Rational Function Arithmetic
Efficient arithmetic on multivariate rational functions arising in generating function computations.
Rational functions are a core data structure in symbolic computation for generating functions, partial fraction decompositions, and algorithmic enumeration. The goal is to develop efficient arithmetic algorithms and implementations for multivariate rational functions.
- Repo: alcyon-ratfun.jl
Milestones
| ID | Title | Due |
|---|---|---|
| M1 | Data structures survey & prototype | 2025-11-25 |
| M2 | Core arithmetic (add, mul, reduce) | 2025-12-20 |
| M3 | Partial fraction decomposition | 2026-01-30 |
| M4 | Benchmarks & final report | 2026-02-28 |
Tasks
| ID | Title | Start | End | Status |
|---|---|---|---|---|
| T1 | Survey sparse multivariate representations | 2025-11-05 | 2025-11-25 | todo |
| T2 | Implement multiplication kernels | 2025-11-26 | 2025-12-20 | todo |
| T3 | Sparse partial fraction pipeline | 2025-12-21 | 2026-01-30 | todo |
| T4 | Benchmarks + write-up | 2026-01-31 | 2026-02-28 | todo |
Deliverables
- Julia package with tests
- Benchmark against existing tools
- Short report (6–8 pages)