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GF2 Class Template Reference

Template class for Galois fields of size . More...

#include <gf2.H>

List of all members.

Public Methods
	GF2 ()
	Default constructor. Returns the "zero" of the field.
	GF2 (int n)
	Conversion int -> GF<n>. Returns "one" added to itself n times.
bool	is_zero () const
	Is this the "zero"?
bool	is_one () const
	Is this the "one"?
bool	is_unit () const
	Does this element have a multiplicative inverse?
const bool	is_euclidean ()
	Does this element belong to an Euclidean ring?
unsigned int	deg () const
	My degree (it makes sense only if is_euclidean()==true).
GF2<FieldSize>	operator+ (GF2< FieldSize > b) const
	Sum.
bool	operator== (GF2< FieldSize > b) const
	Equality.
bool	operator!= (GF2< FieldSize > b) const
	Inequality.
GF2<FieldSize>	operator- (GF2< FieldSize > b) const
	Difference.
GF2<FieldSize>	operator- () const
	Minus.
GF2<FieldSize>	operator * (GF2< FieldSize > b) const
	Product.
void	divmod (GF2< FieldSize > a, GF2< FieldSize > &quot, GF2< FieldSize > &rem)
	Division and remainder. Since GF<n> is a field, rem==0.
Static Public Methods
GF2<FieldSize>	zero ()
	"zero" constructor.
GF2<FieldSize>	one ()
	"one" constructor.
const bool	is_field ()
	Is this a field?
GF2<FieldSize>	string2val (std::string str)
	Conversion from string to GF<n>.
void	regexp (std::string &re, int &idx)
	Regular expression rappresenting an element of GF<>.
Friends
GF2<FieldSize>	inv (GF2< FieldSize > x)
	Multiplicative inverse (it makes sense only if is_unit()==true).
std::ostream&	operator<< (std::ostream &str, GF2< FieldSize > n)
	Output operator.
std::istream&	operator>> (std::istream &str, GF2< FieldSize > &n)
	Input operator.
bool	operator>> (char *str, GF2< FieldSize > &n)
	Input from strings.

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Detailed Description

template<int FieldSize> class GF2

Template class for Galois fields of size .

This is a template for a class which implements a Galois field of size . It is not as general as GF, but it is more efficient since each element is stored as an unsigned integer.

Typical usage

    GF2<16> x, y;            // x and y are values in GF(16)
    std::cin >> x >> y;      // read x and y from stdin
    std::cout << x+inv(y);   // write x+1/y to stdout

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

• gf2.H

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