Version 0.0.4 - Introduce Zeta Coefficients for Number Fields with Examples and Tests

Description:

This is the fourth release of the modular_forms library (v0.0.4-pre-alpha), introducing the computation of Zeta Coefficients for Number Fields, along with corresponding examples and tests. This release keeps adding cool math features and comes with the tests it needs to work smoothly.

Key Updates:

• New Functionality: Added zeta_coeffs_deg2 method to compute Dedekind zeta function coefficients for quadratic number fields using Dirichlet character groups.

• Examples: Incorporated new examples demonstrating usage of the zeta coefficients in various number field contexts.

• Testing: Added comprehensive unit tests validating the correctness of the zeta coefficient computations.

• Documentation: Updated README and code comments to reflect new features and usage patterns.

Testing:

All new features are covered by unit tests ensuring mathematical accuracy and integration within the modular_forms framework.

Notes:

This release remains in pre-alpha stage. While the new functionality is stable for experimentation and research, APIs and implementations may evolve based on further mathematical insights and user feedback.

Version 0.0.3 - Introduction of p-adic Fields and Enhancements to README, Examples, and Tests

Description:

This is the third release of the modular_forms library (v0.0.3-pre-alpha), introducing p-adic field support, improved documentation, and enhanced test coverage. It continues to refine core functionality while expanding the creative and mathematical scope of the project.

Key Updates:

• New Module: Support for p-adic fields, including padic_valuation, padic_norm, and related definitions.

• New Example Added: A fresh Sonic Pi piece titled "Merging Machine and Organism – Warp Up" explores abstract musical mappings beyond the structured Fermat sonification.

• Enhanced README: Usage instructions and project status sections have been reorganized and clarified.

Testing

All new features are covered by unit and integration tests. These validate the mathematical computations and their sonic representations within Sonic Pi, supporting stable creative experimentation.

Notes

This is still a pre-alpha development release. While it is suitable for creative exploration and educational use, APIs and features may evolve based on user feedback and future goals.

Version 0.0.2 - Introduction of L-function and Enhancements to README, Examples, and Tests

Description:

This is the second release of the modular_forms library, introducing the L-function and further refining the core functionality. This version also includes updates to the README and more comprehensive examples, along with additional tests to ensure the stability and correctness of the library.

Key Features:

• New Module: L-functions added to expand the library's capabilities for modular forms and elliptic curve computations.
• Enhanced README with clearer instructions and additional examples to help users get started.
• Minor improvements.

Testing and Quality Assurance:

The new L-function has been thoroughly tested, and integration tests have been added to verify its correctness.

Notes:

As a development release, this version is more feature-complete but may still undergo changes as the library evolves. It is suitable for users interested in exploring modular forms, elliptic curves, and the newly introduced L-function module.

Version 0.0.1-pre-alpha - Initial Release: Exploring Modular Forms and Elliptic Curves with Sonic Pi

Description:

This is the first pre-alpha release of the modular_forms library, a creative toolkit for exploring modular forms and elliptic curves, with a focus on interactivity through Sonic Pi.

Purpose and Scope:

Given the vastness of number theory, this library intentionally focuses on a subset of key definitions and computations without attempting to cover every aspect in full. Below are the primary modules currently implemented:

• Eisenstein Series
• Eta Functions and Eta Quotients
• Theta Functions
• Ramanujan Tau Function
• J-Function
• Hecke Operators
• SL(2, Z) Group
• Dirichlet Characters
• Elliptic Curves (Rationals & Finite Fields)
• Newforms Invariants

Testing and Quality Assurance:

All core modules in this release are accompanied by integration tests, ensuring that the fundamental computations and functions are working as expected. The tests are designed to verify the correctness of the methods, and to provide early feedback on potential issues as development progresses.

Notes:

This version is meant for early-stage exploration and development. It is not feature-complete and may undergo significant changes in future updates. This release is best suited for users interested in the core functionality of the library and its foundational mathematical concepts.