Integer Class Reference

An arbitrary-precision Integer. More...

#include <Integer.hpp>

Simplified semantic inheritance diagram for Integer:

 Full inheritance diagram for Integer:

Public Member Functions
	Integer ()
	Get a zero integer.
	Integer (int a)
	Construct and Integer from an int.
	Integer (const mpz_t &a)
	Construct an integer form a GMP mpz_t.
	Integer (const mpz_class &a)
	Construct an integer from a GMP mpz_class.
	Integer (const Integer &a)
	Copy assignment from another Integer.
	Integer (const RationalNumber &a)
	Attempts to construct an Integer from a rational number. More...
	Integer (const ComplexRationalNumber &a)
	Attempts to construct an Integer from a complex rational number. More...
	Integer (const SmallPrimeField &a)
	Attempts to construct an Integer from a SmallPrimeField. More...
	Integer (const BigPrimeField &a)
	Attempts to construct an Integer from a BigPrimeField. More...
	Integer (const GeneralizedFermatPrimeField &a)
	Attempts to construct an Integer from a GeneralizedFermatPrimeField. More...
	Integer (const DenseUnivariateIntegerPolynomial &a)
	Attempts to construct an Integer from a DenseUnivariateIntegerPolynomial. More...
	Integer (const DenseUnivariateRationalPolynomial &a)
	Attempts to construct an Integer from a DenseUnivariateRationalPolynomial. More...
	Integer (const SparseUnivariatePolynomial< Integer > &a)
	Attempts to construct an Integer from a SparseUnivariatePolynomial<Integer>. More...
	Integer (const SparseUnivariatePolynomial< RationalNumber > &a)
	Attempts to construct an Integer from a SparseUnivariatePolynomial<RationalNumber>. More...
	Integer (const SparseUnivariatePolynomial< ComplexRationalNumber > &a)
	Attempts to construct an Integer from a SparseUnivariatePolynomial<ComplexRationalNumber>. More...
template<class Ring >
	Integer (const SparseUnivariatePolynomial< Ring > &a)
	Attempts to construct an Integer from a SparseUniveraitePolynomial<Ring> for a generic ring. More...
mpz_class &	get_mpz_ref ()
const mpz_class &	get_mpz_ref () const
mpz_class	get_mpz () const
mpz_ptr	get_mpz_t ()
mpz_srcptr	get_mpz_t () const
double	get_d () const
long int	get_si () const
unsigned long int	get_ui () const
bool	isZero () const
	Is a zero. More...
void	zero ()
	Assign to zero. More...
bool	isOne () const
	Is a 1. More...
void	one ()
	Assign to one. More...
bool	isNegativeOne () const
	Is a -1. More...
void	negativeOne ()
	Assign to negative one. More...
int	isConstant () const
	Is a constant. More...
Integer	unitCanonical (Integer *u=NULL, Integer *v=NULL) const
	Obtain the unit normal (a.k.a canonical associate) of an element. More...
Integer &	operator= (const Integer &a)
	Copy assignment.
Integer	operator+ (const Integer &i) const
	Addition.
Integer &	operator+= (const Integer &i)
	Addition assignment.
Integer	operator- (const Integer &i) const
	Subtraction.
Integer &	operator-= (const Integer &i)
	Subtraction assignment.
Integer	operator- () const
	Negation.
Integer	operator* (const Integer &i) const
	Multiplication.
Integer &	operator*= (const Integer &i)
	Multiplication assignment.
Integer	operator^ (long long int e) const
	Exponentiation.
Integer &	operator^= (long long int e)
	Exponentiation assignment.
bool	operator== (const Integer &i) const
	Equality test,. More...
bool	operator!= (const Integer &i) const
	Inequality test,. More...
bool	operator< (const Integer &r) const
bool	operator<= (const Integer &r) const
bool	operator> (const Integer &r) const
bool	operator>= (const Integer &r) const
ExpressionTree	convertToExpressionTree () const
	Convert this to an expression tree. More...
Integer	operator/ (const Integer &i) const
	Exact division.
Integer &	operator/= (const Integer &i)
	Exact division assignment.
bool	divisible (unsigned long int i)
Integer	operator% (const Integer &r) const
	Get the remainder of *this and b;. More...
Integer &	operator%= (const Integer &r)
	Assign *this to be the remainder of *this and b. More...
Integer	gcd (const Integer &other) const
	Get GCD of *this and other.
Factors< Integer >	squareFree () const
	Compute squarefree factorization of *this.
Integer	euclideanSize () const
	Get the euclidean size of *this.
Integer	euclideanDivision (const Integer &b, Integer *q=NULL) const
	Perform the eucldiean division of *this and b. More...
Integer	extendedEuclidean (const Integer &b, Integer *s=NULL, Integer *t=NULL) const
	Perform the extended euclidean division on *this and b. More...
Integer	quotient (const Integer &b) const
	Get the quotient of *this and b.
Integer	remainder (const Integer &b) const
	Get the remainder of *this and b.

Friends
Integer	operator+ (int a, const Integer &r)
Integer	operator- (int a, const Integer &r)
Integer	operator* (int a, const Integer &r)
Integer	operator/ (int a, const Integer &r)
bool	operator< (int a, const Integer &r)
bool	operator<= (int a, const Integer &r)
bool	operator> (int a, const Integer &r)
bool	operator>= (int a, const Integer &r)
Integer	operator+ (long int a, const Integer &r)
Integer	operator- (long int a, const Integer &r)
Integer	operator* (long int a, const Integer &r)
Integer	operator/ (long int a, const Integer &r)
Integer	abs (const Integer &i)
bool	operator< (long int a, const Integer &r)
bool	operator<= (long int a, const Integer &r)
bool	operator> (long int a, const Integer &r)
bool	operator>= (long int a, const Integer &r)

Detailed Description

An arbitrary-precision Integer.

