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FieldAbstract Class Referenceabstract

field base class. More...

#include <abstract.h>

+ Inheritance diagram for FieldAbstract:

Public Types

typedef ElementAbstract Element
 element type.
 
typedef RandIterAbstract RandIter
 Random iterator generator type.
 

Public Member Functions

Object Management

There are no public constructors for this class.

It should only be used in tandem with FieldArchetype.

virtual ~FieldAbstract (void)
 Destructor. More...
 
virtual FieldAbstractclone () const =0
 Virtual copy constructor. More...
 
virtual FieldAbstractoperator= (const FieldAbstract &F)=0
 Assignment operator. More...
 
virtual Elementinit (Element &x, const integer &y) const =0
 Initialization of field element from an integer. More...
 
virtual integerconvert (integer &x, const Element &y) const =0
 Conversion of field element to an integer. More...
 
virtual Elementassign (Element &x, const Element &y) const =0
 Assignment of one field element to another. More...
 
virtual integercardinality (integer &c) const =0
 Cardinality. More...
 
virtual integercharacteristic (integer &c) const =0
 Characteristic. More...
 
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.

virtual bool areEqual (const Element &x, const Element &y) const =0
 Equality of two elements. More...
 
virtual Elementadd (Element &x, const Element &y, const Element &z) const =0
 Addition. More...
 
virtual Elementsub (Element &x, const Element &y, const Element &z) const =0
 Subtraction. More...
 
virtual Elementmul (Element &x, const Element &y, const Element &z) const =0
 Multiplication. More...
 
virtual Elementdiv (Element &x, const Element &y, const Element &z) const =0
 Division. More...
 
virtual Elementneg (Element &x, const Element &y) const =0
 Additive Inverse (Negation). More...
 
virtual Elementinv (Element &x, const Element &y) const =0
 Multiplicative Inverse. More...
 
virtual Elementaxpy (Element &r, const Element &a, const Element &x, const Element &y) const =0
 Natural AXPY. More...
 
Inplace Arithmetic Operations

x <- x op y; x <- op x

virtual bool isZero (const Element &x) const =0
 Zero equality. More...
 
virtual bool isOne (const Element &x) const =0
 One equality. More...
 
virtual bool isMOne (const Element &x) const =0
 MOne equality. More...
 
virtual Elementaddin (Element &x, const Element &y) const =0
 Inplace Addition. More...
 
virtual Elementsubin (Element &x, const Element &y) const =0
 Inplace Subtraction. More...
 
virtual Elementmulin (Element &x, const Element &y) const =0
 Inplace Multiplication. More...
 
virtual Elementdivin (Element &x, const Element &y) const =0
 Inplace Division. More...
 
virtual Elementnegin (Element &x) const =0
 Inplace Additive Inverse (Inplace Negation). More...
 
virtual Elementinvin (Element &x) const =0
 Inplace Multiplicative Inverse. More...
 
virtual Elementaxpyin (Element &r, const Element &a, const Element &x) const =0
 Inplace AXPY. More...
 
Input/Output Operations
virtual std::ostream & write (std::ostream &os) const =0
 Print field. More...
 
virtual std::ostream & write (std::ostream &os, const Element &x) const =0
 Print field element. More...
 
virtual std::istream & read (std::istream &is, Element &x) const =0
 Read field element. More...
 

Protected Member Functions

 FieldAbstract ()
 Default Constructor. More...
 

Friends

class FieldArchetype
 FieldArchetype is friend.
 

Detailed Description

field base class.

Found in the file

See Also
{linbox/field/abstract.h}. Abstract base class used to implement the field archetype to minimize code bloat. All public member functions of this class are purely virtual and must be implemented by all derived classes.

If a template is instantiated on the field archetype, we can change the field it is using by changing the derived class of this class. This allows us to change the field used in a template without having to reinstantiate it. This minimizes code bloat, but it also introduces indirection through the use of pointers and virtual functions which is inefficient.

Constructor & Destructor Documentation

virtual ~FieldAbstract ( void  )
inlinevirtual

Destructor.

Required because of virtual member functions. Virtual.

FieldAbstract ( )
inlineprotected

Default Constructor.

Required by derived classes, but protected because this class should never be constructed by itself.

Member Function Documentation

virtual FieldAbstract* clone ( ) const
pure virtual

Virtual copy constructor.

Required because constructors cannot be virtual. Passes construction on to derived classes. Purely virtual. This function is not part of the common object interface.

Returns
pointer to new object in dynamic memory.

Implemented in FieldEnvelope< Field >, FieldEnvelope< Ring >, and RingEnvelope< Field >.

virtual FieldAbstract& operator= ( const FieldAbstract F)
pure virtual

Assignment operator.

Purely virtual.

Returns
reference to self
Parameters
Fconstant reference to FieldAbstract object

Implemented in RingEnvelope< Field >, FieldEnvelope< Field >, and FieldEnvelope< Ring >.

virtual Element& init ( Element x,
const integer y 
) const
pure virtual

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 already initialized. Purely virtual.

