An arbitrary-precision complex rational number. More...

#include <ComplexRationalNumber.hpp>

Simplified semantic inheritance diagram for ComplexRationalNumber:

Full inheritance diagram for ComplexRationalNumber:

Public Member Functions
	ComplexRationalNumber (const mpq_class &_a, const mpq_class &_b=mpq_class(1))

	ComplexRationalNumber (const ComplexRationalNumber &c)

	ComplexRationalNumber (int _a, int _b=1, int _c=0, int _d=1)

	ComplexRationalNumber (const Integer &c)

	ComplexRationalNumber (const RationalNumber &c)

	ComplexRationalNumber (const SmallPrimeField &c)

	ComplexRationalNumber (const BigPrimeField &c)

	ComplexRationalNumber (const GeneralizedFermatPrimeField &c)

	ComplexRationalNumber (const DenseUnivariateIntegerPolynomial &c)

	ComplexRationalNumber (const DenseUnivariateRationalPolynomial &c)

	ComplexRationalNumber (const SparseUnivariatePolynomial< Integer > &c)

	ComplexRationalNumber (const SparseUnivariatePolynomial< RationalNumber > &c)

	ComplexRationalNumber (const SparseUnivariatePolynomial< ComplexRationalNumber > &c)

template<class Ring >
	ComplexRationalNumber (const SparseUnivariatePolynomial< Ring > &c)

ComplexRationalNumber &	operator= (const ComplexRationalNumber &c)
	Copy assignment.

ComplexRationalNumber &	operator= (const mpq_class &k)

ComplexRationalNumber &	operator= (int k)

ComplexRationalNumber &	setRealPart (const RationalNumber &r)

ComplexRationalNumber &	setRealPart (const mpq_class &k)

ComplexRationalNumber &	setRealPart (int k)

ComplexRationalNumber &	setImaginaryPart (const RationalNumber &r)

ComplexRationalNumber &	setImaginaryPart (const mpq_class &k)

ComplexRationalNumber &	setImaginaryPart (int k)

ComplexRationalNumber &	set (const RationalNumber &ka, const RationalNumber &kb)

ComplexRationalNumber &	set (const mpq_class &ka, const mpq_class &kb)

ComplexRationalNumber &	set (const mpq_class &ka, int kb)

ComplexRationalNumber &	set (int ka, const mpq_class &kb)

ComplexRationalNumber &	set (int ka, int kb)

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...

ComplexRationalNumber	unitCanonical (ComplexRationalNumber u=NULL, ComplexRationalNumber v=NULL) const
	Obtain the unit normal (a.k.a canonical associate) of an element. More...

bool	operator== (const ComplexRationalNumber &c) const
	Equality test,. More...

bool	operator== (const mpq_class &k) const

bool	operator== (int k) const

bool	operator!= (const ComplexRationalNumber &c) const
	Inequality test,. More...

bool	operator!= (const mpq_class &k) const

bool	operator!= (int k) const

ComplexRationalNumber	operator+ (const ComplexRationalNumber &c) const
	Addition.

ComplexRationalNumber &	operator+= (const ComplexRationalNumber &c)
	Addition assignment.

ComplexRationalNumber	operator- (const ComplexRationalNumber &c) const
	Subtraction.

ComplexRationalNumber &	operator-= (const ComplexRationalNumber &c)
	Subtraction assignment.

ComplexRationalNumber	operator- () const
	Negation.

ComplexRationalNumber	operator* (const ComplexRationalNumber &c) const
	Multiplication.

ComplexRationalNumber &	operator*= (const ComplexRationalNumber &c)
	Multiplication assignment.

ComplexRationalNumber &	*operator=** (const mpq_class &c)

ComplexRationalNumber &	*operator=** (int c)

ComplexRationalNumber	operator^ (long long int e) const
	Overload operator ^ replace xor operation by exponentiation. More...

ComplexRationalNumber &	operator^= (long long int e)
	Exponentiation assignment.

ExpressionTree	convertToExpressionTree () const
	Convert this to an expression tree. More...

ComplexRationalNumber	operator/ (const ComplexRationalNumber &c) const
	Exact division. More...

ComplexRationalNumber &	operator/= (const ComplexRationalNumber &c)
	Exact division assignment. More...

ComplexRationalNumber	operator% (const ComplexRationalNumber &c) const
	Get the remainder of *this and b;. More...

ComplexRationalNumber &	operator%= (const ComplexRationalNumber &c)
	Assign this to be the remainder of this and b. More...

ComplexRationalNumber	gcd (const ComplexRationalNumber &c) const
	GCD(a, b) More...

Factors< ComplexRationalNumber >	squareFree () const
	Compute squarefree factorization of *this.

Integer	euclideanSize () const
	Get the euclidean size of *this.

ComplexRationalNumber	euclideanDivision (const ComplexRationalNumber &b, ComplexRationalNumber *q=NULL) const
	Perform the eucldiean division of *this and b. More...

ComplexRationalNumber	extendedEuclidean (const ComplexRationalNumber &b, ComplexRationalNumber s=NULL, ComplexRationalNumber t=NULL) const
	Perform the extended euclidean division on *this and b. More...

ComplexRationalNumber	quotient (const ComplexRationalNumber &b) const
	Get the quotient of *this and b.

ComplexRationalNumber	remainder (const ComplexRationalNumber &b) const
	Get the remainder of *this and b.

