nzmath.finitefield.ExtendedFieldElement Class Reference

Inheritance diagram for nzmath.finitefield.ExtendedFieldElement:

Collaboration diagram for nzmath.finitefield.ExtendedFieldElement:

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
	)

self + other

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

Definition at line 416 of file finitefield.py.

References nzmath.finitefield.ExtendedFieldElement._op(), nzmath.algfield.BasicAlgNumber.field, nzmath.finitefield.ExtendedFieldElement.field, and nzmath.algfield.MatAlgNumber.field.

__eq__()

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

Equality test.

Reimplemented from nzmath.ring.RingElement.

Definition at line 490 of file finitefield.py.

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

Referenced by nzmath.poly.multivar.TermIndices.__ne__(), nzmath.poly.ring.PolynomialRing.__ne__(), nzmath.quad.ReducedQuadraticForm.__ne__(), nzmath.ring.Ring.__ne__(), nzmath.poly.formalsum.FormalSumContainerInterface.__ne__(), nzmath.poly.array.ArrayPoly.__ne__(), nzmath.real.RealField.__ne__(), nzmath.ring.Ideal.__ne__(), and nzmath.prime.FactoredInteger.__ne__().

__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
	)

self * other

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

Definition at line 446 of file finitefield.py.

References nzmath.finitefield.ExtendedFieldElement._op(), nzmath.algfield.BasicAlgNumber.field, nzmath.finitefield.ExtendedFieldElement.field, and nzmath.algfield.MatAlgNumber.field.

__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

)

Definition at line 484 of file finitefield.py.

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

__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__()

def nzmath.finitefield.ExtendedFieldElement.__pow__	(		self,
			index
	)

self ** index

pow() with three arguments is not supported.

Definition at line 471 of file finitefield.py.

References nzmath.matrix.Matrix.__class__, nzmath.matrix.RingMatrix.__class__, nzmath.matrix.RingSquareMatrix.__class__, nzmath.matrix.FieldMatrix.__class__, nzmath.matrix.MatrixRing.__class__, nzmath.matrix.Subspace.__class__, nzmath.algfield.BasicAlgNumber.field, nzmath.finitefield.ExtendedFieldElement.field, nzmath.algfield.MatAlgNumber.field, and nzmath.finitefield.ExtendedFieldElement.rep.

__repr__()

def nzmath.finitefield.ExtendedFieldElement.__repr__

(

self

)

Definition at line 508 of file finitefield.py.

References nzmath.matrix.Matrix.__class__, nzmath.matrix.RingMatrix.__class__, nzmath.matrix.RingSquareMatrix.__class__, nzmath.matrix.FieldMatrix.__class__, nzmath.matrix.MatrixRing.__class__, nzmath.matrix.Subspace.__class__, nzmath.algfield.BasicAlgNumber.field, nzmath.finitefield.ExtendedFieldElement.field, nzmath.algfield.MatAlgNumber.field, and nzmath.finitefield.ExtendedFieldElement.rep.

__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
	)

self - other

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

Definition at line 428 of file finitefield.py.

References nzmath.finitefield.ExtendedFieldElement._op(), nzmath.algfield.BasicAlgNumber.field, nzmath.finitefield.ExtendedFieldElement.field, and nzmath.algfield.MatAlgNumber.field.

__truediv__()

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

Definition at line 458 of file finitefield.py.

_op()

def nzmath.finitefield.ExtendedFieldElement._op (   self,   other,   op  )

private

Do `self (op) other'.
op must be a name of the special method for binary operation.

Definition at line 395 of file finitefield.py.

References nzmath.matrix.Matrix.__class__, nzmath.matrix.RingMatrix.__class__, nzmath.matrix.RingSquareMatrix.__class__, nzmath.matrix.FieldMatrix.__class__, nzmath.matrix.MatrixRing.__class__, nzmath.matrix.Subspace.__class__, nzmath.finitefield.double_embeddings(), nzmath.algfield.BasicAlgNumber.field, nzmath.finitefield.ExtendedFieldElement.field, nzmath.algfield.MatAlgNumber.field, and nzmath.finitefield.ExtendedFieldElement.rep.

