M2::ARingGFFlintBig — arbitrary-degree GF(p^k) via FLINT fq_nmod. More...

#include <vector>
#include <M2/gc-include.h>
#include <M2/math-include.h>
#include <flint/flint.h>
#include <flint/fmpz.h>
#include <flint/fq_nmod.h>
#include <flint/nmod_poly.h>
#include "aring.hpp"
#include "buffer.hpp"
#include "ringelem.hpp"
#include "exceptions.hpp"

Classes
class	M2::ARingGFFlintBig
	aring-style adapter for FLINT's polynomial-quotient representation of finite fields GF(p^n) that are too large for Zech tables. More...
class	M2::ARingGFFlintBig::Element
	A wrapper class for ElementType. More...
class	M2::ARingGFFlintBig::ElementArray
	Fixed-size owned array of fq_nmod_struct slots tied to an ARingGFFlintBig for the matching FLINT context. More...

Namespaces
namespace	M2

Detailed Description

M2::ARingGFFlintBig — arbitrary-degree GF(p^k) via FLINT fq_nmod.

Note: AI-generated documentation. Verify against the source before relying on it.

ARingGFFlintBig (registered as ringID = ring_GFFlintBig) represents a Galois-field element as a degree-less-than-k polynomial over Z/p, stored in FLINT's fq_nmod_struct — which the in-source comment expands as {mp_ptr coeffs; slong alloc; slong length; nmod_t mod;}, i.e. an nmod_poly_struct under another name. Addition is coefficient-wise in Z/p; multiplication is polynomial multiply followed by reduction modulo the primitive polynomial (FLINT picks between schoolbook and Kronecker / FFT variants internally based on degree); inversion is the extended Euclidean algorithm over Z/p[t]. No Zech tables — every operation runs the underlying polynomial arithmetic, so per-op cost grows with k, but q = p^k carries no storage limit. The class inherits from RingInterface directly so its nested Element can hold an fq_nmod_ctx_struct* for the destructor.

The M2-side entry point is rawARingGaloisFieldFlintBig in interface/aring.cpp. There is no in-engine auto-fallback to the small-q aring-gf-flint.hpp; selecting between the Zech-table and polynomial-quotient implementations happens at the user / top-level M2 call site via the separate rawARingGaloisFieldFlintZech and rawARingGaloisFieldFlintBig entry points. The native, FLINT-free alternative is aring-m2-gf.hpp, and aring-tower.hpp handles iterated extensions.

See also: aring-gf-flint.hpp; aring-m2-gf.hpp; aring-tower.hpp; aring.hpp

Definition in file aring-gf-flint-big.hpp.

Classes

Namespaces

Detailed Description