NZMATH  1.2.0
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nzmath.poly.ring.RationalFunctionField Class Reference
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

- Public Attributes inherited from nzmath.ring.QuotientField
- Public Attributes inherited from nzmath.ring.CommutativeRing


 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


Static Private Attributes

dictionary _instances = {}

Detailed Description

The class for rational function fields.

Definition at line 453 of file

Constructor & Destructor Documentation

◆ __init__()

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

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

Definition at line 459 of file

Member Function Documentation

◆ __contains__()

def nzmath.poly.ring.RationalFunctionField.__contains__ (   self,
Return True if an element is in the field.

Definition at line 503 of file

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

◆ __eq__()

◆ __hash__()

◆ __repr__()

◆ __str__()

◆ _get_one()

◆ _get_zero()

◆ createElement()

def nzmath.poly.ring.RationalFunctionField.createElement (   self,
**  seedkwd 
Return an element of the field made from seed.

Definition at line 601 of file

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

References nzmath.poly.ring.RationalFunctionField.coefficient_field.

◆ getCoefficientRing()

◆ getCommonSuperring()

◆ getInstance()

def nzmath.poly.ring.RationalFunctionField.getInstance (   cls,

◆ 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

◆ issubring()

◆ issuperring()

◆ unnest()

Member Data Documentation

◆ _instances

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

Definition at line 457 of file

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

◆ _one

◆ _zero

◆ coefficient_field

◆ number_of_variables

Property Documentation

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

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

Definition at line 629 of file

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

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