NZMATH  1.2.0
About: NZMATH is a Python based number theory oriented calculation system.
  Fossies Dox: NZMATH-1.2.0.tar.gz  ("inofficial" and yet experimental doxygen-generated source code documentation)  

nzmath.real.RealField Class Reference
Inheritance diagram for nzmath.real.RealField:
[legend]
Collaboration diagram for nzmath.real.RealField:
[legend]

Public Member Functions

def __init__ (self)
 
def __str__ (self)
 
def __repr__ (self)
 
def __contains__ (self, element)
 
def __eq__ (self, other)
 
def __ne__ (self, other)
 
def __hash__ (self)
 
def issubring (self, aRing)
 
def issuperring (self, aRing)
 
def createElement (self, seed)
 
def getCharacteristic (self)
 
- Public Member Functions inherited from nzmath.ring.Field
def createElement (self, *args)
 
def isfield (self)
 
def gcd (self, a, b)
 
def getQuotientField (self)
 
- Public Member Functions inherited from nzmath.ring.CommutativeRing
def isdomain (self)
 
def isnoetherian (self)
 
def isufd (self)
 
def ispid (self)
 
def iseuclidean (self)
 
def registerModuleAction (self, action_ring, action)
 
def hasaction (self, action_ring)
 
def getaction (self, action_ring)
 
- Public Member Functions inherited from nzmath.ring.Ring
def getCommonSuperring (self, other)
 

Properties

 one = property(_getOne, None, None, "multiplicative unit.")
 
 zero = property(_getZero, None, None, "additive unit.")
 

Private Member Functions

def _getOne (self)
 
def _getZero (self)
 

Private Attributes

 _one
 
 _zero
 

Additional Inherited Members

- Public Attributes inherited from nzmath.ring.CommutativeRing
 properties
 

Detailed Description

RealField is a class of the field of real numbers.
The class has the single instance 'theRealField'.

Definition at line 131 of file real.py.

Constructor & Destructor Documentation

◆ __init__()

def nzmath.real.RealField.__init__ (   self)
Set field flag True of 'properties' attribute.

Reimplemented from nzmath.ring.Field.

Definition at line 137 of file real.py.

Member Function Documentation

◆ __contains__()

def nzmath.real.RealField.__contains__ (   self,
  element 
)

Definition at line 148 of file real.py.

References nzmath.real.RealField.issubring().

◆ __eq__()

◆ __hash__()

def nzmath.real.RealField.__hash__ (   self)

Reimplemented from nzmath.ring.Ring.

Definition at line 169 of file real.py.

◆ __ne__()

def nzmath.real.RealField.__ne__ (   self,
  other 
)
Inequality test.

Reimplemented from nzmath.ring.Ring.

Definition at line 166 of file real.py.

References nzmath.poly.univar.PolynomialInterface.__eq__(), nzmath.group.Group.__eq__(), nzmath.poly.ratfunc.RationalFunction.__eq__(), nzmath.quad.ReducedQuadraticForm.__eq__(), nzmath.poly.multivar.TermIndices.__eq__(), nzmath.poly.ring.PolynomialRing.__eq__(), nzmath.poly.formalsum.FormalSumContainerInterface.__eq__(), nzmath.factor.misc.FactoredInteger.__eq__(), nzmath.real.Real.__eq__(), nzmath.imaginary.Complex.__eq__(), nzmath.poly.array.ArrayPoly.__eq__(), nzmath.group.GroupElement.__eq__(), nzmath.matrix.Matrix.__eq__(), nzmath.real.RealField.__eq__(), nzmath.intresidue.IntegerResidueClass.__eq__(), nzmath.finitefield.FinitePrimeField.__eq__(), nzmath.imaginary.ComplexField.__eq__(), nzmath.rational.Rational.__eq__(), nzmath.poly.array.ArrayPolyMod.__eq__(), nzmath.module.Module.__eq__(), nzmath.permute.Permute.__eq__(), nzmath.intresidue.IntegerResidueClassRing.__eq__(), nzmath.algfield.NumberField.__eq__(), nzmath.poly.formalsum.DictFormalSum.__eq__(), nzmath.poly.univar.BasicPolynomial.__eq__(), nzmath.poly.formalsum.ListFormalSum.__eq__(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables.__eq__(), nzmath.poly.ring.RationalFunctionField.__eq__(), nzmath.finitefield.ExtendedFieldElement.__eq__(), nzmath.rational.RationalField.__eq__(), nzmath.permute.ExPermute.__eq__(), nzmath.permute.PermGroup.__eq__(), nzmath.prime.Zeta.__eq__(), nzmath.prime.FactoredInteger.__eq__(), nzmath.rational.Integer.__eq__(), nzmath.finitefield.ExtendedField.__eq__(), nzmath.poly.univar.SortedPolynomial.__eq__(), nzmath.rational.IntegerRing.__eq__(), and nzmath.matrix.MatrixRing.__eq__().

◆ __repr__()

◆ __str__()

def nzmath.real.RealField.__str__ (   self)

Definition at line 142 of file real.py.

◆ _getOne()

◆ _getZero()

◆ createElement()

def nzmath.real.RealField.createElement (   self,
  seed 
)
createElement returns an element of the ring with seed.

Reimplemented from nzmath.ring.Ring.

Definition at line 200 of file real.py.

Referenced by nzmath.finitefield.FiniteField.random_element(), and nzmath.finitefield.FiniteField.TonelliShanks().

◆ getCharacteristic()

def nzmath.real.RealField.getCharacteristic (   self)
The characteristic of the real field is zero.

Reimplemented from nzmath.ring.Ring.

Definition at line 203 of file real.py.

◆ issubring()

◆ issuperring()

def nzmath.real.RealField.issuperring (   self,
  other 
)
Report whether the ring is a superring of another ring.

Reimplemented from nzmath.ring.Ring.

Definition at line 193 of file real.py.

Referenced by nzmath.ring.Ring.getCommonSuperring(), and nzmath.real.RealField.issubring().

Member Data Documentation

◆ _one

nzmath.real.RealField._one
private

Definition at line 139 of file real.py.

Referenced by nzmath.real.RealField._getOne(), and nzmath.ring.ResidueClassRing._getOne().

◆ _zero

nzmath.real.RealField._zero
private

Property Documentation

◆ one

nzmath.real.RealField.one = property(_getOne, None, None, "multiplicative unit.")
static

◆ zero

nzmath.real.RealField.zero = property(_getZero, None, None, "additive unit.")
static

Definition at line 184 of file real.py.

Referenced by nzmath.ring.Field.gcd().


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