nzmath.imaginary.ComplexField Class Reference

Inheritance diagram for nzmath.imaginary.ComplexField:

Collaboration diagram for nzmath.imaginary.ComplexField:

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	createElement (self, seed)
def	issubring (self, aRing)
def	issuperring (self, aRing)
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

ComplexField is a class of the field of real numbers.
The class has the single instance 'theComplexField'.

Definition at line 210 of file imaginary.py.

Constructor & Destructor Documentation

__init__()

def nzmath.imaginary.ComplexField.__init__

(

self

)

Set field flag True of 'properties' attribute.

Reimplemented from nzmath.ring.Field.

Definition at line 216 of file imaginary.py.

Member Function Documentation

__contains__()

def nzmath.imaginary.ComplexField.__contains__	(		self,
			element
	)

Definition at line 227 of file imaginary.py.

__eq__()

def nzmath.imaginary.ComplexField.__eq__	(		self,
			other
	)

Equality test.

Reimplemented from nzmath.ring.Ring.

Definition at line 235 of file imaginary.py.

Referenced by nzmath.poly.multivar.TermIndices.__ne__(), nzmath.poly.ring.PolynomialRing.__ne__(), nzmath.quad.ReducedQuadraticForm.__ne__(), nzmath.ring.Ring.__ne__(), nzmath.poly.formalsum.FormalSumContainerInterface.__ne__(), nzmath.poly.array.ArrayPoly.__ne__(), nzmath.real.RealField.__ne__(), nzmath.ring.Ideal.__ne__(), and nzmath.prime.FactoredInteger.__ne__().

__hash__()

def nzmath.imaginary.ComplexField.__hash__

(

self

)

Reimplemented from nzmath.ring.Ring.

Definition at line 241 of file imaginary.py.

__ne__()

def nzmath.imaginary.ComplexField.__ne__	(		self,
			other
	)

Inequality test.

Reimplemented from nzmath.ring.Ring.

Definition at line 238 of file imaginary.py.

__repr__()

def nzmath.imaginary.ComplexField.__repr__

(

self

)

Definition at line 224 of file imaginary.py.

References nzmath.matrix.Matrix.__class__, nzmath.matrix.RingMatrix.__class__, nzmath.matrix.RingSquareMatrix.__class__, nzmath.matrix.FieldMatrix.__class__, nzmath.matrix.MatrixRing.__class__, and nzmath.matrix.Subspace.__class__.

__str__()

def nzmath.imaginary.ComplexField.__str__

(

self

)

Definition at line 221 of file imaginary.py.

_getOne()

def nzmath.imaginary.ComplexField._getOne (   self )

private

Definition at line 247 of file imaginary.py.

References nzmath.imaginary.ComplexField._one, nzmath.algfield.NumberField._one, nzmath.finitefield.FinitePrimeField._one, and nzmath.finitefield.ExtendedField._one.

_getZero()

def nzmath.imaginary.ComplexField._getZero (   self )

private

Definition at line 252 of file imaginary.py.

References nzmath.imaginary.ComplexField._zero, nzmath.algfield.NumberField._zero, nzmath.finitefield.FinitePrimeField._zero, and nzmath.finitefield.ExtendedField._zero.

createElement()

def nzmath.imaginary.ComplexField.createElement	(		self,
			seed
	)

createElement returns an element of the ring with seed.

Reimplemented from nzmath.ring.Ring.

Definition at line 244 of file imaginary.py.

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

getCharacteristic()

def nzmath.imaginary.ComplexField.getCharacteristic

(

self

)

The characteristic of the real field is zero.

Reimplemented from nzmath.ring.Ring.

Definition at line 271 of file imaginary.py.

issubring()

def nzmath.imaginary.ComplexField.issubring	(		self,
			other
	)

Report whether another ring contains the ring as a subring.

Reimplemented from nzmath.ring.Ring.

Definition at line 257 of file imaginary.py.

References nzmath.imaginary.ComplexField.issuperring(), nzmath.finitefield.FinitePrimeField.issuperring(), nzmath.algfield.NumberField.issuperring(), and nzmath.finitefield.ExtendedField.issuperring().

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

issuperring()

def nzmath.imaginary.ComplexField.issuperring	(		self,
			other
	)

Report whether the ring is a superring of another ring.

Reimplemented from nzmath.ring.Ring.

Definition at line 264 of file imaginary.py.

Referenced by nzmath.ring.Ring.getCommonSuperring(), nzmath.poly.ring.PolynomialRing.getCommonSuperring(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables.getCommonSuperring(), nzmath.poly.ring.RationalFunctionField.getCommonSuperring(), nzmath.rational.RationalField.getCommonSuperring(), nzmath.rational.IntegerRing.getCommonSuperring(), nzmath.real.RealField.issubring(), nzmath.imaginary.ComplexField.issubring(), and nzmath.poly.ring.RationalFunctionField.issuperring().

Member Data Documentation

_one

nzmath.imaginary.ComplexField._one

private

Definition at line 218 of file imaginary.py.

Referenced by nzmath.poly.ring.PolynomialRing._get_one(), nzmath.poly.ring.RationalFunctionField._get_one(), nzmath.real.RealField._getOne(), nzmath.imaginary.ComplexField._getOne(), nzmath.intresidue.IntegerResidueClassRing._getOne(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables._getOne(), nzmath.ring.ResidueClassRing._getOne(), nzmath.rational.RationalField._getOne(), nzmath.rational.IntegerRing._getOne(), and nzmath.matrix.MatrixRing._getOne().

_zero

nzmath.imaginary.ComplexField._zero

private

Definition at line 219 of file imaginary.py.

Referenced by nzmath.poly.ring.PolynomialRing._get_zero(), nzmath.poly.ring.RationalFunctionField._get_zero(), nzmath.real.RealField._getZero(), nzmath.imaginary.ComplexField._getZero(), nzmath.intresidue.IntegerResidueClassRing._getZero(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables._getZero(), nzmath.ring.ResidueClassRing._getZero(), nzmath.rational.RationalField._getZero(), nzmath.rational.IntegerRing._getZero(), and nzmath.matrix.MatrixRing._getZero().

Property Documentation

one

nzmath.imaginary.ComplexField.one = property(_getOne, None, None, "multiplicative unit.")

static

Definition at line 250 of file imaginary.py.

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

zero

nzmath.imaginary.ComplexField.zero = property(_getZero, None, None, "additive unit.")

static

Definition at line 255 of file imaginary.py.

Referenced by nzmath.ring.Field.gcd(), and nzmath.matrix.MatrixRing.zeroMatrix().

---

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

• nzmath/imaginary.py