GMPRationalField Class Reference

#include <gmp-rational.h>

Inheritance diagram for GMPRationalField:

Common Object Interface for a LinBox Field.
typedef GMPRationalElement	Element
	element type.
typedef GMPRationalRandIter	RandIter
	Random iterator generator type.
const Element	zero
const Element	one
const Element	neg_one
Public Member Functions
	GMPRationalField (int p=0, int exp=1)
integer &	get_num (integer &x, const Element &y) const
integer &	get_den (integer &x, const Element &y) const
int	sign (const Element &x) const
Object Management
x <- convert (y)
	GMPRationalField (const GMPRationalField &F)
	~GMPRationalField (void)
GMPRationalField &	operator= (const GMPRationalField &F)
Element &	init (Element &x, const integer &y=0) const
integer &	convert (integer &x, const Element &y=0) const
Element &	assign (Element &x, const Element &y) const
integer &	cardinality (integer &c) const
integer &	characteristic (integer &c) const
Arithmetic Operations
x <- y op z; x <- op y These operations require all elements, including x, to be initialized before the operation is called. Uninitialized field elements will give undefined results.
bool	areEqual (const Element &x, const Element &y) const
Element &	add (Element &x, const Element &y, const Element &z) const
Element &	sub (Element &x, const Element &y, const Element &z) const
Element &	mul (Element &x, const Element &y, const Element &z) const
Element &	div (Element &x, const Element &y, const Element &z) const
Element &	neg (Element &x, const Element &y) const
Element &	inv (Element &x, const Element &y) const
Inplace Arithmetic Operations
x <- x op y; x <- op x These operations require all elements, including x, to be initialized before the operation is called. Uninitialized field elements will give undefined results.
bool	isZero (const Element &x) const
bool	isOne (const Element &x) const
Element &	addin (Element &x, const Element &y) const
Element &	subin (Element &x, const Element &y) const
Element &	mulin (Element &x, const Element &y) const
Element &	axpy (Element &r, const Element &a, const Element &x, const Element &y) const
Element &	axpyin (Element &r, const Element &a, const Element &x) const
Element &	divin (Element &x, const Element &y) const
Element &	negin (Element &x) const
Element &	invin (Element &x) const
Input/Output Operations
std::ostream &	write (std::ostream &os) const
std::istream &	read (std::istream &is)
std::ostream &	write (std::ostream &os, const Element &x) const
std::istream &	read (std::istream &is, Element &x) const
Static Public Member Functions
int	getMaxModulus ()

---

Member Typedef Documentation

typedef GMPRationalElement Element

element type.

typedef GMPRationalRandIter RandIter

Random iterator generator type.

---

Constructor & Destructor Documentation

GMPRationalField (  const GMPRationalField &  F  )  [inline]

Copy constructor. Vacuous, since this field is unparametric so there is no need to construct multiple field objects

~GMPRationalField (  void   )  [inline]

Destructor. Also vacuous, since there is no de-initialization system

GMPRationalField (  int  p = 0, int  exp = 1 )  [inline]

---

Member Function Documentation

GMPRationalField& operator= (  const GMPRationalField &  F  )  [inline]

Assignment operator. Also vacuous

Element& init (  Element &  x, const integer &  y = 0 )  const [inline]

Initialization of field element from an integer. Behaves like C++ allocator construct. This function assumes the output field element x has already been constructed, but that it is not necessarily already initialized. In this implementation, this means the _elem_ptr of x exists, but that it may be the null pointer. Returns: reference to field element. Parameters: x  field element to contain output (reference returned). y  constant reference to integer.

integer& convert (  integer &  x, const Element &  y = 0 )  const [inline]

Conversion of field element to an integer. This function assumes the output field element x has already been constructed, but that it is not already initialized. In this implementation, this means the _elem_ptr of y exists, and that it is not the null pointer. Returns floor (numerator (y) / denominator (y)) Returns: reference to integer. Parameters: x  reference to integer to contain output (reference returned). y  constant reference to field element.

Element& assign (  Element &  x, const Element &  y )  const [inline]

Assignment of one field element to another. This function assumes both field elements have already been constructed and initialized. In this implementation, this means for both x and y, _elem_ptr exists and does not point to null. Returns: reference to x Parameters: x  field element (reference returned). y  field element. FIXME: Is this x := y? I am assuming so.

integer& cardinality (  integer &  c  )  const [inline]

Cardinality. Return integer representing cardinality of the field. Returns a non-negative integer for all fields with finite cardinality, and returns -1 to signify a field of infinite cardinality. Returns: constant reference to integer representing cardinality of the field

integer& characteristic (  integer &  c  )  const [inline]

Characteristic. Return integer representing characteristic of the field. Returns a positive integer to all fields with finite characteristic, and returns 0 to signify a field of infinite characteristic. Returns: constant reference to integer representing characteristic of the field.

bool areEqual (  const Element &  x, const Element &  y )  const [inline]

Equality of two elements. This function assumes both field elements have already been constructed and initialized. In this implementation, this means for both x and y, _elem_ptr exists and does not point to null. Returns: boolean true if equal, false if not. Parameters: x  field element y  field element

Element& add (  Element &  x, const Element &  y, const Element &  z )  const [inline]

Addition. x = y + z This function assumes all the field elements have already been constructed and initialized. In this implementation, this means for x, y, and z, _elem_ptr exists and does not point to null. Returns: reference to x. Parameters: x  field element (reference returned). y  field element. z  field element.

