sokobo - Computational Algebra System (CAS)

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        # Define p1 = 1 + 2x + 3x²
poly p2 2 1          # Define p2 = 2 + x
add p1 p2            # Add polynomials
mult p1 p2           # Multiply polynomials
deriv p1             # Derivative of p1
roots p1             # Find roots of p1
factor p1            # Factor polynomial

Complex Numbers

complex c1 3 4       # Define c1 = 3 + 4i
complex c2 1 -2      # Define c2 = 1 - 2i
cadd c1 c2           # Add complex numbers
cmult c1 c2          # Multiply complex numbers
cpower c1 3          # c1^3
croots 8 3           # 3rd roots of unity

Expressions and Calculus

expr f x^2+sin(x)    # Define expression f = x² + sin(x)
deriv f x            # Derivative of f with respect to x
integral f x 0 1     # Integrate f from 0 to 1
series f 0 5         # Taylor series of f around 0, degree 5
limit f 0            # Limit of f as x approaches 0

Matrices

matrix m1 3 3                   # Create 3x3 matrix m1
matrix_raw m1 ([1,2],[3,4])     # Create 2x2 matrix m1 from a raw input
mset m1 0 0 5                   # Set m1[0][0] = 5
mdet m1                         # Determinant of m1
minv m1                         # Inverse of m1
meigen m1                       # Eigenvalues of m1
madj m1                         # Adjoint matrix of m1
mrank m1                        # Rank matrix of m1

Transforms

laplace f t          # Laplace transform of f(t)
ilaplace F s         # Inverse Laplace transform of F(s)
fourier signal       # Fourier transform of signal
ifourier spectrum    # Inverse Fourier transform

Differential Equations

ode euler y'=x+y 0 1 0.1 10    # Solve y'=x+y using Euler method
ode rk4 y'=x+y 0 1 0.1 10      # Solve using Runge-Kutta 4th order
pde heat 1.0 1.0 1.0 50 50     # Solve 1D heat equation

Numerical Methods

root bisect f -1 1             # Find root using bisection method
root newton f df 1             # Find root using Newton-Raphson
optimize golden f -1 1         # Find minimum using golden section
interpolate lagrange x_vals y_vals  # Lagrange interpolation

Project Structure

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

Building and installing

See the BUILDING document.

Contributing

See the CONTRIBUTING document.

Licensing