NZMATH  1.2.0
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nzmath.ring.CommutativeRing Class Reference
Inheritance diagram for nzmath.ring.CommutativeRing:
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Collaboration diagram for nzmath.ring.CommutativeRing:
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Public Member Functions

def __init__ (self)
 
def getQuotientField (self)
 
def isdomain (self)
 
def isnoetherian (self)
 
def isufd (self)
 
def ispid (self)
 
def iseuclidean (self)
 
def isfield (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 getCharacteristic (self)
 
def issubring (self, other)
 
def issuperring (self, other)
 
def getCommonSuperring (self, other)
 
def __eq__ (self, other)
 
def __hash__ (self)
 
def __ne__ (self, other)
 

Public Attributes

 properties
 

Private Attributes

 _actions
 
 _actions_order
 

Detailed Description

CommutativeRing is an abstract subclass of Ring
whose multiplication is commutative.

Definition at line 88 of file ring.py.

Constructor & Destructor Documentation

◆ __init__()

def nzmath.ring.CommutativeRing.__init__ (   self)
Initialize 'properties' attribute by an object of
CommutativeRingProperties.

Reimplemented from nzmath.ring.Ring.

Reimplemented in nzmath.rational.IntegerRing, nzmath.rational.RationalField, nzmath.imaginary.ComplexField, nzmath.ring.Field, and nzmath.real.RealField.

Definition at line 94 of file ring.py.

Member Function Documentation

◆ getaction()

def nzmath.ring.CommutativeRing.getaction (   self,
  action_ring 
)
Return the registered action for 'action_ring'.

Definition at line 180 of file ring.py.

References nzmath.ring.CommutativeRing._actions, and nzmath.ring.CommutativeRing._actions_order.

◆ getQuotientField()

def nzmath.ring.CommutativeRing.getQuotientField (   self)
getQuotientField returns the quotient field of the ring
if available, otherwise raises exception.

Reimplemented in nzmath.rational.IntegerRing, nzmath.rational.RationalField, nzmath.poly.ring.RationalFunctionField, nzmath.poly.multiutil.PolynomialRingAnonymousVariables, nzmath.ring.Field, and nzmath.poly.ring.PolynomialRing.

Definition at line 107 of file ring.py.

◆ hasaction()

def nzmath.ring.CommutativeRing.hasaction (   self,
  action_ring 
)
Return True if 'action_ring' is registered to provide action.

Definition at line 169 of file ring.py.

References nzmath.ring.CommutativeRing._actions, and nzmath.ring.CommutativeRing._actions_order.

◆ isdomain()

def nzmath.ring.CommutativeRing.isdomain (   self)
isdomain returns True if the ring is actually a domain,
False if not, or None if uncertain.

Definition at line 114 of file ring.py.

References nzmath.ring.CommutativeRing.properties.

◆ iseuclidean()

def nzmath.ring.CommutativeRing.iseuclidean (   self)
iseuclidean returns True if the ring is actually a Euclidean
domain, False if not, or None if uncertain.

Definition at line 142 of file ring.py.

References nzmath.ring.CommutativeRing.properties.

◆ isfield()

def nzmath.ring.CommutativeRing.isfield (   self)
isfield returns True if the ring is actually a field,
False if not, or None if uncertain.

Reimplemented in nzmath.intresidue.IntegerResidueClassRing, and nzmath.ring.Field.

Definition at line 149 of file ring.py.

References nzmath.ring.CommutativeRing.properties.

◆ isnoetherian()

def nzmath.ring.CommutativeRing.isnoetherian (   self)
isnoetherian returns True if the ring is actually a Noetherian
domain, False if not, or None if uncertain.

Definition at line 121 of file ring.py.

References nzmath.ring.CommutativeRing.properties.

◆ ispid()

def nzmath.ring.CommutativeRing.ispid (   self)
ispid returns True if the ring is actually a principal
ideal domain, False if not, or None if uncertain.

Definition at line 135 of file ring.py.

References nzmath.ring.CommutativeRing.properties.

◆ isufd()

def nzmath.ring.CommutativeRing.isufd (   self)
isufd returns True if the ring is actually a unique
factorization domain, False if not, or None if uncertain.

Definition at line 128 of file ring.py.

References nzmath.ring.CommutativeRing.properties.

◆ registerModuleAction()

def nzmath.ring.CommutativeRing.registerModuleAction (   self,
  action_ring,
  action 
)
Register a ring 'action_ring', which act on the ring through
'action' so the ring be an 'action_ring' module.

Definition at line 156 of file ring.py.

References nzmath.ring.CommutativeRing._actions, nzmath.ring.CommutativeRing._actions_order, nzmath.ring.Ring.issubring(), and nzmath.bigrange.range().

Referenced by nzmath.finitefield.FinitePrimeField.__init__().

Member Data Documentation

◆ _actions

nzmath.ring.CommutativeRing._actions
private

◆ _actions_order

nzmath.ring.CommutativeRing._actions_order
private

◆ properties


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