NZMATH  1.2.0
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nzmath.poly.multiutil.PolynomialRingAnonymousVariables Class Reference
Inheritance diagram for nzmath.poly.multiutil.PolynomialRingAnonymousVariables:
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Collaboration diagram for nzmath.poly.multiutil.PolynomialRingAnonymousVariables:
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Public Member Functions

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

Public Attributes

 number_of_variables
 
- Public Attributes inherited from nzmath.ring.CommutativeRing
 properties
 

Properties

 one = property(_getOne, None, None, "multiplicative unit")
 
 zero = property(_getZero, None, None, "additive unit")
 

Private Member Functions

def _getOne (self)
 
def _getZero (self)
 

Private Attributes

 _coefficient_ring
 
 _one
 
 _zero
 

Static Private Attributes

dictionary _instances = {}
 

Detailed Description

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

Definition at line 413 of file multiutil.py.

Constructor & Destructor Documentation

◆ __init__()

def nzmath.poly.multiutil.PolynomialRingAnonymousVariables.__init__ (   self,
  coeffring,
  number_of_variables 
)

Definition at line 421 of file multiutil.py.

Member Function Documentation

◆ __contains__()

def nzmath.poly.multiutil.PolynomialRingAnonymousVariables.__contains__ (   self,
  element 
)
`in' operator is provided for checking the element be in the
ring.

Definition at line 477 of file multiutil.py.

References nzmath.poly.multiutil.RingElementProvider._coefficient_ring, and nzmath.poly.multiutil.PolynomialRingAnonymousVariables._coefficient_ring.

◆ __eq__()

◆ __hash__()

◆ __repr__()

◆ __str__()

◆ _getOne()

◆ _getZero()

◆ createElement()

def nzmath.poly.multiutil.PolynomialRingAnonymousVariables.createElement (   self,
  seed 
)

◆ extgcd()

def nzmath.poly.multiutil.PolynomialRingAnonymousVariables.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 581 of file multiutil.py.

◆ gcd()

def nzmath.poly.multiutil.PolynomialRingAnonymousVariables.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 569 of file multiutil.py.

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

◆ getCoefficientRing()

◆ getCommonSuperring()

◆ getInstance()

def nzmath.poly.multiutil.PolynomialRingAnonymousVariables.getInstance (   cls,
  coeffring,
  number_of_variables 
)
Return an instance of the class with specified coefficient ring
and number of variables.

Definition at line 593 of file multiutil.py.

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

◆ getQuotientField()

def nzmath.poly.multiutil.PolynomialRingAnonymousVariables.getQuotientField (   self)
getQuotientField returns the quotient field of the ring
if coefficient ring has its quotient field.  Otherwise,
an exception will be raised.

Reimplemented from nzmath.ring.CommutativeRing.

Definition at line 440 of file multiutil.py.

References nzmath.poly.multiutil.RingElementProvider._coefficient_ring, nzmath.poly.multiutil.PolynomialRingAnonymousVariables._coefficient_ring, nzmath.poly.multiutil.NestProvider.number_of_variables, nzmath.poly.multiutil.PolynomialRingAnonymousVariables.number_of_variables, and nzmath.bigrange.range().

◆ issubring()

◆ issuperring()

Member Data Documentation

◆ _coefficient_ring

nzmath.poly.multiutil.PolynomialRingAnonymousVariables._coefficient_ring
private

Definition at line 425 of file multiutil.py.

Referenced by nzmath.poly.ring.PolynomialRing.__contains__(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables.__contains__(), nzmath.poly.ring.PolynomialRing.__eq__(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables.__eq__(), nzmath.poly.uniutil.RingPolynomial.__getitem__(), nzmath.poly.ring.PolynomialRing.__hash__(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables.__hash__(), nzmath.poly.ring.PolynomialRing.__repr__(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables.__repr__(), nzmath.poly.uniutil.RingPolynomial.__repr__(), nzmath.poly.ring.PolynomialRing.__str__(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables.__str__(), nzmath.poly.ring.PolynomialRing._constant_polynomial(), nzmath.poly.ring.PolynomialRing._prepared_polynomial(), nzmath.poly.ring.PolynomialRing._zero_polynomial(), nzmath.poly.ring.PolynomialRing.createElement(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables.createElement(), nzmath.poly.ring.PolynomialRing.getCharacteristic(), nzmath.poly.ring.PolynomialRing.getCoefficientRing(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables.getCoefficientRing(), nzmath.poly.uniutil.RingPolynomial.getCoefficientRing(), nzmath.poly.ring.PolynomialRing.getCommonSuperring(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables.getCommonSuperring(), nzmath.poly.ring.PolynomialRing.getQuotientField(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables.getQuotientField(), nzmath.poly.uniutil.RingElementProvider.getRing(), nzmath.poly.uniutil.RingPolynomial.ismonic(), nzmath.poly.ring.PolynomialRing.issubring(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables.issubring(), nzmath.poly.ring.PolynomialRing.issuperring(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables.issuperring(), and nzmath.poly.uniutil.RingElementProvider.set_coefficient_ring().

◆ _instances

dictionary nzmath.poly.multiutil.PolynomialRingAnonymousVariables._instances = {}
staticprivate

◆ _one

◆ _zero

◆ number_of_variables

nzmath.poly.multiutil.PolynomialRingAnonymousVariables.number_of_variables

Definition at line 432 of file multiutil.py.

Referenced by nzmath.poly.ring.PolynomialRing.__eq__(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables.__eq__(), nzmath.poly.ring.RationalFunctionField.__eq__(), nzmath.poly.ring.PolynomialRing.__hash__(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables.__hash__(), nzmath.poly.ring.RationalFunctionField.__hash__(), nzmath.poly.ring.PolynomialRing.__repr__(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables.__repr__(), nzmath.poly.ring.RationalFunctionField.__repr__(), nzmath.poly.ring.PolynomialRing.__str__(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables.__str__(), nzmath.poly.ring.RationalFunctionField.__str__(), nzmath.poly.ring.PolynomialRing._constant_polynomial(), nzmath.poly.ring.PolynomialRing._prepared_polynomial(), nzmath.poly.ring.PolynomialRing._zero_polynomial(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables.createElement(), nzmath.poly.multivar.BasicPolynomial.erase_variable(), nzmath.poly.ring.PolynomialRing.getCommonSuperring(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables.getCommonSuperring(), nzmath.poly.ring.RationalFunctionField.getCommonSuperring(), nzmath.poly.ring.PolynomialRing.getQuotientField(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables.getQuotientField(), nzmath.poly.ratfunc.RationalFunction.getRing(), nzmath.poly.ring.PolynomialRing.issubring(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables.issubring(), nzmath.poly.ring.RationalFunctionField.issubring(), nzmath.poly.ring.PolynomialRing.issuperring(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables.issuperring(), nzmath.poly.ring.RationalFunctionField.issuperring(), nzmath.poly.multiutil.RingElementProvider.set_coefficient_ring(), and nzmath.poly.ring.RationalFunctionField.unnest().

Property Documentation

◆ one

nzmath.poly.multiutil.PolynomialRingAnonymousVariables.one = property(_getOne, None, None, "multiplicative unit")
static

◆ zero

nzmath.poly.multiutil.PolynomialRingAnonymousVariables.zero = property(_getZero, None, None, "additive unit")
static

Definition at line 567 of file multiutil.py.

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


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