Inheritance diagram for nzmath.poly.ring.RationalFunctionField:

Collaboration diagram for nzmath.poly.ring.RationalFunctionField:

Public Member Functions
def	__init__ (self, field, number_of_variables)

def	__repr__ (self)

def	__str__ (self)

def	__eq__ (self, other)

def	__contains__ (self, element)

def	__hash__ (self)

def	getQuotientField (self)

def	getCoefficientRing (self)

def	issubring (self, other)

def	issuperring (self, other)

def	getCharacteristic (self)

def	getCommonSuperring (self, other)

def	unnest (self)

def	createElement (self, seedarg, *seedkwd)

def	getInstance (cls, coefffield, number_of_variables)

Public Member Functions inherited from nzmath.ring.QuotientField
def	__init__ (self, domain)

Public Member Functions inherited from nzmath.ring.Field
def	__init__ (self)

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)

Public Attributes
	coefficient_field

	number_of_variables

Public Attributes inherited from nzmath.ring.QuotientField
	basedomain

Public Attributes inherited from nzmath.ring.CommutativeRing
	properties

Properties
	one = property(_get_one, None, None, "multiplicative unit.")

	zero = property(_get_zero, None, None, "additive unit.")

Private Member Functions
def	_get_one (self)

def	_get_zero (self)

Private Attributes
	_one

	_zero

Static Private Attributes
dictionary	_instances = {}

Detailed Description

The class for rational function fields.

Definition at line 453 of file ring.py.

Constructor & Destructor Documentation

◆ init()

def nzmath.poly.ring.RationalFunctionField.__init__	(	self,
		field,
		number_of_variables
	)

RationalFunctionField(field, number_of_variables)

field: The field of coefficients.
number_of_variables: The number of variables.

Definition at line 459 of file ring.py.

Member Function Documentation

◆ contains()

def nzmath.poly.ring.RationalFunctionField.__contains__	(	self,
		element
	)

Return True if an element is in the field.

Definition at line 503 of file ring.py.

References nzmath.poly.ring.RationalFunctionField.issubring().

◆ eq()

def nzmath.poly.ring.RationalFunctionField.__eq__	(	self,
		other
	)

equality test

Reimplemented from nzmath.ring.Ring.

Definition at line 486 of file ring.py.

References nzmath.poly.ring.RationalFunctionField.coefficient_field, nzmath.poly.ring.PolynomialRing.number_of_variables, nzmath.poly.ratfunc.RationalFunction.number_of_variables, nzmath.poly.multiutil.NestProvider.number_of_variables, nzmath.poly.multivar.BasicPolynomial.number_of_variables, nzmath.poly.multiutil.PolynomialRingAnonymousVariables.number_of_variables, nzmath.poly.ring.RationalFunctionField.number_of_variables, nzmath.poly.multiutil.NestProvider.unnest(), and nzmath.poly.ring.RationalFunctionField.unnest().

Referenced by nzmath.quad.ReducedQuadraticForm.__ne__(), nzmath.ring.Ring.__ne__(), nzmath.real.RealField.__ne__(), nzmath.ring.Ideal.__ne__(), and nzmath.prime.FactoredInteger.__ne__().

◆ hash()

def nzmath.poly.ring.RationalFunctionField.__hash__ ( self )

Return hash corresponding to equality.

Reimplemented from nzmath.ring.Ring.

Definition at line 511 of file ring.py.

References nzmath.poly.ring.RationalFunctionField.coefficient_field, nzmath.poly.ring.PolynomialRing.number_of_variables, nzmath.poly.ratfunc.RationalFunction.number_of_variables, nzmath.poly.multiutil.NestProvider.number_of_variables, nzmath.poly.multivar.BasicPolynomial.number_of_variables, nzmath.poly.multiutil.PolynomialRingAnonymousVariables.number_of_variables, and nzmath.poly.ring.RationalFunctionField.number_of_variables.

◆ repr()

def nzmath.poly.ring.RationalFunctionField.__repr__ ( self )

Return 'RationalFunctionField(Field, #vars)'

Definition at line 474 of file ring.py.

References nzmath.matrix.Matrix.__class__, nzmath.matrix.RingMatrix.__class__, nzmath.matrix.RingSquareMatrix.__class__, nzmath.matrix.FieldMatrix.__class__, nzmath.matrix.MatrixRing.__class__, nzmath.matrix.Subspace.__class__, nzmath.poly.ring.RationalFunctionField.coefficient_field, nzmath.poly.ring.PolynomialRing.number_of_variables, nzmath.poly.ratfunc.RationalFunction.number_of_variables, nzmath.poly.multiutil.NestProvider.number_of_variables, nzmath.poly.multivar.BasicPolynomial.number_of_variables, nzmath.poly.multiutil.PolynomialRingAnonymousVariables.number_of_variables, and nzmath.poly.ring.RationalFunctionField.number_of_variables.

