FriCAS seriesSolve Replication

A Python implementation replicating the power series differential equation solving functionality of FriCAS's seriesSolve function, built on top of SymPy.

Overview

This project provides tools for solving ordinary differential equations using power series methods, similar to the capabilities found in the FriCAS computer algebra system. The implementation focuses on finding series solutions around specified points with given initial conditions.

Features

Solve first and higher-order ordinary differential equations
Power series expansion around arbitrary points
Support for initial value problems
Integration with SymPy's symbolic computation capabilities
Educational examples demonstrating various ODE types

Installation

Prerequisites

Python 3.7+
SymPy

Setup

git clone https://github.com/Foadsf/fricas-seriessolve
cd fricas_seriessolve
pip install sympy

Usage

Basic Example

from seriessolve import solve_ode_series
import sympy as sp

x = sp.symbols('x')
y = sp.Function('y')

# Solve dy/dx + y = 0 with y(0) = 1
equation = sp.Eq(sp.diff(y(x), x) + y(x), 0)
solution = solve_ode_series(equation, y(x), x, 0, [1], precision=10)
print(solution)

Running Examples

python examples/000_basic_ode.py

Project Structure

fricas_seriessolve/
├── seriessolve.py          # Main library implementation
├── examples/               # Example scripts
│   └── 000_basic_ode.py   # Basic ODE examples
├── README.md              # This file
├── lessons_learned.md     # Development notes and lessons
└── .gitignore            # Git ignore patterns

Examples Included

Exponential Decay: First-order linear ODE
Harmonic Oscillator: Second-order ODE with cosine solution
Sine Solution: Harmonic oscillator with different initial conditions
Airy's Equation: Advanced example showing current limitations

Current Limitations

Airy's equation and similar cases require enhancement of the undetermined coefficients method
Complex differential equations may not always reduce to simple polynomial series
Limited to ODEs that SymPy can handle or simple recurrence relations

Contributing

This project is educational and focuses on replicating FriCAS functionality. Contributions should maintain compatibility with the original FriCAS seriesSolve behavior.

License

This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/4.0/ or send a letter to Creative Commons, PO Box 1866, Mountain View, CA 94042, USA.

Acknowledgments

FriCAS computer algebra system for the original seriesSolve implementation
SymPy project for providing the symbolic computation foundation