Element& sub (  Element &  x, const Element &  y, const Element &  z )  const [inline]

Subtraction. x = y - z This function assumes all the field elements have already been constructed and initialized. In this implementation, this means for x, y, and z, _elem_ptr exists and does not point to null. Returns: reference to x. Parameters: x  field element (reference returned). y  field element. z  field element.

Element& mul (  Element &  x, const Element &  y, const Element &  z )  const [inline]

Multiplication. x = y * z This function assumes all the field elements have already been constructed and initialized. In this implementation, this means for x, y, and z, _elem_ptr exists and does not point to null. Returns: reference to x. Parameters: x  field element (reference returned). y  field element. z  field element.

Element& div (  Element &  x, const Element &  y, const Element &  z )  const [inline]

Division. x = y / z This function assumes all the field elements have already been constructed and initialized. In this implementation, this means for x, y, and z, _elem_ptr exists and does not point to null. Returns: reference to x. Parameters: x  field element (reference returned). y  field element. z  field element.

Element& neg (  Element &  x, const Element &  y )  const [inline]

Additive Inverse (Negation). x = - y This function assumes both field elements have already been constructed and initialized. In this implementation, this means for both x and y _elem_ptr exists and does not point to null. Returns: reference to x. Parameters: x  field element (reference returned). y  field element.

Element& inv (  Element &  x, const Element &  y )  const [inline]

Multiplicative Inverse. x = 1 / y This function assumes both field elements have already been constructed and initialized. In this implementation, this means for both x and y _elem_ptr exists and does not point to null. Returns: reference to x. Parameters: x  field element (reference returned). y  field element.

bool isZero (  const Element &  x  )  const [inline]

Zero equality. Test if field element is equal to zero. This function assumes the field element has already been constructed and initialized. In this implementation, this means the _elem_ptr of x exists and does not point to null. Returns: boolean true if equals zero, false if not. Parameters: x  field element.

bool isOne (  const Element &  x  )  const [inline]

One equality. Test if field element is equal to one. This function assumes the field element has already been constructed and initialized. In this implementation, this means the _elem_ptr of x exists and does not point to null. Returns: boolean true if equals one, false if not. Parameters: x  field element.

Element& addin (  Element &  x, const Element &  y )  const [inline]

Inplace Addition. x += y This function assumes both field elements have already been constructed and initialized. In this implementation, this means for both x and y _elem_ptr exists and does not point to null. Returns: reference to x. Parameters: x  field element (reference returned). y  field element.

Element& subin (  Element &  x, const Element &  y )  const [inline]

Inplace Subtraction. x -= y This function assumes both field elements have already been constructed and initialized. In this implementation, this means for both x and y _elem_ptr exists and does not point to null. Returns: reference to x. Parameters: x  field element (reference returned). y  field element.

Element& mulin (  Element &  x, const Element &  y )  const [inline]

Inplace Multiplication. x *= y This function assumes both field elements have already been constructed and initialized. In this implementation, this means for both x and y _elem_ptr exists and does not point to null. Returns: reference to x. Parameters: x  field element (reference returned). y  field element.

Element& axpy (  Element &  r, const Element &  a, const Element &  x, const Element &  y )  const [inline]

Element& axpyin (  Element &  r, const Element &  a, const Element &  x )  const [inline]

Element& divin (  Element &  x, const Element &  y )  const [inline]

Inplace Division. x /= y This function assumes both field elements have already been constructed and initialized. In this implementation, this means for both x and y _elem_ptr exists and does not point to null. Returns: reference to x. Parameters: x  field element (reference returned). y  field element.

Element& negin (  Element &  x  )  const [inline]

Inplace Additive Inverse (Inplace Negation). x = - x This function assumes the field element has already been constructed and initialized. In this implementation, this means the _elem_ptr of x exists and does not point to null. Returns: reference to x. Parameters: x  field element (reference returned).

Element& invin (  Element &  x  )  const [inline]

Inplace Multiplicative Inverse. x = 1 / x This function assumes the field elementhas already been constructed and initialized. In this implementation, this means the _elem_ptr of x exists and does not point to null. Returns: reference to x. Parameters: x  field element (reference returned).

std::ostream& write (  std::ostream &  os  )  const [inline]

Print field. Returns: output stream to which field is written. Parameters: os  output stream to which field is written. This does not do much...

std::istream& read (  std::istream &  is  )  [inline]

Read field. Returns: input stream from which field is read. Parameters: is  input stream from which field is read. This does not do much either... FIXME: Read the same thing written above, and throw an exception if the strings do not match.

std::ostream& write (  std::ostream &  os, const Element &  x )  const [inline]

Print field element. This function assumes the field element has already been constructed and initialized. In this implementation, this means for the _elem_ptr for x exists and does not point to null. Returns: output stream to which field element is written. Parameters: os  output stream to which field element is written. x  field element.

std::istream& read (  std::istream &  is, Element &  x )  const [inline]

Read field element. This function assumes the field element has already been constructed and initialized. In this implementation, this means for the _elem_ptr for x exists and does not point to null. Returns: input stream from which field element is read. Parameters: is  input stream from which field element is read. x  field element. FIXME: Avoid the magical limit on size here FIXME: Right now it skips over everything until it finds something that looks like a number. Is this really the correct policy?

int getMaxModulus (   )  [inline, static]

integer& get_num (  integer &  x, const Element &  y )  const [inline]

integer& get_den (  integer &  x, const Element &  y )  const [inline]

int sign (  const Element &  x  )  const [inline]

---

Field Documentation

const Element zero

const Element one

const Element neg_one

---