◆ str()

def nzmath.poly.ring.RationalFunctionField.__str__ ( self )

Return K()()

Definition at line 480 of file ring.py.

References nzmath.poly.ring.RationalFunctionField.coefficient_field, nzmath.poly.ring.PolynomialRing.number_of_variables, nzmath.poly.ratfunc.RationalFunction.number_of_variables, nzmath.poly.multiutil.NestProvider.number_of_variables, nzmath.poly.multivar.BasicPolynomial.number_of_variables, nzmath.poly.multiutil.PolynomialRingAnonymousVariables.number_of_variables, and nzmath.poly.ring.RationalFunctionField.number_of_variables.

◆ _get_one()

def nzmath.poly.ring.RationalFunctionField._get_one ( self )

private

getter for one

Definition at line 608 of file ring.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.finitefield.ExtendedField._one, nzmath.matrix.MatrixRing._one, and nzmath.ring.QuotientField.basedomain.

◆ _get_zero()

def nzmath.poly.ring.RationalFunctionField._get_zero ( self )

private

Definition at line 620 of file ring.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.finitefield.ExtendedField._zero, nzmath.matrix.MatrixRing._zero, and nzmath.ring.QuotientField.basedomain.

◆ createElement()

def nzmath.poly.ring.RationalFunctionField.createElement	(		self,
		*	seedarg,
		**	seedkwd
	)

Return an element of the field made from seed.

Definition at line 601 of file ring.py.

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

◆ getCharacteristic()

def nzmath.poly.ring.RationalFunctionField.getCharacteristic ( self )

The characteristic of a rational function field is same as of
its coefficient field.

Reimplemented from nzmath.ring.Ring.

Definition at line 562 of file ring.py.

References nzmath.poly.ring.RationalFunctionField.coefficient_field.

◆ getCoefficientRing()

def nzmath.poly.ring.RationalFunctionField.getCoefficientRing ( self )

Return the coefficient field.
This method is provided for common interface with PolynomialRing.

Definition at line 523 of file ring.py.

References nzmath.poly.ring.RationalFunctionField.coefficient_field.

Referenced by nzmath.poly.uniutil.DomainPolynomial.discriminant(), nzmath.poly.uniutil.FieldPolynomial.discriminant(), nzmath.poly.multiutil.PseudoDivisionProvider.exact_division(), nzmath.poly.multiutil.GcdProvider.gcd(), nzmath.poly.multiutil.PseudoDivisionProvider.pseudo_divmod(), nzmath.poly.multiutil.PseudoDivisionProvider.pseudo_floordiv(), nzmath.poly.multiutil.PseudoDivisionProvider.pseudo_mod(), nzmath.poly.uniutil.SubresultantGcdProvider.resultant(), nzmath.poly.uniutil.FieldPolynomial.resultant(), nzmath.poly.uniutil.SubresultantGcdProvider.subresultant_extgcd(), and nzmath.poly.uniutil.DomainPolynomial.to_field_polynomial().

◆ getCommonSuperring()

def nzmath.poly.ring.RationalFunctionField.getCommonSuperring	(	self,
		other
	)

Return common superring.

Reimplemented from nzmath.ring.Ring.

Definition at line 569 of file ring.py.

◆ getInstance()

def nzmath.poly.ring.RationalFunctionField.getInstance	(	cls,
		coefffield,
		number_of_variables
	)

Return an instance of the class with specified coefficient ring
and number of variables.

Definition at line 632 of file ring.py.

References nzmath.poly.ring.PolynomialRing._instances, nzmath.finitefield.FinitePrimeField._instances, nzmath.intresidue.IntegerResidueClassRing._instances, nzmath.poly.multiutil.PolynomialRingAnonymousVariables._instances, nzmath.poly.ring.RationalFunctionField._instances, and nzmath.matrix.MatrixRing._instances.

◆ getQuotientField()

def nzmath.poly.ring.RationalFunctionField.getQuotientField ( self )

Return the quotient field (the field itself).

Reimplemented from nzmath.ring.Field.

Definition at line 517 of file ring.py.

◆ issubring()

def nzmath.poly.ring.RationalFunctionField.issubring	(	self,
		other
	)

Return True if self is a subring of the other.

Reimplemented from nzmath.ring.Ring.

Definition at line 530 of file ring.py.

