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

def __init__ (self)
 
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)
 

Private Attributes

 _one
 
 _zero
 

Detailed Description

Ring is an abstract class which expresses that
the derived classes are (in mathematical meaning) rings.

Definition of ring is as follows:
  Ring is a structure with addition and multiplication.  It is an
  abelian group with addition, and a monoid with multiplication.
  The multiplication obeys the distributive law.

Definition at line 8 of file ring.py.

Constructor & Destructor Documentation

◆ __init__()

def nzmath.ring.Ring.__init__ (   self)
Initialize _one and _zero for later use for properties 'one'
and 'zero'.

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

Definition at line 19 of file ring.py.

Member Function Documentation

◆ __eq__()

◆ __hash__()

◆ __ne__()

def nzmath.ring.Ring.__ne__ (   self,
  other 
)
Inequality test.

Reimplemented in nzmath.intresidue.IntegerResidueClassRing, nzmath.finitefield.FinitePrimeField, nzmath.imaginary.ComplexField, nzmath.real.RealField, and nzmath.poly.ring.PolynomialRing.

Definition at line 81 of file ring.py.

References nzmath.poly.univar.PolynomialInterface.__eq__(), nzmath.group.Group.__eq__(), nzmath.poly.ratfunc.RationalFunction.__eq__(), nzmath.quad.ReducedQuadraticForm.__eq__(), nzmath.poly.multivar.TermIndices.__eq__(), nzmath.poly.ring.PolynomialRing.__eq__(), nzmath.poly.formalsum.FormalSumContainerInterface.__eq__(), nzmath.ring.Ring.__eq__(), nzmath.factor.misc.FactoredInteger.__eq__(), nzmath.real.Real.__eq__(), nzmath.imaginary.Complex.__eq__(), nzmath.poly.array.ArrayPoly.__eq__(), nzmath.group.GroupElement.__eq__(), nzmath.matrix.Matrix.__eq__(), nzmath.real.RealField.__eq__(), nzmath.intresidue.IntegerResidueClass.__eq__(), nzmath.finitefield.FinitePrimeField.__eq__(), nzmath.imaginary.ComplexField.__eq__(), nzmath.rational.Rational.__eq__(), nzmath.poly.array.ArrayPolyMod.__eq__(), nzmath.module.Module.__eq__(), nzmath.permute.Permute.__eq__(), nzmath.intresidue.IntegerResidueClassRing.__eq__(), nzmath.algfield.NumberField.__eq__(), nzmath.poly.formalsum.DictFormalSum.__eq__(), nzmath.poly.univar.BasicPolynomial.__eq__(), nzmath.poly.formalsum.ListFormalSum.__eq__(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables.__eq__(), nzmath.poly.ring.RationalFunctionField.__eq__(), nzmath.finitefield.ExtendedFieldElement.__eq__(), nzmath.rational.RationalField.__eq__(), nzmath.permute.ExPermute.__eq__(), nzmath.permute.PermGroup.__eq__(), nzmath.prime.Zeta.__eq__(), nzmath.prime.FactoredInteger.__eq__(), nzmath.rational.Integer.__eq__(), nzmath.finitefield.ExtendedField.__eq__(), nzmath.poly.univar.SortedPolynomial.__eq__(), nzmath.rational.IntegerRing.__eq__(), and nzmath.matrix.MatrixRing.__eq__().

◆ createElement()

◆ getCharacteristic()

def nzmath.ring.Ring.getCharacteristic (   self)
Return the characteristic of the ring.

The Characteristic of a ring is the smallest positive integer
n s.t. n * a = 0 for any element a of the ring, or 0 if there
is no such natural number.

Reimplemented in nzmath.matrix.MatrixRing, nzmath.rational.IntegerRing, nzmath.poly.ring.RationalFunctionField, nzmath.rational.RationalField, nzmath.algfield.NumberField, nzmath.imaginary.ComplexField, nzmath.intresidue.IntegerResidueClassRing, nzmath.real.RealField, nzmath.poly.ring.PolynomialRing, and nzmath.finitefield.FiniteField.

Definition at line 36 of file ring.py.

◆ getCommonSuperring()

def nzmath.ring.Ring.getCommonSuperring (   self,
  other 
)
Return common super ring of self and another ring.

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

Definition at line 58 of file ring.py.

References nzmath.ring.Ring.issubring(), nzmath.poly.ring.PolynomialRing.issubring(), nzmath.real.RealField.issubring(), nzmath.finitefield.FinitePrimeField.issubring(), nzmath.imaginary.ComplexField.issubring(), nzmath.algfield.NumberField.issubring(), nzmath.intresidue.IntegerResidueClassRing.issubring(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables.issubring(), nzmath.poly.ring.RationalFunctionField.issubring(), nzmath.rational.RationalField.issubring(), nzmath.finitefield.ExtendedField.issubring(), nzmath.rational.IntegerRing.issubring(), nzmath.matrix.MatrixRing.issubring(), nzmath.ring.Ring.issuperring(), nzmath.poly.ring.PolynomialRing.issuperring(), nzmath.real.RealField.issuperring(), nzmath.imaginary.ComplexField.issuperring(), nzmath.finitefield.FinitePrimeField.issuperring(), nzmath.algfield.NumberField.issuperring(), nzmath.intresidue.IntegerResidueClassRing.issuperring(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables.issuperring(), nzmath.poly.ring.RationalFunctionField.issuperring(), nzmath.rational.RationalField.issuperring(), nzmath.finitefield.ExtendedField.issuperring(), nzmath.rational.IntegerRing.issuperring(), and nzmath.matrix.MatrixRing.issuperring().

◆ issubring()

◆ issuperring()

Member Data Documentation

◆ _one

nzmath.ring.Ring._one
private

Definition at line 27 of file ring.py.

Referenced by nzmath.ring.ResidueClassRing._getOne().

◆ _zero

nzmath.ring.Ring._zero
private

Definition at line 28 of file ring.py.

Referenced by nzmath.ring.ResidueClassRing._getZero().


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