Returns
reference to field element.
Parameters
xfield element to contain output (reference returned).
yinteger.

Implemented in FieldEnvelope< Field >, RingEnvelope< Field >, and FieldEnvelope< Ring >.

virtual integer& convert ( integer x,
const Element y 
) const
pure virtual

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. Purely virtual.

Returns
reference to integer.
Parameters
xreference to interger to contain output (reference returned).
yconstant field element.

Implemented in FieldEnvelope< Field >, FieldEnvelope< Ring >, and RingEnvelope< Field >.

virtual Element& assign ( Element x,
const Element y 
) const
pure virtual

Assignment of one field element to another.

This function assumes both field elements have already been constructed and initialized. Purely virtual.

Returns
reference to x
Parameters
xfield element (reference returned).
yfield element.

Implemented in FieldEnvelope< Field >, FieldEnvelope< Ring >, and RingEnvelope< Field >.

virtual integer& cardinality ( integer c) const
pure virtual

Cardinality.

Return integer representing cardinality of the domain. Returns a non-negative integer for all domains with finite cardinality, and returns -1 to signify a domain of infinite cardinality. Purely virtual.

Returns
integer representing cardinality of the domain

Implemented in FieldEnvelope< Field >, FieldEnvelope< Ring >, and RingEnvelope< Field >.

virtual integer& characteristic ( integer c) const
pure virtual

Characteristic.

Return integer representing characteristic of the domain. Returns a positive integer to all domains with finite characteristic, and returns 0 to signify a domain of infinite characteristic. Purely virtual.

Returns
integer representing characteristic of the domain.

Implemented in FieldEnvelope< Field >, FieldEnvelope< Ring >, and RingEnvelope< Field >.

virtual bool areEqual ( const Element x,
const Element y 
) const
pure virtual

Equality of two elements.

This function assumes both field elements have already been constructed and initialized. Purely virtual.

Returns
boolean true if equal, false if not.
Parameters
xfield element
yfield element

Implemented in FieldEnvelope< Field >, FieldEnvelope< Ring >, and RingEnvelope< Field >.

virtual Element& add ( Element x,
const Element y,
const Element z 
) const
pure virtual

Addition.

x = y + z This function assumes all the field elements have already been constructed and initialized. Purely virtual.

Returns
reference to x.
Parameters
xfield element (reference returned).
yfield element.
zfield element.

Implemented in FieldEnvelope< Field >, FieldEnvelope< Ring >, and RingEnvelope< Field >.

virtual Element& sub ( Element x,
const Element y,
const Element z 
) const
pure virtual

Subtraction.

x = y - z This function assumes all the field elements have already been constructed and initialized. Purely virtual.

Returns
reference to x.
Parameters
xfield element (reference returned).
yfield element.
zfield element.

Implemented in FieldEnvelope< Field >, FieldEnvelope< Ring >, and RingEnvelope< Field >.

virtual Element& mul ( Element x,
const Element y,
const Element z 
) const
pure virtual

Multiplication.

x = y * z This function assumes all the field elements have already been constructed and initialized. Purely virtual.

Returns
reference to x.
Parameters
xfield element (reference returned).
yfield element.
zfield element.

Implemented in FieldEnvelope< Field >, FieldEnvelope< Ring >, and RingEnvelope< Field >.

virtual Element& div ( Element x,
const Element y,
const Element z 
) const
pure virtual

Division.

x = y / z This function assumes all the field elements have already been constructed and initialized. Purely virtual.

Returns
reference to x.
Parameters
xfield element (reference returned).
yfield element.
zfield element.

Implemented in FieldEnvelope< Field >, FieldEnvelope< Ring >, and RingEnvelope< Field >.

virtual Element& neg ( Element x,
const Element y 
) const
pure virtual

Additive Inverse (Negation).

x = - y This function assumes both field elements have already been constructed and initialized. Purely virtual.

Returns
reference to x.
Parameters
xfield element (reference returned).
yfield element.

Implemented in FieldEnvelope< Field >, FieldEnvelope< Ring >, and RingEnvelope< Field >.

virtual Element& inv ( Element x,
const Element y 
) const
pure virtual

Multiplicative Inverse.

x = 1 / y This function assumes both field elements have already been constructed and initialized. Purely virtual.

Returns
reference to x.
Parameters
xfield element (reference returned).
yfield element.

Implemented in FieldEnvelope< Field >, FieldEnvelope< Ring >, and RingEnvelope< Field >.

virtual Element& axpy ( Element r,
const Element a,
const Element x,
const Element y 
) const
pure virtual

Natural AXPY.

r = a * x + y This function assumes all field elements have already been constructed and initialized. Purely virtual.

Returns
reference to r.
Parameters
rfield element (reference returned).
afield element.
xfield element.
yfield element.

