NZMATH  1.2.0
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nzmath.poly.ring.RationalFunctionField Class Reference
Inheritance diagram for nzmath.poly.ring.RationalFunctionField:
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Collaboration diagram for nzmath.poly.ring.RationalFunctionField:
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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__()

◆ __hash__()

◆ __repr__()

◆ __str__()

◆ _get_one()

◆ _get_zero()

◆ 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()

◆ getCommonSuperring()

◆ getInstance()

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

◆ 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()

◆ issuperring()

◆ unnest()

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

◆ _zero

◆ coefficient_field

◆ number_of_variables

Property Documentation

◆ one

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

◆ 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: