Parent class for rational, quadratic and rc7 integers. More...

#include <algebraicinteger.h>

Inheritance diagram for AlgebraicInteger:

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Public Member Functions
virtual AlgebraicInteger *	aiCopyToInteger (const int &n) const =0
	Create an algebraic integer from an integer. More...

virtual AlgebraicInteger *	copy () const =0
	Create a copy of an algebraic integer. More...

virtual void	set (const int &n)=0
	Assign an integer to the algebraic integer. More...

virtual void	set (AlgebraicInteger *ai)=0
	Assign an algebraic integer to the algebraic integer. More...

virtual void	removeSquareFactors ()=0
	Remove all the square factors of the algebraic integer.

virtual bool	bIsInvertible () const =0
	Check whether the number is invertible. More...

virtual bool	bIsSquareOfIvertible () const =0
	Check whether the number is the square of an invertible element. More...

virtual void	gcd (const AlgebraicInteger *ai)=0
	this becomes the gcd of this and the parameter More...

virtual bool	bIsDivisbleBy (const AlgebraicInteger *ai) const =0
	Check whether *this is divisible by the parameter. More...

virtual void	divideBy (const AlgebraicInteger *ai)=0
	Performs the division of this by the parameter Remark: we do not check that the this is divisible by *ai. If it is not the case, the division will be an approximation! More...

virtual void	multiplyBy (const int &n)=0
	Performs the multiplication of *this by the parameter. More...

virtual void	multiplyBy (const AlgebraicInteger *ai)=0
	Performs the multiplication of *this by the parameter. More...

virtual void	add (const AlgebraicInteger *ai)=0
	Performs the addition of *this by the parameter. More...

virtual void	substract (const AlgebraicInteger *ai)=0
	Substracts the parameter from *this. More...

virtual void	opp ()=0
	Computes the opp.

virtual bool	bIsLessThan (const int &n) const =0
	Check whether *this < n.

virtual bool	bIsLessThan (const AlgebraicInteger &ai) const =0
	Check whether *this < ai.

virtual bool	bIsLessOEThan (const AlgebraicInteger &ai) const =0
	Check whether *this <= ai.

virtual bool	bIsGreaterThan (const int &n) const =0
	Check whether *this > n.

virtual bool	bIsGreaterOEThan (const int &n) const =0
	Check whether *this >= n.

virtual bool	bIsEqualTo (const AlgebraicInteger &ai) const =0
	Check whether *this == ai.

virtual bool	bIsEqualTo (const int &n) const =0
	Check whether *this == n.

bool	operator== (const AlgebraicInteger &ai) const
	Check whether *this == ai.

bool	operator!= (const int &n) const
	Check whether *this != n.

bool	operator!= (const AlgebraicInteger &ai) const
	Check whether *this != ai.

virtual ostream &	print (ostream &) const
	Print the number.

virtual string	to_string (const string &strFormat="generic", const bool &bProtect=false) const =0
	Convert to string. More...

virtual double	to_double () const =0
	Convert to double (approximation)

virtual string	get_classname () const =0
	Return the type (string)

Friends
ostream &	operator<< (ostream &, AlgebraicInteger const &)

Detailed Description

Parent class for rational, quadratic and rc7 integers.

Member Function Documentation

AlgebraicInteger::add ( const AlgebraicInteger * ai )

pure virtual

Performs the addition of *this by the parameter.

Parameters

ai(	const AlgebraicInteger* ) Pointer to the summand

Implemented in QuadraticIntegerBig, RCyclotomic7Integer, QuadraticInteger, and RationalInteger.

AlgebraicInteger::aiCopyToInteger ( const int & n ) const

pure virtual

Create an algebraic integer from an integer.

Parameters

n(	const int ): Integer

Returns: Pointer to the algebraic integer created

Implemented in QuadraticIntegerBig, RCyclotomic7Integer, QuadraticInteger, and RationalInteger.

AlgebraicInteger::bIsDivisbleBy ( const AlgebraicInteger * ai ) const

pure virtual

Check whether *this is divisible by the parameter.

