An abstract class defining the interface of a field. More...

#include <BPASField.hpp>

Simplified semantic inheritance diagram for BPASField< Derived >:

Full inheritance diagram for BPASField< Derived >:

Public Member Functions
virtual Derived	inverse () const =0
	Get the inverse of *this. More...

Public Member Functions inherited from BPASEuclideanDomain< Derived >
virtual Integer	euclideanSize () const =0
	Get the euclidean size of *this.

virtual Derived	euclideanDivision (const Derived &b, Derived *q=NULL) const =0
	Perform the eucldiean division of *this and b. More...

virtual Derived	extendedEuclidean (const Derived &b, Derived s=NULL, Derived t=NULL) const =0
	Perform the extended euclidean division on *this and b. More...

virtual Derived	quotient (const Derived &b) const =0
	Get the quotient of *this and b. More...

virtual Derived	remainder (const Derived &b) const =0
	Get the remainder of *this and b. More...

virtual Derived	operator% (const Derived &b) const =0
	Get the remainder of *this and b;. More...

virtual Derived &	operator%= (const Derived &b)=0
	Assign this to be the remainder of this and b. More...

Public Member Functions inherited from BPASGCDDomain< Derived >
virtual Derived	gcd (const Derived &other) const =0
	Get GCD of *this and other. More...

virtual Factors< Derived >	squareFree () const =0
	Compute squarefree factorization of *this. More...

Public Member Functions inherited from BPASIntegralDomain< Derived >
virtual Derived	operator/ (const Derived &d) const =0
	Exact division. More...

virtual Derived &	operator/= (const Derived &d)=0
	Exact division assignment. More...

Public Member Functions inherited from BPASRing< Derived >
virtual mpz_class	getCharacteristic () const
	The characteristic of this ring class.

virtual bool	isZero () const =0
	Determine if *this ring element is zero, that is the additive identity. More...

virtual void	zero ()=0
	Make *this ring element zero.

virtual bool	isOne () const =0
	Determine if *this ring element is one, that is the multiplication identity. More...

virtual void	one ()=0
	Make *this ring element one.

virtual Derived	unitCanonical (Derived u=NULL, Derived v=NULL) const =0
	Obtain the unit normal (a.k.a canonical associate) of an element. More...

virtual Derived &	operator= (const Derived &)=0
	Copy assignment.

virtual Derived	operator+ (const Derived &) const =0
	Addition.

virtual Derived &	operator+= (const Derived &)=0
	Addition assignment.

virtual Derived	operator- (const Derived &) const =0
	Subtraction.

virtual Derived &	operator-= (const Derived &)=0
	Subtraction assignment.

virtual Derived	operator- () const =0
	Negation.

virtual Derived	operator* (const Derived &) const =0
	Multiplication.

virtual Derived &	operator*= (const Derived &)=0
	Multiplication assignment.

virtual Derived	operator^ (long long int e) const =0
	Exponentiation.

virtual Derived &	operator^= (long long int e)=0
	Exponentiation assignment.

virtual bool	operator== (const Derived &) const =0
	Equality test,. More...

virtual bool	operator!= (const Derived &) const =0
	Inequality test,. More...

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

virtual std::string	toString () const
	Convert the Ring element to a string. More...

Public Member Functions inherited from ExpressionTreeConvert
virtual ExpressionTree	convertToExpressionTree () const =0
	Convert this to an expression tree. More...