Proposal: "gfun-Style Interface for Recurrences/ODEs"

[Vishal Shahi]

## [t: enhancement] [c: algebra] Implement gfun-style interface for recurrence/ODE tools and document equivalence with Maple

## Overview
Hello SageMath Community,

I’m preparing a GitHub issue to enhance SageMath’s support for recurrences and differential equations by creating a unified interface that mirrors Maple’s gfun library.

## Key Proposal
- **Scope:**  
  Unify `ore_algebra`, `rec_sequences`, and FLINT under a standardized API.
- **Enhancements:**  
  - Add missing gfun functions (e.g., `listtoalgeq`, `rectoproc`).
  - Improve boundary condition handling.
- **Documentation:**  
  Write tutorials mapping gfun workflows to Sage equivalents (e.g., `diffeqtorec` ↔ `ore_algebra` tools).

## Example Code
```
from sage.rings import QQ
from ore_algebra import OreAlgebra

R.<n> = QQ[]
A.<Sn> = OreAlgebra(R, 'Sn')
rec = Sn^2 - Sn - 1  # Fibonacci recurrence

gfun_solver = GFunInterface()
gfun_solver.rectoproc(rec)  # Output: Generating function
```
Request for Feedback

- Does this scope align with SageMath’s ODE/recurrence tools roadmap?

- What critical gfun functionalities are still missing in Sage? (e.g., hybrid symbolic-numeric solving)

This project aims to reduce dependency on Maple for combinatorialists and strengthen Sage’s ODE/recurrence ecosystem. Your insights are crucial!

Best regards,
Vishal Shahi