Kutta, Adams-Bashforth)
PDE solvers for heat, wave, and Laplace equations
Linear system solvers (Gaussian elimination, LU decomposition, iterative methods)
Statistical functions and regression analysis
Special functions (Gamma, Beta, Error, Bessel, Legendre, Hermite)

Building

Using Make

make

Using CMake

mkdir build
cd build
cmake ..
make

Usage

Run the executable:

./sokobo

Compile all:

g++ -std=c++23 -Wall -Wextra -O3 -Isource source/*.cpp -o sokobo

*

Unit Testing

Matrices

g++ -std=c++23 -Wall -Wextra -O3 -Itest -Isource -Isource/include test/matrix_test.cpp source/matrix.cpp source/complex_number.cpp -o matrix_test -lm

Example Commands

Polynomials

poly p1 1 2 3
poly p2 2 1
add p1 p2
mult p1 p2
deriv p1
roots p1
factor p1

Complex Numbers

complex c1 3 4
complex c2 1 -2
cadd c1 c2
cmult c1 c2
cpower c1 3
croots 8 3

Expressions and Calculus

expr f x^2+sin(x)
deriv f x
integral f x 0 1
series f 0 5
limit f 0

Matrices

matrix m1 3 3
matrix_raw m1 ([1,2],[3,4])
mset m1 0 0 5
mdet m1
minv m1
meigen m1
madj m1
mrank m1

Transforms

laplace f t
ilaplace F s
fourier signal
ifourier spectrum

Differential Equations

ode euler y'=x+y 0 1 0.1 10
ode rk4 y'=x+y 0 1 0.1 10
pde heat 1.0 1.0 1.0 50 50

Numerical Methods

root bisect f -1 1
root newton f df 1
optimize golden f -1 1
interpolate lagrange x_vals y_vals

Project Structure

sokobo/
├── include/
│   ├── expression.h
│   ├── polynomial.h
│   ├── complex_number.h
│   ├── matrix.h
│   ├── calculus.h
│   ├── laplace.h
│   ├── fourier.h
│   ├── differential_equations.h
│   ├── numerical_methods.h
│   └── cli.h
├── src/

Building and Installing

See BUILDING.md for detailed instructions.

Contributing

See CONTRIBUTING.md for guidelines.

License

Please choose an appropriate license (recommended: GNU AGPLv3).