infnum

infnum is a Python library that provides infinite and infinitesimal numbers using the Levi-Civita Field. It uses JAX under the hood.

Installation

You can install infnum via pip:

pip install infnum

Usage

Creating Levi-Civita Numbers

The main constructor expects a dictionary with numerical keys and values. The keys represent the exponents and the values the coefficients. In the following example, note that ε⁻³ is an infinite number.

from infnum import LeviCivitaNumber

# Create a Levi-Civita number from a real number
num = LeviCivitaNumber.from_number(5.0) # 5.0
print(num)  # Output: 5.0
# Create a Levi-Civita number with infinitesimal parts
num = LeviCivitaNumber({0: 1.0, 1: 2.0, 2: 3.0, -3: 4.0}) # -4.0ε⁻³ + 1.0 + 2.0ε + 3.0ε² 
print(num)  # Output: -4.0ε⁻³ + 1.0 + 2.0ε + 3.0ε² 

Operations

Levi-Civita numbers support arithmetic operations like addition, subtraction, multiplication, and division. Division is truncated to 8 terms by default since it may result in an infinite series, but the higher terms are infinitesimal with respect to the lower terms.

You may compare Levi-Civita numbers using the <, <=, >, >=, ==, != operators, which considers the lexicographical order of the coefficients.

Testing

Levi-Civita numbers come with unit tests to ensure correctness. You can run the tests using:

python -m unittest discover tests

Contributing

Contributions are welcome! Please feel free to submit a Pull Request.

License

This project is licensed under the Apache 2 License.

TODO

• add complex number support
• support non-integer powers for non-pure terms