Proposal: New GitHub Issue for GSoC 2025 Project "gfun-Style Interface for Recurrences/ODEs"

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Vishal Shahi

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Apr 2, 2025, 8:56:50 AMApr 2

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Hello SageMath Community,

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

Key Proposal :->

Issue Title:

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

Scope:

Unify ore_algebra, rec_sequences, and FLINT under a standardized API.
Add missing gfun functions (e.g.,listtoalgeq, rectoproc) and improve boundary condition handling.
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!