nzmath.rational.RationalField Class Reference

Inheritance diagram for nzmath.rational.RationalField:

Collaboration diagram for nzmath.rational.RationalField:

Public Member Functions
def	__init__ (self)
def	__contains__ (self, element)
def	__eq__ (self, other)
def	classNumber (self)
def	getQuotientField (self)
def	getCharacteristic (self)
def	createElement (self, numerator, denominator=1)
def	__str__ (self)
def	__repr__ (self)
def	__hash__ (self)
def	issubring (self, other)
def	issuperring (self, other)
def	getCommonSuperring (self, other)
Public Member Functions inherited from nzmath.ring.QuotientField
def	__init__ (self, domain)
Public Member Functions inherited from nzmath.ring.Field
def	createElement (self, *args)
def	isfield (self)
def	gcd (self, a, b)
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	createElement (self, seed)
def	__ne__ (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.QuotientField
	basedomain
Public Attributes inherited from nzmath.ring.CommutativeRing
	properties

Detailed Description

RationalField is a class of field of rationals.
The class has the single instance 'theRationalField'.

Definition at line 517 of file rational.py.

Constructor & Destructor Documentation

__init__()

def nzmath.rational.RationalField.__init__

(

self

)

Set field flag True of 'properties' attribute.

Reimplemented from nzmath.ring.Field.

Definition at line 523 of file rational.py.

Member Function Documentation

__contains__()

def nzmath.rational.RationalField.__contains__	(		self,
			element
	)

Definition at line 526 of file rational.py.

References nzmath.rational.isIntegerObject().

__eq__()

def nzmath.rational.RationalField.__eq__	(		self,
			other
	)

Equality test.

Reimplemented from nzmath.ring.Ring.

Definition at line 533 of file rational.py.

Referenced by nzmath.ring.Ring.__ne__(), nzmath.real.RealField.__ne__(), and nzmath.ring.Ideal.__ne__().

__hash__()

def nzmath.rational.RationalField.__hash__

(

self

)

Return a hash number (always 1).

Reimplemented from nzmath.ring.Ring.

Definition at line 565 of file rational.py.

__repr__()

def nzmath.rational.RationalField.__repr__

(

self

)

Definition at line 562 of file rational.py.

__str__()

def nzmath.rational.RationalField.__str__

(

self

)

Definition at line 559 of file rational.py.

_getOne()

def nzmath.rational.RationalField._getOne (   self )

private

Definition at line 622 of file rational.py.

References nzmath.imaginary.ComplexField._one, nzmath.poly.ring.PolynomialRing._one, nzmath.algfield.NumberField._one, nzmath.intresidue.IntegerResidueClassRing._one, nzmath.finitefield.FinitePrimeField._one, nzmath.poly.multiutil.PolynomialRingAnonymousVariables._one, nzmath.poly.ring.RationalFunctionField._one, nzmath.rational.RationalField._one, nzmath.finitefield.ExtendedField._one, and nzmath.matrix.MatrixRing._one.

_getZero()

def nzmath.rational.RationalField._getZero (   self )

private

Definition at line 630 of file rational.py.

References nzmath.imaginary.ComplexField._zero, nzmath.poly.ring.PolynomialRing._zero, nzmath.intresidue.IntegerResidueClassRing._zero, nzmath.algfield.NumberField._zero, nzmath.finitefield.FinitePrimeField._zero, nzmath.poly.multiutil.PolynomialRingAnonymousVariables._zero, nzmath.poly.ring.RationalFunctionField._zero, nzmath.rational.RationalField._zero, nzmath.finitefield.ExtendedField._zero, and nzmath.matrix.MatrixRing._zero.

classNumber()

def nzmath.rational.RationalField.classNumber

(

self

)

The class number of the rational field is one.

Definition at line 539 of file rational.py.

createElement()

def nzmath.rational.RationalField.createElement	(		self,
			numerator,
			denominator = 1
	)

createElement returns a Rational object.
If the number of arguments is one, it must be an integer or a rational.
If the number of arguments is two, they must be integers.