Constructor & Destructor Documentation

Integer() [1/11]

Integer::Integer ( const RationalNumber &  a )

explicit

Attempts to construct an Integer from a rational number.

If the conversion is not exact, causes an error.

Integer() [2/11]

Integer::Integer ( const ComplexRationalNumber &  a )

explicit

Attempts to construct an Integer from a complex rational number.

If the conversion is not exact, causes an error.

Integer() [3/11]

Integer::Integer ( const SmallPrimeField &  a )

explicit

Attempts to construct an Integer from a SmallPrimeField.

If the conversion is not exact, causes an error.

Integer() [4/11]

Integer::Integer ( const BigPrimeField &  a )

explicit

Attempts to construct an Integer from a BigPrimeField.

If the conversion is not exact, causes an error.

Integer() [5/11]

Integer::Integer ( const GeneralizedFermatPrimeField &  a )

explicit

Attempts to construct an Integer from a GeneralizedFermatPrimeField.

If the conversion is not exact, causes an error.

Integer() [6/11]

Integer::Integer ( const DenseUnivariateIntegerPolynomial &  a )

explicit

Attempts to construct an Integer from a DenseUnivariateIntegerPolynomial.

If the conversion is not exact, causes an error.

Integer() [7/11]

Integer::Integer ( const DenseUnivariateRationalPolynomial &  a )

explicit

Attempts to construct an Integer from a DenseUnivariateRationalPolynomial.

If the conversion is not exact, causes an error.

Integer() [8/11]

Integer::Integer ( const SparseUnivariatePolynomial< Integer > &  a )

explicit

Attempts to construct an Integer from a SparseUnivariatePolynomial<Integer>.

If the conversion is not exact, causes an error.

Integer() [9/11]

Integer::Integer ( const SparseUnivariatePolynomial< RationalNumber > &  a )

explicit

Attempts to construct an Integer from a SparseUnivariatePolynomial<RationalNumber>.

If the conversion is not exact, causes an error.

Integer() [10/11]

Integer::Integer ( const SparseUnivariatePolynomial< ComplexRationalNumber > &  a )

explicit

Attempts to construct an Integer from a SparseUnivariatePolynomial<ComplexRationalNumber>.

If the conversion is not exact, causes an error.

Integer() [11/11]

template<class Ring >

Integer::Integer ( const SparseUnivariatePolynomial< Ring > &  a )

explicit

Attempts to construct an Integer from a SparseUniveraitePolynomial<Ring> for a generic ring.

If the conversion is not exact, causes an error.

Member Function Documentation

convertToExpressionTree()

ExpressionTree Integer::convertToExpressionTree ( ) const

inlinevirtual

Convert this to an expression tree.

returns an expression tree describing *this.

Implements ExpressionTreeConvert.

euclideanDivision()

Integer Integer::euclideanDivision ( const Integer &  b, Integer *  q = NULL  ) const

virtual

Perform the eucldiean division of *this and b.

Returns the remainder. If q is not NULL, then returns the quotient in q.

Implements BPASEuclideanDomain< Integer >.

extendedEuclidean()

Integer Integer::extendedEuclidean ( const Integer &  b, Integer *  s = NULL, Integer *  t = NULL  ) const

virtual

Perform the extended euclidean division on *this and b.

Returns the GCD. If s and t are not NULL, returns the bezout coefficients in them.

Implements BPASEuclideanDomain< Integer >.

isConstant()

int Integer::isConstant ( ) const

inline

Is a constant.

Parameters

isNegativeOne()

bool Integer::isNegativeOne ( ) const

inline

Is a -1.

Parameters

isOne()

bool Integer::isOne ( ) const

inlinevirtual

Is a 1.

Parameters

Implements BPASRing< Integer >.

isZero()

bool Integer::isZero ( ) const

inlinevirtual

Is a zero.

Parameters

Implements BPASRing< Integer >.

negativeOne()

void Integer::negativeOne ( )

inline

Assign to negative one.

Parameters

one()

void Integer::one ( )

inlinevirtual

Assign to one.

Parameters

Implements BPASRing< Integer >.

operator!=()

bool Integer::operator!= ( const Integer &  i ) const

inlinevirtual

Inequality test,.

returns true iff not equal.

Implements BPASRing< Integer >.

operator%()

Integer Integer::operator% ( const Integer &  b ) const

inlinevirtual

Get the remainder of *this and b;.

Parameters

b	the divisor

Returns

the remainder

Implements BPASEuclideanDomain< Integer >.

operator%=()

Integer& Integer::operator%= ( const Integer &  b )

inlinevirtual

Assign *this to be the remainder of *this and b.

Parameters

b	the divisor

Returns

this after assignment.

Implements BPASEuclideanDomain< Integer >.

operator==()

bool Integer::operator== ( const Integer &  i ) const

inlinevirtual

Equality test,.

returns true iff equal

Implements BPASRing< Integer >.

unitCanonical()

Integer Integer::unitCanonical ( Integer *  u = NULL, Integer *  v = NULL  ) const

virtual

Obtain the unit normal (a.k.a canonical associate) of an element.

If either parameters u, v, are non-NULL then the units are returned such that b = ua, v = u^-1. Where b is the unit normal of a, and is the returned value.

Implements BPASRing< Integer >.

zero()

void Integer::zero ( )

inlinevirtual

Assign to zero.

Parameters

Implements BPASRing< Integer >.

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

• include/Ring/Integer.hpp