Implemented in FieldEnvelope< Field >, FieldEnvelope< Ring >, and RingEnvelope< Field >.

virtual bool isZero ( const Element x) const
pure virtual

Zero equality.

Test if field element is equal to zero. This function assumes the field element has already been constructed and initialized. Purely virtual.

Returns
boolean true if equals zero, false if not.
Parameters
xfield element.

Implemented in FieldEnvelope< Field >, FieldEnvelope< Ring >, and RingEnvelope< Field >.

virtual bool isOne ( const Element x) const
pure virtual

One equality.

Test if field element is equal to one. This function assumes the field element has already been constructed and initialized. Purely virtual.

Returns
boolean true if equals one, false if not.
Parameters
xfield element.

Implemented in FieldEnvelope< Field >, FieldEnvelope< Ring >, and RingEnvelope< Field >.

virtual bool isMOne ( const Element x) const
pure virtual

MOne equality.

Test if field element is equal to one. This function assumes the field element has already been constructed and initialized. Purely virtual.

Returns
boolean true if equals one, false if not.
Parameters
xfield element.

Implemented in FieldEnvelope< Field >, and FieldEnvelope< Ring >.

virtual Element& addin ( Element x,
const Element y 
) const
pure virtual

Inplace Addition.

x += y This function assumes both field elements have already been constructed and initialized. Purely virtual.

Returns
reference to x.
Parameters
xfield element (reference returned).
yfield element.

Implemented in FieldEnvelope< Field >, FieldEnvelope< Ring >, and RingEnvelope< Field >.

virtual Element& subin ( Element x,
const Element y 
) const
pure virtual

Inplace Subtraction.

x -= y This function assumes both field elements have already been constructed and initialized. Purely virtual.

Returns
reference to x.
Parameters
xfield element (reference returned).
yfield element.

Implemented in FieldEnvelope< Field >, FieldEnvelope< Ring >, and RingEnvelope< Field >.

virtual Element& mulin ( Element x,
const Element y 
) const
pure virtual

Inplace Multiplication.

x *= y This function assumes both field elements have already been constructed and initialized. Purely virtual.

Returns
reference to x.
Parameters
xfield element (reference returned).
yfield element.

Implemented in FieldEnvelope< Field >, FieldEnvelope< Ring >, and RingEnvelope< Field >.

virtual Element& divin ( Element x,
const Element y 
) const
pure virtual

Inplace Division.

x /= y This function assumes both field elements have already been constructed and initialized. Purely virtual.

Returns
reference to x.
Parameters
xfield element (reference returned).
yfield element.

Implemented in FieldEnvelope< Field >, FieldEnvelope< Ring >, and RingEnvelope< Field >.

virtual Element& negin ( Element x) const
pure virtual

Inplace Additive Inverse (Inplace Negation).

x = - x This function assumes the field element has already been constructed and initialized. Purely virtual.

Returns
reference to x.
Parameters
xfield element (reference returned).

Implemented in FieldEnvelope< Field >, FieldEnvelope< Ring >, and RingEnvelope< Field >.

virtual Element& invin ( Element x) const
pure virtual

Inplace Multiplicative Inverse.

x = 1 / x This function assumes the field elementhas already been constructed and initialized. Purely virtual.

Returns
reference to x.
Parameters
xfield element (reference returned).

Implemented in FieldEnvelope< Field >, FieldEnvelope< Ring >, and RingEnvelope< Field >.

virtual Element& axpyin ( Element r,
const Element a,
const Element x 
) const
pure virtual

Inplace AXPY.

r += a * x This function assumes all field elements have already been constructed and initialized. Purely virtual

Returns
reference to r.
Parameters
rfield element (reference returned).
afield element.
xfield element.

Implemented in FieldEnvelope< Field >, FieldEnvelope< Ring >, and RingEnvelope< Field >.

virtual std::ostream& write ( std::ostream &  os) const
pure virtual

Print field.

Purely virtual.

Returns
output stream to which field is written.
Parameters
osoutput stream to which field is written.

Implemented in FieldEnvelope< Field >, FieldEnvelope< Ring >, and RingEnvelope< Field >.

virtual std::ostream& write ( std::ostream &  os,
const Element x 
) const
pure virtual

Print field element.

This function assumes the field element has already been constructed and initialized. Purely virtual.

Returns
output stream to which field element is written.
Parameters
osoutput stream to which field element is written.
xfield element.

Implemented in FieldEnvelope< Field >, FieldEnvelope< Ring >, and RingEnvelope< Field >.

virtual std::istream& read ( std::istream &  is,
Element x 
) const
pure virtual

Read field element.

This function assumes the field element has already been constructed and initialized. Purely virtual.

Returns
input stream from which field element is read.
Parameters
isinput stream from which field element is read.
xfield element.

Implemented in FieldEnvelope< Field >, FieldEnvelope< Ring >, and RingEnvelope< Field >.


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