Definition at line 551 of file rational.py.

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

getCharacteristic()

def nzmath.rational.RationalField.getCharacteristic

(

self

)

The characteristic of the rational field is zero.

Reimplemented from nzmath.ring.Ring.

Definition at line 547 of file rational.py.

getCommonSuperring()

def nzmath.rational.RationalField.getCommonSuperring	(		self,
			other
	)

Return common superring of the ring and another ring.

Reimplemented from nzmath.ring.Ring.

Definition at line 608 of file rational.py.

References nzmath.poly.ring.PolynomialRing.issubring(), nzmath.finitefield.FinitePrimeField.issubring(), nzmath.imaginary.ComplexField.issubring(), nzmath.algfield.NumberField.issubring(), nzmath.intresidue.IntegerResidueClassRing.issubring(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables.issubring(), nzmath.poly.ring.RationalFunctionField.issubring(), nzmath.rational.RationalField.issubring(), nzmath.finitefield.ExtendedField.issubring(), nzmath.matrix.MatrixRing.issubring(), nzmath.poly.ring.PolynomialRing.issuperring(), nzmath.imaginary.ComplexField.issuperring(), nzmath.finitefield.FinitePrimeField.issuperring(), nzmath.algfield.NumberField.issuperring(), nzmath.intresidue.IntegerResidueClassRing.issuperring(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables.issuperring(), nzmath.poly.ring.RationalFunctionField.issuperring(), nzmath.rational.RationalField.issuperring(), nzmath.finitefield.ExtendedField.issuperring(), and nzmath.matrix.MatrixRing.issuperring().

getQuotientField()

def nzmath.rational.RationalField.getQuotientField

(

self

)

getQuotientField returns the rational field itself.

Reimplemented from nzmath.ring.Field.

Definition at line 543 of file rational.py.

issubring()

def nzmath.rational.RationalField.issubring	(		self,
			other
	)

reports whether another ring contains the rational field as
subring.

If other is also the rational field, the output is True.  If
other is the integer ring, the output is False.  In other
cases it depends on the implementation of another ring's
issuperring method.

Reimplemented from nzmath.ring.Ring.

Definition at line 571 of file rational.py.

Referenced by nzmath.ring.Ring.getCommonSuperring(), nzmath.rational.RationalField.getCommonSuperring(), and nzmath.rational.IntegerRing.getCommonSuperring().

issuperring()

def nzmath.rational.RationalField.issuperring	(		self,
			other
	)

reports whether the rational number field contains another
ring as subring.

If other is also the rational number field or the ring of
integer, the output is True.  In other cases it depends on the
implementation of another ring's issubring method.

Reimplemented from nzmath.ring.Ring.

Definition at line 591 of file rational.py.

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

Member Data Documentation

_one

nzmath.rational.RationalField._one

private

Definition at line 625 of file rational.py.

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

_zero

nzmath.rational.RationalField._zero

private

Definition at line 633 of file rational.py.

Referenced by nzmath.real.RealField._getZero(), nzmath.ring.ResidueClassRing._getZero(), nzmath.rational.RationalField._getZero(), and nzmath.rational.IntegerRing._getZero().

Property Documentation

one

nzmath.rational.RationalField.one = property(_getOne, None, None, "multiplicative unit.")

static

Definition at line 628 of file rational.py.

Referenced by nzmath.ring.Field.gcd(), nzmath.finitefield.FiniteField.Legendre(), nzmath.finitefield.FiniteField.order(), nzmath.finitefield.FiniteField.sqrt(), and nzmath.finitefield.FiniteField.TonelliShanks().

zero

nzmath.rational.RationalField.zero = property(_getZero, None, None, "additive unit.")

static

Definition at line 636 of file rational.py.

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

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

• nzmath/rational.py