scikit-complexity

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Package
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Introduction

A Python package to create and simulate complex systems.

Prerequisites

Either sagemath-standard or an installation of SageMath is required with a version greater than 10.0.

Installation

Initially, create a Python virtual environment with one of the following two ways:

• Use the command sage -python -m venv --system-site-packages .venv to create and activate Python virtual environment with all the prerequisites installed:

• Use one of the standard ways to create a Python virtual environment and install the package sagemath-standard.

You can install scikit-complexity either as a normal user or for development purposes.

User

For user installation, scikit-complexity is currently available on the PyPi's repository, and you can install it via pip:

pip install scikit-complexity

Development

Development installation requires to clone the repository and change directory to the project's root:

git clone https://github.com/georgedouzas/scikit-complexity.git
cd scikit-complexity

Finally, use PDM to select the virtual environment and install the project as well as the main and development dependencies:

pdm use .venv
pdm install

Usage

One of the scikit-complexity main goals is to provide a unified interface for modelling various complex systems. For example, let's define two independent harmonic oscillators that oscillate in the axes x and y:

from sage.all import assume, symbolic_expression, var, cos, sin, sqrt
from skcomplex.physics import (
    ClassicalMechanicsSystem,
    ExternalForce,
    PointParticle,
)
from skcomplex.spaces import EuclideanSpace
k, x__1, y__2 = var('k x__1 y__2')
assume(k > 0)
system = ClassicalMechanicsSystem(
    particles=[PointParticle('1'), PointParticle('2')],
    external_interactions=[
        ExternalForce('elastic1', '1', [-k * x__1, 0]),
        ExternalForce('elastic2', '2', [0, -k * y__2])
    ],
    space=EuclideanSpace('euclidean', n_dim=2),
)

We can simulate the system and solve the dynamical equations:

system.simulate()
var('_K1 _K2 m__1 m__2 t')
assert system.simulation_results_['dynamic_equations']['solutions'] == {
    '1': [_K2*cos(sqrt(k)*t/sqrt(m__1)) + _K1*sin(sqrt(k)*t/sqrt(m__1)), _K2*t + _K1],
    '2': [_K2*t + _K1, _K2*cos(sqrt(k)*t/sqrt(m__2)) + _K1*sin(sqrt(k)*t/sqrt(m__2))]
}