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nzmath.finitefield.ExtendedFieldElement Class Reference
Inheritance diagram for nzmath.finitefield.ExtendedFieldElement:
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Collaboration diagram for nzmath.finitefield.ExtendedFieldElement:
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Public Member Functions

def __init__ (self, representative, field)
 
def getRing (self)
 
def __add__ (self, other)
 
def __sub__ (self, other)
 
def __rsub__ (self, other)
 
def __mul__ (self, other)
 
def __truediv__ (self, other)
 
def inverse (self)
 
def __pow__ (self, index)
 
def __neg__ (self)
 
def __pos__ (self)
 
def __eq__ (self, other)
 
def __hash__ (self)
 
def __ne__ (self, other)
 
def __nonzero__ (self)
 
def __repr__ (self)
 
def trace (self)
 
def norm (self)
 
- Public Member Functions inherited from nzmath.finitefield.FiniteFieldElement
def __init__ (self)
 
- Public Member Functions inherited from nzmath.ring.FieldElement
def exact_division (self, other)
 
- Public Member Functions inherited from nzmath.ring.CommutativeRingElement
def mul_module_action (self, other)
 
- Public Member Functions inherited from nzmath.ring.RingElement
def __init__ (self, *args, **kwd)
 

Public Attributes

 field
 
 rep
 

Private Member Functions

def _op (self, other, op)
 

Static Private Attributes

def __radd__ = __add__
 
def __rmul__ = __mul__
 
def __div__ = __truediv__
 

Detailed Description

ExtendedFieldElement is a class for an element of F_q.

Definition at line 362 of file finitefield.py.

Constructor & Destructor Documentation

◆ __init__()

def nzmath.finitefield.ExtendedFieldElement.__init__ (   self,
  representative,
  field 
)
FiniteExtendedFieldElement(representative, field) creates
an element of the finite extended field F_q.

The argument representative has to be a polynomial with
base field coefficients, i.e., if F_q is over F_{p^k}
the representative has to F_{p^k} polynomial.

Another argument field mut be an instance of
ExtendedField.

Definition at line 366 of file finitefield.py.

Member Function Documentation

◆ __add__()

def nzmath.finitefield.ExtendedFieldElement.__add__ (   self,
  other 
)

◆ __eq__()

◆ __hash__()

def nzmath.finitefield.ExtendedFieldElement.__hash__ (   self)

Reimplemented from nzmath.ring.RingElement.

Definition at line 499 of file finitefield.py.

References nzmath.finitefield.ExtendedFieldElement.rep.

◆ __mul__()

def nzmath.finitefield.ExtendedFieldElement.__mul__ (   self,
  other 
)

◆ __ne__()

def nzmath.finitefield.ExtendedFieldElement.__ne__ (   self,
  other 
)
Inequality test.

Reimplemented from nzmath.ring.RingElement.

Definition at line 502 of file finitefield.py.

◆ __neg__()

def nzmath.finitefield.ExtendedFieldElement.__neg__ (   self)

◆ __nonzero__()

def nzmath.finitefield.ExtendedFieldElement.__nonzero__ (   self)

Definition at line 505 of file finitefield.py.

References nzmath.finitefield.ExtendedFieldElement.rep.

◆ __pos__()

def nzmath.finitefield.ExtendedFieldElement.__pos__ (   self)

Definition at line 487 of file finitefield.py.

◆ __pow__()

◆ __repr__()

◆ __rsub__()

def nzmath.finitefield.ExtendedFieldElement.__rsub__ (   self,
  other 
)
other - self

other can be an element of either F_q, F_p or Z.

Definition at line 438 of file finitefield.py.

References nzmath.finitefield.ExtendedFieldElement._op().

◆ __sub__()

def nzmath.finitefield.ExtendedFieldElement.__sub__ (   self,
  other 
)

◆ __truediv__()

def nzmath.finitefield.ExtendedFieldElement.__truediv__ (   self,
  other 
)

Definition at line 458 of file finitefield.py.

◆ _op()

◆ getRing()

def nzmath.finitefield.ExtendedFieldElement.getRing (   self)
Return the field to which the element belongs.

Reimplemented from nzmath.ring.RingElement.

Definition at line 389 of file finitefield.py.

References nzmath.algfield.BasicAlgNumber.field, nzmath.finitefield.ExtendedFieldElement.field, and nzmath.algfield.MatAlgNumber.field.

Referenced by nzmath.poly.multiutil.RingPolynomial.__add__(), nzmath.ring.QuotientFieldElement.__add__(), nzmath.poly.uniutil.RingPolynomial.__add__(), nzmath.ring.QuotientFieldElement.__eq__(), nzmath.poly.uniutil.FieldPolynomial.__pow__(), nzmath.poly.multiutil.RingPolynomial.__radd__(), nzmath.poly.uniutil.RingPolynomial.__radd__(), nzmath.poly.multiutil.RingPolynomial.__rsub__(), nzmath.ring.QuotientFieldElement.__rsub__(), nzmath.poly.uniutil.RingPolynomial.__rsub__(), nzmath.ring.QuotientFieldElement.__rtruediv__(), nzmath.poly.multiutil.RingPolynomial.__sub__(), nzmath.ring.QuotientFieldElement.__sub__(), nzmath.poly.uniutil.RingPolynomial.__sub__(), nzmath.ring.QuotientFieldElement.__truediv__(), nzmath.poly.uniutil.PrimeCharacteristicFunctionsProvider._small_index_mod_pow(), nzmath.ring.CommutativeRingElement.exact_division(), nzmath.poly.uniutil.DivisionProvider.extgcd(), nzmath.poly.uniutil.PrimeCharacteristicFunctionsProvider.factor(), nzmath.poly.uniutil.DivisionProvider.mod_pow(), nzmath.poly.uniutil.PrimeCharacteristicFunctionsProvider.mod_pow(), nzmath.poly.uniutil.PseudoDivisionProvider.monic_pow(), nzmath.ring.CommutativeRingElement.mul_module_action(), and nzmath.poly.uniutil.SubresultantGcdProvider.subresultant_gcd().

◆ inverse()

◆ norm()

def nzmath.finitefield.ExtendedFieldElement.norm (   self)

◆ trace()

def nzmath.finitefield.ExtendedFieldElement.trace (   self)

Member Data Documentation

◆ __div__

def nzmath.finitefield.ExtendedFieldElement.__div__ = __truediv__
staticprivate

Definition at line 461 of file finitefield.py.

◆ __radd__

def nzmath.finitefield.ExtendedFieldElement.__radd__ = __add__
staticprivate

Definition at line 426 of file finitefield.py.

◆ __rmul__

def nzmath.finitefield.ExtendedFieldElement.__rmul__ = __mul__
staticprivate

Definition at line 456 of file finitefield.py.

◆ field

◆ rep


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