itpp::GFX Class Reference

Polynomials over GF(q)[x], where q=2^m, m=1,...,16. More...

#include <itpp/comm/galois.h>

List of all members.

Public Member Functions
	GFX ()
	Constructor.
	GFX (int qvalue)
	Constructor.
	GFX (int qvalue, int indegree)
	Constructor.
	GFX (int qvalue, const ivec &invalues)
	Constructor.
	GFX (int qvalue, char *invalues)
	Constructor.
	GFX (int qvalue, std::string invalues)
	Constructor.
	GFX (const GFX &ingfx)
	Copy constructor.
int	get_size () const
	Return q.
int	get_degree () const
	Return degree of GF(q)[x].
void	set_degree (int indegree)
	Resize the polynomial to the given indegree. If the new polynomial is bigger, then the new coefficients are set to zero.
int	get_true_degree () const
	Return true degree of GF(q)[x].
void	set (int qvalue, const char *invalues)
	Set the GF(q)[x] polynomial.
void	set (int qvalue, const std::string invalues)
	Set the GF(q)[x] polynomial.
void	set (int qvalue, const ivec &invalues)
	Set the GF(q)[x] polynomial.
void	clear ()
	Set all coefficients to zero.
GF	operator[] (int index) const
	Acces to individual element in the GF(q)[x] polynomial.
GF &	operator[] (int index)
	Acces to individual element in the GF(q)[x] polynomial.
void	operator= (const GFX &ingfx)
	Copy.
void	operator+= (const GFX &ingfx)
	sum of two GF(q)[x]
GFX	operator+ (const GFX &ingfx) const
	sum of two GF(q)[x]
void	operator-= (const GFX &ingfx)
	Difference of two GF(q), same as sum for q=2^m.
GFX	operator- (const GFX &ingfx) const
	Difference of two GF(q), same as sum for q=2^m.
void	operator *= (const GFX &ingfx)
	product of two GF(q)[x]
GFX	operator * (const GFX &ingfx) const
	product of two GF(q)[x]
GF	operator() (const GF &ingf)
	Evaluate polynom at alpha^inexp.
Friends
GFX	operator * (const GF &ingf, const GFX &ingfx)
	Multiply a GF element with a GF(q)[x].
GFX	operator * (const GFX &ingfx, const GF &ingf)
	Multiply a GF(q)[x] with a GF element.
GFX	operator/ (const GFX &ingfx, const GF &ingf)
	Divide a GF(q)[x] with a GF element.
std::ostream &	operator<< (std::ostream &os, const GFX &ingfx)
	Output stream.
Related Functions
(Note that these are not member functions.)
GFX	divgfx (const GFX &c, const GFX &g)
	Int division of GF[q](x) polynomials: m(x) = c(x)/g(x).
GFX	modgfx (const GFX &a, const GFX &b)
	Function that performs int division of gf[q](x) polynomials (a(x)/g(x)) and returns the reminder.

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Detailed Description

Polynomials over GF(q)[x], where q=2^m, m=1,...,16.

Definition at line 156 of file galois.h.

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Constructor & Destructor Documentation

itpp::GFX::GFX (   )  [inline]

Constructor. Definition at line 363 of file galois.h.

itpp::GFX::GFX (  int  qvalue  )  [inline]

Constructor. Definition at line 369 of file galois.h. References it_assert0.

itpp::GFX::GFX (  int  qvalue, int  indegree )  [inline]

Constructor. Definition at line 395 of file galois.h. References it_assert0, and itpp::Array< T >::set_size().

itpp::GFX::GFX (  int  qvalue, const ivec &  invalues )  [inline]

Constructor. Definition at line 404 of file galois.h. References set().

itpp::GFX::GFX (  int  qvalue, char *  invalues )  [inline]

Constructor. Definition at line 409 of file galois.h. References set().

itpp::GFX::GFX (  int  qvalue, std::string  invalues )  [inline]

Constructor. Definition at line 414 of file galois.h. References set().

itpp::GFX::GFX (  const GFX &  ingfx  )  [inline]

Copy constructor. Definition at line 419 of file galois.h. References coeffs, degree, and q.