ComplexRationalNumber	inverse () const
	Get the inverse of *this. More...

RationalNumber	realPart () const

RationalNumber	imaginaryPart () const

ComplexRationalNumber	conjugate () const

void	print (std::ostream &out) const
	Print the Ring element. More...

Detailed Description

An arbitrary-precision complex rational number.

Member Function Documentation

◆ convertToExpressionTree()

ExpressionTree ComplexRationalNumber::convertToExpressionTree ( ) const

inlinevirtual

Convert this to an expression tree.

returns an expression tree describing *this.

Implements ExpressionTreeConvert.

◆ euclideanDivision()

ComplexRationalNumber ComplexRationalNumber::euclideanDivision	(	const ComplexRationalNumber &	b,
		ComplexRationalNumber *	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< ComplexRationalNumber >.

◆ extendedEuclidean()

ComplexRationalNumber ComplexRationalNumber::extendedEuclidean	(	const ComplexRationalNumber &	b,
		ComplexRationalNumber *	s = `NULL`,
		ComplexRationalNumber *	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< ComplexRationalNumber >.

◆ gcd()

ComplexRationalNumber ComplexRationalNumber::gcd ( const ComplexRationalNumber & c ) const

inlinevirtual

GCD(a, b)

Parameters

b	The other rational number

Implements BPASGCDDomain< ComplexRationalNumber >.

◆ inverse()

ComplexRationalNumber ComplexRationalNumber::inverse ( ) const

inlinevirtual

Get the inverse of *this.

Returns: the inverse

Implements BPASField< ComplexRationalNumber >.

◆ isConstant()

int ComplexRationalNumber::isConstant ( ) const

inline

Is a constant.

Parameters

◆ isNegativeOne()

bool ComplexRationalNumber::isNegativeOne ( ) const

inline

Is a -1.

Parameters

◆ isOne()

bool ComplexRationalNumber::isOne ( ) const

inlinevirtual

Is a 1.

Parameters

Implements BPASRing< ComplexRationalNumber >.

◆ isZero()

bool ComplexRationalNumber::isZero ( ) const

inlinevirtual

Is a zero.

Parameters

Implements BPASRing< ComplexRationalNumber >.

◆ negativeOne()

void ComplexRationalNumber::negativeOne ( )

inline

Assign to negative one.

Parameters

◆ one()

void ComplexRationalNumber::one ( )

inlinevirtual

Assign to one.

Parameters

Implements BPASRing< ComplexRationalNumber >.

◆ operator!=()

bool ComplexRationalNumber::operator!= ( const ComplexRationalNumber & ) const

inlinevirtual

Inequality test,.

returns true iff not equal.

Implements BPASRing< ComplexRationalNumber >.

◆ operator%()

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

inlinevirtual

Get the remainder of *this and b;.

Parameters

b	the divisor

Returns: the remainder

Implements BPASEuclideanDomain< ComplexRationalNumber >.

◆ operator%=()

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

inlinevirtual

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

Parameters

b	the divisor

Returns: this after assignment.

Implements BPASEuclideanDomain< ComplexRationalNumber >.

◆ operator/()

ComplexRationalNumber ComplexRationalNumber::operator/ ( const ComplexRationalNumber & d ) const

inlinevirtual

Exact division.

Parameters

d	the divisor.

Returns: the equotient.

Implements BPASIntegralDomain< ComplexRationalNumber >.

◆ operator/=()

ComplexRationalNumber& ComplexRationalNumber::operator/= ( const ComplexRationalNumber & d )

inlinevirtual

Exact division assignment.

Parameters

d	the divisor.

Returns: a reference to this after assignment.

Implements BPASIntegralDomain< ComplexRationalNumber >.

◆ operator==()

bool ComplexRationalNumber::operator== ( const ComplexRationalNumber & ) const

inlinevirtual

Equality test,.

returns true iff equal

Implements BPASRing< ComplexRationalNumber >.

◆ operator^()

ComplexRationalNumber ComplexRationalNumber::operator^ ( long long int e ) const

inlinevirtual

Overload operator ^ replace xor operation by exponentiation.

Parameters

e	The exponentiation

Implements BPASRing< ComplexRationalNumber >.

◆ print()

void ComplexRationalNumber::print ( std::ostream & ostream ) const

virtual

Print the Ring element.

Derived classes may override this to get custom printing that may be more expressive (and prettier) than expression tree printing.

Reimplemented from BPASRing< ComplexRationalNumber >.

◆ unitCanonical()

ComplexRationalNumber ComplexRationalNumber::unitCanonical	(	ComplexRationalNumber *	u = `NULL`,
		ComplexRationalNumber *	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< ComplexRationalNumber >.

◆ zero()

void ComplexRationalNumber::zero ( )

inlinevirtual

Assign to zero.

Parameters

Implements BPASRing< ComplexRationalNumber >.

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

include/Ring/ComplexRationalNumber.hpp

Public Member Functions

Detailed Description

Member Function Documentation

◆ convertToExpressionTree()

◆ euclideanDivision()

◆ extendedEuclidean()

◆ gcd()

◆ inverse()

◆ isConstant()

◆ isNegativeOne()

◆ isOne()

◆ isZero()

◆ negativeOne()

◆ one()

◆ operator!=()

◆ operator%()

◆ operator%=()

◆ operator/()

◆ operator/=()

◆ operator==()

◆ operator^()

◆ print()

◆ unitCanonical()

◆ zero()