linbox

field specification and archetypical instance. More...
#include <archetype.h>
Public Types  
Common Object Interface for a LinBox Field.  
These methods are required of all LinBox fields.  
typedef ElementArchetype  Element 
the type in which field elements are represented.  
typedef RandIterArchetype  RandIter 
An object of this type is a generator of random field elements.  
Public Member Functions  
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.  
bool  areEqual (const Element &x, const Element &y) const 
Equality of two elements. More...  
Element &  add (Element &x, const Element &y, const Element &z) const 
Addition, x <– y + z. More...  
Element &  sub (Element &x, const Element &y, const Element &z) const 
Subtraction, x <– y  z. More...  
Element &  mul (Element &x, const Element &y, const Element &z) const 
Multiplication, x <– y * z. More...  
Element &  div (Element &x, const Element &y, const Element &z) const 
Division, x <– y / z. More...  
Element &  neg (Element &x, const Element &y) const 
Additive Inverse (Negation), x <–  y. More...  
Element &  inv (Element &x, const Element &y) const 
Multiplicative Inverse, x <– 1 / y. More...  
Element &  axpy (Element &r, const Element &a, const Element &x, const Element &y) const 
Field element AXPY, r <– a * x + y. More...  
Predicates  
bool  isZero (const Element &x) const 
Zero equality. More...  
bool  isOne (const Element &x) const 
One equality. More...  
bool  isMOne (const Element &x) const 
MOne equality. More...  
Inplace Arithmetic Operations  
x < x op y; x < op x These operations require all elements, including x, to be initialized before the operation is called. Uninitialized field elements will give undefined results.  
Element &  addin (Element &x, const Element &y) const 
Inplace Addition. More...  
Element &  subin (Element &x, const Element &y) const 
Inplace Subtraction. More...  
Element &  mulin (Element &x, const Element &y) const 
Inplace Multiplication. More...  
Element &  divin (Element &x, const Element &y) const 
Inplace Division. More...  
Element &  negin (Element &x) const 
Inplace Additive Inverse (Inplace Negation). More...  
Element &  invin (Element &x) const 
Inplace Multiplicative Inverse. More...  
Element &  axpyin (Element &r, const Element &a, const Element &x) const 
Inplace AXPY. More...  
Input/Output Operations  
std::ostream &  write (std::ostream &os) const 
Print field. More...  
std::ostream &  write (std::ostream &os, const Element &x) const 
Print field element. More...  
std::istream &  read (std::istream &is, Element &x) const 
Read field element. More...  
ImplementationSpecific Methods.  
These methods are not required of all LinBox\ Fields and are included only for this implementation of the archetype.  
FieldArchetype (FieldAbstract *field_ptr, ElementAbstract *elem_ptr, RandIterAbstract *randIter_ptr=0)  
Constructor. More...  
template<class Field_qcq >  
FieldArchetype (Field_qcq *f)  
Constructor. More...  
Protected Member Functions  
template<class Field_qcq >  
void  constructor (FieldAbstract *trait, Field_qcq *field_ptr) 
Template method for constructing archetype from a derived class of FieldAbstract. More...  
template<class Field_qcq >  
void  constructor (void *trait, Field_qcq *field_ptr) 
Template method for constructing archetype from a class not derived from FieldAbstract. More...  
FieldArchetype ()  
Only authorize inhertied classes to use the empty constructor.  
Protected Attributes  
FieldAbstract *  _field_ptr 
Pointer to FieldAbstract object. More...  
ElementAbstract *  _elem_ptr 
Pointer to ElementAbstract object. More...  
RandIterAbstract *  _randIter_ptr 
Pointer to RandIterAbstract object. More...  
Object Management  
Element  one 
Copy constructor. More...  
Element  zero 
Copy constructor. More...  
Element  mOne 
Copy constructor. More...  
FieldArchetype (const FieldArchetype &F)  
Copy constructor. More...  
~FieldArchetype (void)  
Destructor. More...  
FieldArchetype &  operator= (const FieldArchetype &F) 
Assignment operator. More...  
Element &  init (Element &x, const integer &n=0) const 
Initialization of field element from an integer. More...  
integer &  convert (integer &n, const Element &y=0) const 
Conversion of field element to an integer. More...  
Element &  assign (Element &x, const Element &y) const 
Assignment of one field element to another. More...  
integer &  cardinality (integer &c) const 
Cardinality. More...  
integer &  characteristic (integer &c) const 
Characteristic. More...  
field specification and archetypical instance.
The FieldArchetype and its encapsulated element class contain pointers to the FieldAbstract and its encapsulated field element, respectively. FieldAbstract then uses virtual member functions to define operations on its encapsulated field element. This field element has no knowledge of the field properties being used on it which means the field object must supply these operations.
It does not contain elements zero and one because they can be created whenever necessary, although it might be beneficial from an efficiency stand point to include them. However, because of archetype use three, the elements themselves cannot be contained, but rather pointers to them.