References nzmath.poly.ring.RationalFunctionField.coefficient_field, nzmath.poly.ring.PolynomialRing.number_of_variables, nzmath.poly.ratfunc.RationalFunction.number_of_variables, nzmath.poly.multiutil.NestProvider.number_of_variables, nzmath.poly.multivar.BasicPolynomial.number_of_variables, nzmath.poly.multiutil.PolynomialRingAnonymousVariables.number_of_variables, and nzmath.poly.ring.RationalFunctionField.number_of_variables.

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

◆ issuperring()

def nzmath.poly.ring.RationalFunctionField.issuperring	(	self,
		other
	)

Return True if self is a superring of the other.

Reimplemented from nzmath.ring.Ring.

Definition at line 542 of file ring.py.

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

◆ unnest()

def nzmath.poly.ring.RationalFunctionField.unnest ( self )

if self is a nested RationalFunctionField i.e. its
coefficientField is also a RationalFunctionField, then the
function returns one level unnested RationalFunctionField.

For example:
RationalFunctionField(RationalFunctionField(Q, 1), 1).unnest()
returns
RationalFunctionField(Q, 2).

Definition at line 588 of file ring.py.

References nzmath.poly.ring.RationalFunctionField.coefficient_field, nzmath.poly.ring.PolynomialRing.number_of_variables, nzmath.poly.ratfunc.RationalFunction.number_of_variables, nzmath.poly.multiutil.NestProvider.number_of_variables, nzmath.poly.multivar.BasicPolynomial.number_of_variables, nzmath.poly.multiutil.PolynomialRingAnonymousVariables.number_of_variables, and nzmath.poly.ring.RationalFunctionField.number_of_variables.

Referenced by nzmath.poly.ring.RationalFunctionField.__eq__(), nzmath.poly.multiutil.PseudoDivisionProvider.exact_division(), nzmath.poly.multiutil.GcdProvider.gcd(), nzmath.poly.multiutil.PseudoDivisionProvider.pseudo_divmod(), nzmath.poly.multiutil.PseudoDivisionProvider.pseudo_floordiv(), and nzmath.poly.multiutil.PseudoDivisionProvider.pseudo_mod().

Member Data Documentation

◆ _instances

dictionary nzmath.poly.ring.RationalFunctionField._instances = {}

staticprivate

Definition at line 457 of file ring.py.

Referenced by nzmath.poly.ring.RationalFunctionField.getInstance().

◆ _one

nzmath.poly.ring.RationalFunctionField._one

private

Definition at line 615 of file ring.py.

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

◆ _zero

nzmath.poly.ring.RationalFunctionField._zero

private

Definition at line 626 of file ring.py.

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

◆ coefficient_field

nzmath.poly.ring.RationalFunctionField.coefficient_field

Definition at line 471 of file ring.py.

◆ number_of_variables

nzmath.poly.ring.RationalFunctionField.number_of_variables

Definition at line 472 of file ring.py.

Referenced by nzmath.poly.ring.RationalFunctionField.__eq__(), nzmath.poly.ring.RationalFunctionField.__hash__(), nzmath.poly.ring.RationalFunctionField.__repr__(), nzmath.poly.ring.RationalFunctionField.__str__(), nzmath.poly.ring.RationalFunctionField.getCommonSuperring(), nzmath.poly.ring.RationalFunctionField.issubring(), nzmath.poly.ring.RationalFunctionField.issuperring(), nzmath.poly.multiutil.RingElementProvider.set_coefficient_ring(), and nzmath.poly.ring.RationalFunctionField.unnest().

Property Documentation

◆ one

nzmath.poly.ring.RationalFunctionField.one = property(_get_one, None, None, "multiplicative unit.")

static

Definition at line 618 of file ring.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.poly.ring.RationalFunctionField.zero = property(_get_zero, None, None, "additive unit.")

static

Definition at line 629 of file ring.py.

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

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

nzmath/poly/ring.py

Public Member Functions

Public Attributes

Properties

Private Member Functions

Private Attributes

Static Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ __init__()

Member Function Documentation

◆ __contains__()

◆ __eq__()

◆ __hash__()

◆ __repr__()

◆ __str__()

◆ _get_one()

◆ _get_zero()

◆ createElement()

◆ getCharacteristic()

◆ getCoefficientRing()

◆ getCommonSuperring()

◆ getInstance()

◆ getQuotientField()

◆ issubring()

◆ issuperring()

◆ unnest()

Member Data Documentation

◆ _instances

◆ _one

◆ _zero

◆ coefficient_field

◆ number_of_variables

Property Documentation

◆ one

◆ zero

◆ init()

◆ contains()

◆ eq()

◆ hash()

◆ repr()

◆ str()