M2::ARingZZp Class Reference

aring-style adapter for Z/p using a discrete-log (Zech) representation: every non-zero residue is its index relative to a primitive generator a. More...

#include <aring-zzp.hpp>

Inheritance diagram for M2::ARingZZp:

Public Types
typedef Z_mod	ring_type
typedef int	ElementType
typedef int	elem
typedef std::vector< elem >	ElementContainerType

Public Member Functions
	ARingZZp (size_t prime)
	~ARingZZp ()
size_t	characteristic () const
size_t	cardinality () const
void	text_out (buffer &o) const
unsigned int	computeHashValue (const elem &a) const
void	init_set (elem &result, elem a) const
void	set (elem &result, elem a) const
bool	is_unit (ElementType f) const
bool	is_zero (ElementType f) const
bool	is_equal (ElementType f, ElementType g) const
int	compare_elems (ElementType f, ElementType g) const
void	to_ring_elem (ring_elem &result, const ElementType &a) const
void	from_ring_elem (ElementType &result, const ring_elem &a) const
ElementType	from_ring_elem_const (const ring_elem &a) const
void	init (elem &result) const
void	set_zero (elem &result) const
void	set_from_long (elem &result, long a) const
void	set_var (elem &result, int v) const
void	set_from_mpz (elem &result, mpz_srcptr a) const
bool	set_from_mpq (elem &result, mpq_srcptr a) const
bool	set_from_BigReal (elem &result, gmp_RR a) const
void	negate (elem &result, elem a) const
void	invert (elem &result, elem a) const
void	add (elem &result, elem a, elem b) const
void	subtract (elem &result, elem a, elem b) const
int	modulus_add (int a, int b, int p) const
int	modulus_sub (int a, int b, int p) const
void	subtract_multiple (elem &result, elem a, elem b) const
void	mult (elem &result, elem a, elem b) const
void	divide (elem &result, elem a, elem b) const
void	power (elem &result, elem a, int n) const
void	power_mpz (elem &result, elem a, mpz_srcptr n) const
void	swap (ElementType &a, ElementType &b) const
void	elem_text_out (buffer &o, ElementType a, bool p_one=true, bool p_plus=false, bool p_parens=false) const
void	syzygy (ElementType a, ElementType b, ElementType &x, ElementType &y) const
void	random (ElementType &result) const
void	eval (const RingMap *map, const elem f, int first_var, ring_elem &result) const
long	coerceToLongInteger (const elem &f) const
long	coerceToNonnegativeLongInteger (const elem &f) const

Static Public Member Functions
static int	findPrimitiveRoot (int P)
static void	clear (elem &result)
Static Public Member Functions inherited from our_new_delete
static void *	operator new (size_t size)
static void *	operator new[] (size_t size)
static void	operator delete (void *obj)
static void	operator delete[] (void *obj)
static void *	operator new (size_t size, void *existing_memory)
static void *	operator new[] (size_t size, void *existing_memory)
static void	operator delete (void *obj, void *existing_memory)
static void	operator delete[] (void *obj, void *existing_memory)

Static Public Attributes
static const RingID	ringID = ring_ZZp

Private Member Functions
void	initialize_tables ()

Private Attributes
size_t	charac
int	p
int	p1
int	minus_one
int	prim_root
int *	log_table
int *	exp_table

Detailed Description

aring-style adapter for Z/p using a discrete-log (Zech) representation: every non-zero residue is its index relative to a primitive generator a.

Note

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

Encoding: 0 means 0, p-1 means 1, and 1..p-2 are the exponents of a^n mod p covering residues 2..p-1. Multiplication / division collapse to integer add / sub mod p-1 with no table hit; addition uses precomputed exp / log tables. ringID = ring_ZZp. The aring twin of CoefficientRingZZp.

Definition at line 66 of file aring-zzp.hpp.

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The documentation for this class was generated from the following files:

• Macaulay2/e/aring-zzp.hpp
• Macaulay2/e/aring-zzp.cpp