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

def __init__ (self, coeffring, number_of_variables=1)
 
def getCoefficientRing (self)
 
def getQuotientField (self)
 
def __eq__ (self, other)
 
def __ne__ (self, other)
 
def __hash__ (self)
 
def __repr__ (self)
 
def __str__ (self)
 
def __contains__ (self, element)
 
def issubring (self, other)
 
def issuperring (self, other)
 
def getCommonSuperring (self, other)
 
def getCharacteristic (self)
 
def createElement (self, seed)
 
def gcd (self, a, b)
 
def extgcd (self, a, b)
 
def getInstance (cls, coeffring, number_of_variables=1)
 
- Public Member Functions inherited from nzmath.ring.CommutativeRing
def __init__ (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 Attributes

 number_of_variables
 
- 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 _zero_polynomial (self)
 
def _constant_polynomial (self, seed)
 
def _prepared_polynomial (self, preparation)
 
def _get_one (self)
 
def _get_zero (self)
 

Private Attributes

 _coefficient_ring
 
 _one
 
 _zero
 

Static Private Attributes

dictionary _instances = {}
 

Detailed Description

The class of uni-/multivariate polynomial ring.
There's no need to specify the variable names.

Definition at line 12 of file ring.py.

Constructor & Destructor Documentation

◆ __init__()

def nzmath.poly.ring.PolynomialRing.__init__ (   self,
  coeffring,
  number_of_variables = 1 
)
PolynomialRing(coeffring)
creates a polynomial ring for univariate polynomials, while
PolynomialRing(coeffring, n)
creates a polynomial ring for multivariate polynomials.

Definition at line 20 of file ring.py.

Member Function Documentation

◆ __contains__()

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

◆ __eq__()

◆ __hash__()

◆ __ne__()

◆ __repr__()

◆ __str__()

◆ _constant_polynomial()

◆ _get_one()

◆ _get_zero()

◆ _prepared_polynomial()

◆ _zero_polynomial()

◆ createElement()

◆ extgcd()

def nzmath.poly.ring.PolynomialRing.extgcd (   self,
  a,
  b 
)
Return the tuple (u, v, d): d is the greatest common divisor
of given polynomials, and they satisfy d = u*a + v*b. The
polynomials must be in the polynomial ring.  If the
coefficient ring is a field, the result is monic.

Definition at line 243 of file ring.py.

◆ gcd()

def nzmath.poly.ring.PolynomialRing.gcd (   self,
  a,
  b 
)
Return the greatest common divisor of given polynomials.
The polynomials must be in the polynomial ring.
If the coefficient ring is a field, the result is monic.

Definition at line 231 of file ring.py.

Referenced by nzmath.rational.IntegerRing.lcm().

◆ getCharacteristic()

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

◆ getCoefficientRing()

◆ getCommonSuperring()

◆ getInstance()

def nzmath.poly.ring.PolynomialRing.getInstance (   cls,
  coeffring,
  number_of_variables = 1 
)

◆ getQuotientField()

◆ issubring()

◆ issuperring()

Member Data Documentation

◆ _coefficient_ring

◆ _instances

dictionary nzmath.poly.ring.PolynomialRing._instances = {}
staticprivate

◆ _one

◆ _zero

◆ number_of_variables

Property Documentation

◆ one

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

◆ zero

nzmath.poly.ring.PolynomialRing.zero = property(_get_zero, None, None, "additive unit")
static

Definition at line 229 of file ring.py.

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


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