Referenced by nzmath.finitefield.ExtendedFieldElement.__add__(), nzmath.finitefield.ExtendedFieldElement.__mul__(), nzmath.finitefield.ExtendedFieldElement.__rsub__(), and nzmath.finitefield.ExtendedFieldElement.__sub__().

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()

def nzmath.finitefield.ExtendedFieldElement.inverse

(

self

)

Return the inverse of the element.

Definition at line 463 of file finitefield.py.

References nzmath.matrix.Matrix.__class__, nzmath.matrix.RingMatrix.__class__, nzmath.matrix.RingSquareMatrix.__class__, nzmath.matrix.FieldMatrix.__class__, nzmath.matrix.MatrixRing.__class__, nzmath.matrix.Subspace.__class__, nzmath.gcd.extgcd(), nzmath.algfield.BasicAlgNumber.field, nzmath.finitefield.ExtendedFieldElement.field, nzmath.algfield.MatAlgNumber.field, and nzmath.finitefield.ExtendedFieldElement.rep.

Referenced by nzmath.permute.Permute.__pow__(), nzmath.intresidue.IntegerResidueClass.__pow__(), nzmath.permute.ExPermute.__pow__(), nzmath.module.Ideal.__pow__(), nzmath.matrix.RingSquareMatrix.__pow__(), nzmath.permute.Permute.__rdiv__(), nzmath.permute.ExPermute.__rdiv__(), and nzmath.ring.QuotientFieldElement.__rtruediv__().

norm()

def nzmath.finitefield.ExtendedFieldElement.norm

(

self

)

Return the absolute norm.

Definition at line 527 of file finitefield.py.

References nzmath.compatibility.card(), nzmath.algfield.BasicAlgNumber.field, nzmath.finitefield.ExtendedFieldElement.field, and nzmath.algfield.MatAlgNumber.field.

Referenced by nzmath.module.Ideal.isPrime().

trace()

def nzmath.finitefield.ExtendedFieldElement.trace

(

self

)

Return the absolute trace.

Definition at line 511 of file finitefield.py.

References nzmath.compatibility.card(), nzmath.algfield.BasicAlgNumber.field, nzmath.finitefield.ExtendedFieldElement.field, and nzmath.algfield.MatAlgNumber.field.

Referenced by nzmath.matrix.RingSquareMatrix._characteristicPolyList().

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

nzmath.finitefield.ExtendedFieldElement.field

Definition at line 379 of file finitefield.py.

Referenced by nzmath.finitefield.ExtendedFieldElement.__add__(), nzmath.finitefield.ExtendedFieldElement.__eq__(), nzmath.finitefield.ExtendedFieldElement.__mul__(), nzmath.finitefield.ExtendedFieldElement.__neg__(), nzmath.finitefield.ExtendedFieldElement.__pow__(), nzmath.finitefield.ExtendedFieldElement.__repr__(), nzmath.finitefield.ExtendedFieldElement.__sub__(), nzmath.finitefield.ExtendedFieldElement._op(), nzmath.finitefield.ExtendedFieldElement.getRing(), nzmath.finitefield.ExtendedFieldElement.inverse(), nzmath.finitefield.ExtendedFieldElement.norm(), and nzmath.finitefield.ExtendedFieldElement.trace().

rep

nzmath.finitefield.ExtendedFieldElement.rep

Definition at line 384 of file finitefield.py.

Referenced by nzmath.finitefield.ExtendedFieldElement.__eq__(), nzmath.finitefield.ExtendedFieldElement.__hash__(), nzmath.finitefield.ExtendedFieldElement.__nonzero__(), nzmath.finitefield.ExtendedFieldElement.__pow__(), nzmath.finitefield.ExtendedFieldElement.__repr__(), nzmath.finitefield.ExtendedFieldElement._op(), and nzmath.finitefield.ExtendedFieldElement.inverse().

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

• nzmath/finitefield.py