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:
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## 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

_orderfactor

## Detailed Description

```The base class for all finite fields.
```

Definition at line 35 of file finitefield.py.

## ◆ __init__()

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

Reimplemented in nzmath.finitefield.FinitePrimeField.

Definition at line 39 of file finitefield.py.

## ◆ card()

 def nzmath.finitefield.FiniteField.card ( self )

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

Definition at line 47 of file finitefield.py.

## ◆ 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()

 def nzmath.finitefield.FiniteField.Legendre ( self, element )
```Return generalize Legendre Symbol for FiniteField.
```

Reimplemented in nzmath.finitefield.FinitePrimeField.

Definition at line 87 of file finitefield.py.

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

## ◆ 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()

 def nzmath.finitefield.FiniteField.random_element ( self, * args )

## ◆ sqrt()

 def nzmath.finitefield.FiniteField.sqrt ( self, element )

## ◆ TonelliShanks()

 def nzmath.finitefield.FiniteField.TonelliShanks ( self, element )

## ◆ _orderfactor

 nzmath.finitefield.FiniteField._orderfactor
private

Definition at line 45 of file finitefield.py.

## ◆ char

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