ffPoly

ffPoly is a software library and related set of mathematical concepts centered on efficient polynomial arithmetic using the fast Fourier transform (FFT). The library provides data structures and algorithms for manipulating polynomials, performing fast convolution, and enabling scalable evaluation and interpolation. It supports polynomials over various numeric domains, including real and complex fields, and can operate with modular arithmetic to support finite fields often used in coding theory.

Design goals include high performance, numerical stability, and broad language interoperability. The core is written in C++ with optional bindings to Python and other languages, and it can be paired with external FFT backends such as FFTW or custom implementations. It also offers a modular arithmetic backend for arithmetic in polynomial rings, enabling operations like multiplication, division, inversion, and factorization within specified domains.

Typical use cases are in digital signal processing, numerical simulations requiring polynomial approximations, and computer algebra tasks where fast polynomial multiplication is beneficial. The project emphasizes a clean, well-documented API, unit-tested components, and cross-platform compatibility.

ffPoly is released under a permissive open-source license and is maintained by a community of contributors. It has inspired related projects focusing on polynomial arithmetic, FFT-based algorithms, and symbolic-numeric computing.

See also: Fast Fourier transform, Polynomial ring, Polynomial interpolation, Convolution, Computer algebra systems.