inline 
Copy constructor.
Each field class is expected to provide a copy constructor. This is required to allow field objects to be passed by value into functions.
In this archetype implementation, this means copying the field to which F._field_ptr
points, the element to which F._elem_ptr
points, and the random element generator to which F._randIter_ptr
points.

inline 
Destructor.
This destroys the field object, but it does not destroy any field element objects.
In this archetype implementation, destruction is deletion of the field object to which _field_ptr
points, the field element to which _elem_ptr
points, and the random element generator to which _randIter_ptr
points.

inline 
Constructor.
Constructs field from pointer to FieldAbstract and its encapsulated element and random element generator. Not part of the interface. Creates new copies of field, element, and random iterator generator objects in dynamic memory.
field_ptr  pointer to FieldAbstract. 
elem_ptr  pointer to ElementAbstract, which is the encapsulated element of FieldAbstract. 
randIter_ptr  pointer to RandIterAbstract, which is the encapsulated random iterator generator of FieldAbstract. 

inline 
Constructor.
Constructs field from ANYTHING matching the interface using the enveloppe as a FieldAbstract and its encapsulated element and random element generator if needed.
f 

inline 
Assignment operator.
In this archetype implementation, this means copying the field to which F._field_ptr
points, the element to which F._elem_ptr
points, and the random element generator to which F._randIter_ptr
points.
F  FieldArchetype object. 
Initialization of field element from an integer.
x becomes the image of n under the natural map from the integers to the prime subfield. It is the result obtained from adding n 1's in the field.
This function assumes the output field element x has already been constructed, but that it is not necessarily already initialized. In this archetype implementation, this means the _elem_ptr
of x exists, but that it may be the null pointer.
x  output field element. 
n  input integer. 
Conversion of field element to an integer.
The meaning of conversion is specific to each field class. However, if x is in the prime subfield, the integer n returned is such that an init from n will reproduce x. Most often, .
n  output integer. 
y  input field element. 
Assignment of one field element to another.
This function assumes both field elements have already been constructed and initialized.
In this archetype implementation, this means for both x and y, _elem_ptr
exists and does not point to null.
x  destination field element. 
y  source field element. 
Cardinality.
Return c, integer representing cardinality of the field. c becomes a nonnegative integer for all fields with finite cardinality, and 1 to signify a field of infinite cardinality.
Characteristic.
Return c, integer representing characteristic of the field (the least positive n such that the sum of n copies of x is 0 for all field elements x). c becomes a positive integer for all fields with finite characteristic, and 0 to signify a field of infinite characteristic.
Equality of two elements.
This function assumes both field elements have already been constructed and initialized.
In this implementation, this means for both x and y, _elem_ptr
exists and does not point to null.
x  field element 
y  field element 
Addition, x <– y + z.
This function assumes all the field elements have already been constructed and initialized.
In this implementation, this means for x, y, and z, _elem_ptr
exists and does not point to null.
Subtraction, x <– y  z.
This function assumes all the field elements have already been constructed and initialized.
In this implementation, this means for x, y, and z, _elem_ptr
exists and does not point to null.
Multiplication, x <– y * z.
This function assumes all the field elements have already been constructed and initialized.
In this implementation, this means for x, y, and z, _elem_ptr
exists and does not point to null.
Division, x <– y / z.
This function assumes all the field elements have already been constructed and initialized.
In this implementation, this means for x, y, and z, _elem_ptr
exists and does not point to null.
Additive Inverse (Negation), x <–  y.
This function assumes both field elements have already been constructed and initialized.
In this implementation, this means for both x and y _elem_ptr
exists and does not point to null.
Multiplicative Inverse, x <– 1 / y.
Requires that y is a unit (i.e. nonzero in a field). This function assumes both field elements have already been constructed and initialized.
In this implementation, this means for both x and y _elem_ptr
exists and does not point to null.
Field element AXPY, r <– a * x + y.
This function assumes all field elements have already been constructed and initialized.

