NZMATH  1.2.0
About: NZMATH is a Python based number theory oriented calculation system.
  Fossies Dox: NZMATH-1.2.0.tar.gz  ("inofficial" and yet experimental doxygen-generated source code documentation)  

nzmath.finitefield.FiniteField Class Reference
Inheritance diagram for nzmath.finitefield.FiniteField:
[legend]
Collaboration diagram for nzmath.finitefield.FiniteField:
[legend]

Public Member Functions

def __init__ (self, characteristic)
 
def card (self)
 
def getCharacteristic (self)
 
def order (self, elem)
 
def random_element (self, *args)
 
def primitive_element (self)
 
def Legendre (self, element)
 
def TonelliShanks (self, element)
 
def sqrt (self, element)
 
- Public Member Functions inherited from nzmath.ring.Field
def __init__ (self)
 
def createElement (self, *args)
 
def isfield (self)
 
def gcd (self, a, b)
 
def getQuotientField (self)
 
- 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 issubring (self, other)
 
def issuperring (self, other)
 
def getCommonSuperring (self, other)
 
def __eq__ (self, other)
 
def __hash__ (self)
 
def __ne__ (self, other)
 

Public Attributes

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

Private Attributes

 _orderfactor
 

Detailed Description

The base class for all finite fields.

Definition at line 35 of file finitefield.py.

Constructor & Destructor Documentation

◆ __init__()

def nzmath.finitefield.FiniteField.__init__ (   self,
  characteristic 
)

Reimplemented in nzmath.finitefield.FinitePrimeField.

Definition at line 39 of file finitefield.py.

Member Function Documentation

◆ card()

◆ getCharacteristic()

def nzmath.finitefield.FiniteField.getCharacteristic (   self)
Return the characteristic of the field.

Reimplemented from nzmath.ring.Ring.

Definition at line 51 of file finitefield.py.

References nzmath.finitefield.FiniteField.char.

Referenced by nzmath.finitefield.ExtendedField.__contains__().

◆ Legendre()

◆ order()

def nzmath.finitefield.FiniteField.order (   self,
  elem 
)
Find and return the order of the element in the multiplicative
group of the field.

Definition at line 57 of file finitefield.py.

References nzmath.finitefield.FiniteField._orderfactor, nzmath.finitefield.FiniteField.card(), nzmath.real.RealField.one, nzmath.poly.ring.PolynomialRing.one, nzmath.imaginary.ComplexField.one, nzmath.intresidue.IntegerResidueClassRing.one, nzmath.algfield.NumberField.one, nzmath.finitefield.FinitePrimeField.one, nzmath.poly.multiutil.PolynomialRingAnonymousVariables.one, nzmath.ring.ResidueClassRing.one, nzmath.poly.ring.RationalFunctionField.one, nzmath.rational.RationalField.one, nzmath.finitefield.ExtendedField.one, nzmath.rational.IntegerRing.one, and nzmath.matrix.MatrixRing.one.

Referenced by nzmath.poly.uniutil.DivisionProvider.__divmod__(), nzmath.poly.uniutil.DivisionProvider.__floordiv__(), nzmath.poly.uniutil.DivisionProvider.__mod__(), nzmath.poly.uniutil.DivisionProvider._populate_reduced(), nzmath.poly.uniutil.DivisionProvider._populate_reduced_more(), nzmath.poly.uniutil.PrimeCharacteristicFunctionsProvider.distinct_degree_factorization(), nzmath.poly.uniutil.PseudoDivisionProvider.exact_division(), nzmath.poly.uniutil.DivisionProvider.extgcd(), nzmath.poly.uniutil.PrimeCharacteristicFunctionsProvider.factor(), nzmath.poly.uniutil.DivisionProvider.gcd(), nzmath.poly.uniutil.PrimeCharacteristicFunctionsProvider.isirreducible(), nzmath.poly.multiutil.NestProvider.leading_variable(), nzmath.poly.uniutil.DivisionProvider.mod(), nzmath.poly.uniutil.PseudoDivisionProvider.monic_divmod(), nzmath.poly.uniutil.PseudoDivisionProvider.monic_floordiv(), nzmath.poly.uniutil.PseudoDivisionProvider.monic_mod(), nzmath.poly.uniutil.PseudoDivisionProvider.pseudo_divmod(), nzmath.poly.uniutil.PseudoDivisionProvider.pseudo_floordiv(), nzmath.poly.uniutil.PseudoDivisionProvider.pseudo_mod(), nzmath.poly.uniutil.KaratsubaProvider.ring_mul_karatsuba(), nzmath.poly.uniutil.PrimeCharacteristicFunctionsProvider.split_same_degrees(), nzmath.poly.uniutil.KaratsubaProvider.square_karatsuba(), and nzmath.poly.uniutil.PrimeCharacteristicFunctionsProvider.squarefree_decomposition().

◆ primitive_element()

def nzmath.finitefield.FiniteField.primitive_element (   self)
Return a primitive element of the field, i.e., a generator of
the multiplicative group.

Reimplemented in nzmath.finitefield.ExtendedField, and nzmath.finitefield.FinitePrimeField.

Definition at line 80 of file finitefield.py.

◆ random_element()

◆ sqrt()

◆ TonelliShanks()

def nzmath.finitefield.FiniteField.TonelliShanks (   self,
  element 
)
Return square root of element if exist.
assume that characteristic have to be more than three.

Definition at line 106 of file finitefield.py.

References nzmath.finitefield.FiniteField.card(), nzmath.finitefield.FiniteField.char, nzmath.lattice.Lattice.createElement(), nzmath.ring.Ring.createElement(), nzmath.group.Group.createElement(), nzmath.poly.ring.PolynomialRing.createElement(), nzmath.real.RealField.createElement(), nzmath.imaginary.ComplexField.createElement(), nzmath.intresidue.IntegerResidueClassRing.createElement(), nzmath.algfield.NumberField.createElement(), nzmath.finitefield.FinitePrimeField.createElement(), nzmath.poly.multiutil.PolynomialRingAnonymousVariables.createElement(), nzmath.rational.RationalField.createElement(), nzmath.permute.PermGroup.createElement(), nzmath.poly.ring.RationalFunctionField.createElement(), nzmath.finitefield.ExtendedField.createElement(), nzmath.rational.IntegerRing.createElement(), nzmath.matrix.MatrixRing.createElement(), nzmath.finitefield.FiniteField.Legendre(), nzmath.real.RealField.one, nzmath.poly.ring.PolynomialRing.one, nzmath.imaginary.ComplexField.one, nzmath.intresidue.IntegerResidueClassRing.one, nzmath.algfield.NumberField.one, nzmath.finitefield.FinitePrimeField.one, nzmath.poly.multiutil.PolynomialRingAnonymousVariables.one, nzmath.ring.ResidueClassRing.one, nzmath.poly.ring.RationalFunctionField.one, nzmath.rational.RationalField.one, nzmath.finitefield.ExtendedField.one, nzmath.rational.IntegerRing.one, nzmath.matrix.MatrixRing.one, nzmath.finitefield.FiniteField.random_element(), and nzmath.finitefield.FiniteField.sqrt().

Referenced by nzmath.finitefield.FiniteField.sqrt().

Member Data Documentation

◆ _orderfactor

◆ char


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