Rational Function Arithmetic

Efficient arithmetic on multivariate rational functions arising in generating function computations.

normal master

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.

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)
5

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.

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)