inline 
Zero equality.
Test if field element is equal to zero. This function assumes the field element has already been constructed and initialized.
In this implementation, this means the _elem_ptr
of x exists and does not point to null.
x  field element. 

inline 
One equality.
Test if field element is equal to one. This function assumes the field element has already been constructed and initialized.
In this implementation, this means the _elem_ptr
of x exists and does not point to null.
x  field element. 

inline 
MOne equality.
Test if field element is equal to one. This function assumes the field element has already been constructed and initialized.
In this implementation, this means the _elem_ptr
of x exists and does not point to null.
x  field element. 
Inplace Addition.
x += y This function assumes both field elements have already been constructed and initialized.
In this implementation, this means for both x and y _elem_ptr
exists and does not point to null.
x  field element (reference returned). 
y  field element. 
Inplace Subtraction.
x = y This function assumes both field elements have already been constructed and initialized.
In this implementation, this means for both x and y _elem_ptr
exists and does not point to null.
x  field element (reference returned). 
y  field element. 
Inplace Multiplication.
x *= y This function assumes both field elements have already been constructed and initialized.
In this implementation, this means for both x and y _elem_ptr
exists and does not point to null.
x  field element (reference returned). 
y  field element. 
Inplace Division.
x /= y This function assumes both field elements have already been constructed and initialized.
In this implementation, this means for both x and y _elem_ptr
exists and does not point to null.
x  field element (reference returned). 
y  field element. 
Inplace Additive Inverse (Inplace Negation).
x =  x This function assumes the field element has already been constructed and initialized.
In this implementation, this means the _elem_ptr
of x exists and does not point to null.
x  field element (reference returned). 
Inplace Multiplicative Inverse.
x = 1 / x This function assumes the field elementhas already been constructed and initialized.
In this implementation, this means the _elem_ptr
of x exists and does not point to null.
x  field element (reference returned). 
Inplace AXPY.
r += a * x This function assumes all field elements have already been constructed and initialized.
r  field element (reference returned). 
a  field element. 
x  field element. 

inline 
Print field.
os  output stream to which field is written. 

inline 
Print field element.
This function assumes the field element has already been constructed and initialized.
In this implementation, this means for the _elem_ptr
for x exists and does not point to null.
os  output stream to which field element is written. 
x  field element. 

inline 
Read field element.
This function assumes the field element has already been constructed and initialized.
In this implementation, this means for the _elem_ptr
for x exists and does not point to null.
is  input stream from which field element is read. 
x  field element. 

inlineprotected 
Template method for constructing archetype from a derived class of FieldAbstract.
This class is needed to help the constructor differentiate between classes derived from FieldAbstract and classes that aren't. Should be called with the same argument to both parameters?
trait  pointer to FieldAbstract or class derived from it 
field_ptr  pointer to class derived from FieldAbstract 

inlineprotected 
Template method for constructing archetype from a class not derived from FieldAbstract.
This class is needed to help the constructor differentiate between classes derived from FieldAbstract and classes that aren't. Should be called with the same argument to both parameters?
trait  pointer to class not derived from FieldAbstract 
field_ptr  pointer to class not derived from FieldAbstract 
Element one 
Copy constructor.
Each field class is expected to provide a copy constructor. This is required to allow field objects to be passed by value into functions.
In this archetype implementation, this means copying the field to which F._field_ptr
points, the element to which F._elem_ptr
points, and the random element generator to which F._randIter_ptr
points.
Element zero 
Copy constructor.
Each field class is expected to provide a copy constructor. This is required to allow field objects to be passed by value into functions.
In this archetype implementation, this means copying the field to which F._field_ptr
points, the element to which F._elem_ptr
points, and the random element generator to which F._randIter_ptr
points.
Element mOne 
Copy constructor.
Each field class is expected to provide a copy constructor. This is required to allow field objects to be passed by value into functions.
In this archetype implementation, this means copying the field to which F._field_ptr
points, the element to which F._elem_ptr
points, and the random element generator to which F._randIter_ptr
points.

mutableprotected 
Pointer to FieldAbstract object.
Not part of the interface. Included to allow for archetype use three.

mutableprotected 
Pointer to ElementAbstract object.
Not part of the interface. Included to allow for archetype use three.

mutableprotected 
Pointer to RandIterAbstract object.
Not part of the interface. Included to allow for archetype use three.