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Member Function Documentation

int itpp::GFX::get_size (   )  const [inline]

Return q. Definition at line 426 of file galois.h. Referenced by divgfx(), and modgfx().

int itpp::GFX::get_degree (   )  const [inline]

Return degree of GF(q)[x]. Definition at line 431 of file galois.h. Referenced by divgfx(), and modgfx().

void itpp::GFX::set_degree (  int  indegree  )  [inline]

Resize the polynomial to the given indegree. If the new polynomial is bigger, then the new coefficients are set to zero. Definition at line 436 of file galois.h. References it_assert0, and itpp::Array< T >::set_size(). Referenced by itpp::Reed_Solomon::decode(), divgfx(), and modgfx().

int itpp::GFX::get_true_degree (   )  const [inline]

Return true degree of GF(q)[x]. Definition at line 443 of file galois.h. Referenced by divgfx(), and modgfx().

void itpp::GFX::set (  int  qvalue, const char *  invalues )  [inline]

Set the GF(q)[x] polynomial. Definition at line 385 of file galois.h. Referenced by itpp::BCH::BCH(), GFX(), itpp::Reed_Solomon::Reed_Solomon(), and set().

void itpp::GFX::set (  int  qvalue, const std::string  invalues )  [inline]

Set the GF(q)[x] polynomial. Definition at line 390 of file galois.h. References set().

void itpp::GFX::set (  int  qvalue, const ivec &  invalues )  [inline]

Set the GF(q)[x] polynomial. Definition at line 375 of file galois.h. References it_assert0, itpp::Array< T >::set_size(), and itpp::Vec< Num_T >::size().

void itpp::GFX::clear (   )  [inline]

Set all coefficients to zero. Definition at line 454 of file galois.h. References it_assert0. Referenced by itpp::Reed_Solomon::decode(), divgfx(), and modgfx().

GF itpp::GFX::operator[] (  int  index  )  const [inline]

Acces to individual element in the GF(q)[x] polynomial. Definition at line 191 of file galois.h. References it_assert0.

GF& itpp::GFX::operator[] (  int  index  )  [inline]

Acces to individual element in the GF(q)[x] polynomial. Definition at line 194 of file galois.h. References it_assert0.

void itpp::GFX::operator= (  const GFX &  ingfx  )  [inline]

Copy. Definition at line 461 of file galois.h. References coeffs, degree, and q.

void itpp::GFX::operator+= (  const GFX &  ingfx  )  [inline]

sum of two GF(q)[x] Definition at line 468 of file galois.h. References coeffs, degree, it_assert0, q, itpp::Array< T >::set_size(), and itpp::Array< T >::size().

GFX itpp::GFX::operator+ (  const GFX &  ingfx  )  const [inline]

sum of two GF(q)[x] Definition at line 480 of file galois.h.

void itpp::GFX::operator-= (  const GFX &  ingfx  )  [inline]

Difference of two GF(q), same as sum for q=2^m. Definition at line 487 of file galois.h.

GFX itpp::GFX::operator- (  const GFX &  ingfx  )  const [inline]

Difference of two GF(q), same as sum for q=2^m. Definition at line 492 of file galois.h.

void itpp::GFX::operator *= (  const GFX &  ingfx  )  [inline]

product of two GF(q)[x] Definition at line 499 of file galois.h. References coeffs, degree, it_assert0, q, itpp::Array< T >::set_size(), and itpp::Array< T >::size().

GFX itpp::GFX::operator * (  const GFX &  ingfx  )  const [inline]

product of two GF(q)[x] Definition at line 513 of file galois.h.

GF itpp::GFX::operator() (  const GF &  ingf  )  [inline]

Evaluate polynom at alpha^inexp. Definition at line 543 of file galois.h. References itpp::GF::get_size(), and it_assert0.

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Friends And Related Function Documentation

GFX operator * (  const GF &  ingf, const GFX &  ingfx )  [friend]

Multiply a GF element with a GF(q)[x].

GFX operator * (  const GFX &  ingfx, const GF &  ingf )  [friend]

Multiply a GF(q)[x] with a GF element.

GFX operator/ (  const GFX &  ingfx, const GF &  ingf )  [friend]

Divide a GF(q)[x] with a GF element.

std::ostream& operator<< (  std::ostream &  os, const GFX &  ingfx )  [friend]

Output stream. Definition at line 104 of file galois.cpp.

GFX divgfx (  const GFX &  c, const GFX &  g )  [related]

Int division of GF[q](x) polynomials: m(x) = c(x)/g(x). The reminder r(x) is not returned by this function. Definition at line 125 of file galois.cpp. References clear(), get_degree(), get_size(), get_true_degree(), and set_degree().

GFX modgfx (  const GFX &  a, const GFX &  b )  [related]

Function that performs int division of gf[q](x) polynomials (a(x)/g(x)) and returns the reminder. Definition at line 150 of file galois.cpp. References clear(), get_degree(), get_size(), get_true_degree(), and set_degree().

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

• itpp/comm/galois.h

Generated on Fri Jan 11 08:51:42 2008 for IT++ by Doxygen 1.3.9.1