aring-gf-flint.hpp File Reference

M2::ARingGFFlint — small GF(p^k) via FLINT Zech-logarithm tables. 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/fq_zech.h>
#include <flint/nmod_poly.h>
#include "interface/random.h"
#include "aring.hpp"
#include "buffer.hpp"
#include "ringelem.hpp"
#include "exceptions.hpp"

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Classes
class	M2::ARingGFFlint
	aring-style adapter for FLINT's Zech-logarithm representation of small finite fields GF(p^n). More...
class	M2::ARingGFFlint::Element
	A wrapper class for ElementType. More...
class	M2::ARingGFFlint::ElementArray
	Fixed-size owned array of fq_zech_struct slots tied to an ARingGFFlint for the matching FLINT context. More...

Namespaces
namespace	M2

Detailed Description

M2::ARingGFFlint — small GF(p^k) via FLINT Zech-logarithm tables.

Note

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

ARingGFFlint (registered as ringID = ring_GFFlintZech) represents a Galois field GF(q) of small order via FLINT's fq_zech_* interface. The element type is FLINT's fq_zech_struct, which wraps a single mp_limb_t Zech log index of a chosen primitive root; every non-zero operation reduces to O(1) integer arithmetic on that index (multiplication is (i + j) mod (q - 1), addition uses a Zech table built once at construction). One word per element and no per-call allocations make this the fastest path for small q; FLINT's Zech table sizing imposes the upper limit on q. The class inherits from RingInterface directly (not SimpleARing<ARingGFFlint>) so its nested Element can hold an fq_zech_ctx_struct* for the destructor.

The context is initialised via fq_zech_ctx_init_modulus against a user-supplied minimal polynomial; the M2-side entry point is rawARingGaloisFieldFlintZech in interface/aring.cpp. Larger extensions are reached by the separate rawARingGaloisFieldFlintBig entry point (which builds an ARingGFFlintBig from aring-gf-flint-big.hpp using polynomial-quotient fq_nmod_* arithmetic). The native aring-m2-gf.hpp path provides the same algebra without a FLINT dependency, and GF.hpp is the legacy table-based class.

See also

aring-gf-flint-big.hpp

aring-m2-gf.hpp

GF.hpp

aring.hpp

Definition in file aring-gf-flint.hpp.