Parameters

ai(	const AlgebraicInteger* ) Pointer to the divisor

Returns: True if *this is divisible by the parameter

Implemented in QuadraticIntegerBig, RCyclotomic7Integer, QuadraticInteger, and RationalInteger.

AlgebraicInteger::bIsInvertible ( ) const

pure virtual

Check whether the number is invertible.

Returns: True if invertible or not

Implemented in QuadraticIntegerBig, RCyclotomic7Integer, QuadraticInteger, and RationalInteger.

AlgebraicInteger::bIsSquareOfIvertible ( ) const

pure virtual

Check whether the number is the square of an invertible element.

Returns: True if invertible or not

Implemented in QuadraticIntegerBig, QuadraticInteger, RCyclotomic7Integer, and RationalInteger.

AlgebraicInteger::copy ( ) const

pure virtual

Create a copy of an algebraic integer.

Returns: Pointer to the algebraic integer created

Implemented in QuadraticIntegerBig, RCyclotomic7Integer, QuadraticInteger, and RationalInteger.

AlgebraicInteger::divideBy ( const AlgebraicInteger * ai )

pure virtual

Performs the division of *this by the parameter Remark: we do not check that the *this is divisible by *ai. If it is not the case, the division will be an approximation!

Parameters

ai(	const AlgebraicInteger* ) Pointer to the divisor

Implemented in QuadraticIntegerBig, RCyclotomic7Integer, QuadraticInteger, and RationalInteger.

AlgebraicInteger::gcd ( const AlgebraicInteger * ai )

pure virtual

*this becomes the gcd of *this and the parameter

Parameters

ai(	const AlgebraicInteger* ) The other algebraic integer

Implemented in QuadraticIntegerBig, RCyclotomic7Integer, QuadraticInteger, and RationalInteger.

AlgebraicInteger::multiplyBy ( const int & n )

pure virtual

Performs the multiplication of *this by the parameter.

Parameters

ai(	const AlgebraicInteger* ) Pointer to the multiplicand

Implemented in QuadraticIntegerBig, RCyclotomic7Integer, QuadraticInteger, and RationalInteger.

AlgebraicInteger::multiplyBy ( const AlgebraicInteger * ai )

pure virtual

Performs the multiplication of *this by the parameter.

Parameters

ai(	const AlgebraicInteger* ) Pointer to the multiplicand

Implemented in QuadraticIntegerBig, QuadraticInteger, RCyclotomic7Integer, and RationalInteger.

AlgebraicInteger::set ( const int & n )

pure virtual

Assign an integer to the algebraic integer.

Parameters

n(	const int& ) Integer

Implemented in QuadraticIntegerBig, QuadraticInteger, RCyclotomic7Integer, and RationalInteger.

AlgebraicInteger::set ( AlgebraicInteger * ai )

pure virtual

Assign an algebraic integer to the algebraic integer.

Parameters

ai(	AlgebraicInteger* ) Pointer to the algebraic integer

Implemented in QuadraticIntegerBig, QuadraticInteger, RCyclotomic7Integer, and RationalInteger.

AlgebraicInteger::substract ( const AlgebraicInteger * ai )

pure virtual

Substracts the parameter from *this.

Parameters

ai(	const AlgebraicInteger* ) Pointer to the subtrahend

Implemented in QuadraticIntegerBig, RCyclotomic7Integer, QuadraticInteger, and RationalInteger.

string AlgebraicInteger::to_string	(	const string &	strFormat = `"generic"`,
		const bool &	bProtect = `false`
	)		const

pure virtual

Convert to string.

Parameters

strFormat(	const string& ): Format for the output; can be: generic, mathematica, pari, latex
bProtect(	const bool& ): If true, avoid certain characters (for example if the string is used in for a file name)

Implemented in QuadraticIntegerBig, RCyclotomic7Integer, QuadraticInteger, and RationalInteger.

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

algebraicinteger.h
algebraicinteger.cpp

Public Member Functions

Friends

Detailed Description

Member Function Documentation