nzmath.finitefield.FinitePrimeFieldElement Class Reference

Inheritance diagram for nzmath.finitefield.FinitePrimeFieldElement:

Collaboration diagram for nzmath.finitefield.FinitePrimeFieldElement:

Public Member Functions
def	__init__ (self, representative, modulus, modulus_is_prime=True)
def	__repr__ (self)
def	__str__ (self)
def	getRing (self)
def	order (self)
Public Member Functions inherited from nzmath.intresidue.IntegerResidueClass
def	__init__ (self, representative, modulus)
def	__mul__ (self, other)
def	__rmul__ (self, other)
def	__div__ (self, other)
def	__mod__ (self, other)
def	__divmod__ (self, other)
def	__rdiv__ (self, other)
def	__add__ (self, other)
def	__sub__ (self, other)
def	__rsub__ (self, other)
def	__pow__ (self, other)
def	__neg__ (self)
def	__pos__ (self)
def	__nonzero__ (self)
def	__eq__ (self, other)
def	__ne__ (self, other)
def	__hash__ (self)
def	inverse (self)
def	getModulus (self)
def	getResidue (self)
def	minimumNonNegative (self)
def	minimumAbsolute (self)
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 Member Functions inherited from nzmath.finitefield.FiniteFieldElement
def	__init__ (self)
Public Member Functions inherited from nzmath.ring.FieldElement
def	exact_division (self, other)

Public Attributes
	ring
	n
	orderfactor
Public Attributes inherited from nzmath.intresidue.IntegerResidueClass
	m
	n

Additional Inherited Members
Static Public Attributes inherited from nzmath.intresidue.IntegerResidueClass
def	toInteger = minimumNonNegative

Detailed Description

The class for finite prime field element.

Definition at line 159 of file finitefield.py.

Constructor & Destructor Documentation

__init__()

def nzmath.finitefield.FinitePrimeFieldElement.__init__	(		self,
			representative,
			modulus,
			modulus_is_prime = True
	)

Definition at line 163 of file finitefield.py.

Member Function Documentation

__repr__()

def nzmath.finitefield.FinitePrimeFieldElement.__repr__

(

self

)

Reimplemented from nzmath.intresidue.IntegerResidueClass.

Definition at line 173 of file finitefield.py.

References nzmath.intresidue.IntegerResidueClass.m, and nzmath.finitefield.FinitePrimeFieldElement.n.

__str__()

def nzmath.finitefield.FinitePrimeFieldElement.__str__

(

self

)

Definition at line 176 of file finitefield.py.

References nzmath.intresidue.IntegerResidueClass.m, and nzmath.finitefield.FinitePrimeFieldElement.n.

getRing()

def nzmath.finitefield.FinitePrimeFieldElement.getRing

(

self

)

Return the finite prime field to which the element belongs.

Reimplemented from nzmath.intresidue.IntegerResidueClass.

Definition at line 179 of file finitefield.py.

References nzmath.intresidue.IntegerResidueClass.m, and nzmath.finitefield.FinitePrimeFieldElement.ring.

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().

order()

def nzmath.finitefield.FinitePrimeFieldElement.order

(

self

)

Find and return the order of the element in the multiplicative
group of F_p.

Definition at line 187 of file finitefield.py.

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().

Member Data Documentation

n

nzmath.finitefield.FinitePrimeFieldElement.n

Definition at line 192 of file finitefield.py.

Referenced by nzmath.intresidue.IntegerResidueClass.__add__(), nzmath.intresidue.IntegerResidueClass.__eq__(), nzmath.intresidue.IntegerResidueClass.__hash__(), nzmath.intresidue.IntegerResidueClass.__mul__(), nzmath.intresidue.IntegerResidueClass.__neg__(), nzmath.intresidue.IntegerResidueClass.__nonzero__(), nzmath.intresidue.IntegerResidueClass.__pos__(), nzmath.intresidue.IntegerResidueClass.__pow__(), nzmath.intresidue.IntegerResidueClass.__repr__(), nzmath.finitefield.FinitePrimeFieldElement.__repr__(), nzmath.intresidue.IntegerResidueClass.__rsub__(), nzmath.finitefield.FinitePrimeFieldElement.__str__(), nzmath.intresidue.IntegerResidueClass.__sub__(), nzmath.intresidue.IntegerResidueClass.getResidue(), nzmath.intresidue.IntegerResidueClass.inverse(), nzmath.intresidue.IntegerResidueClass.minimumAbsolute(), and nzmath.intresidue.IntegerResidueClass.minimumNonNegative().

orderfactor

nzmath.finitefield.FinitePrimeFieldElement.orderfactor

Definition at line 195 of file finitefield.py.

ring

nzmath.finitefield.FinitePrimeFieldElement.ring

Definition at line 171 of file finitefield.py.

Referenced by nzmath.ring.Ideal.__add__(), nzmath.poly.ring.PolynomialIdeal.__contains__(), nzmath.poly.multiutil.PolynomialIdeal.__contains__(), nzmath.ring.Ideal.__eq__(), nzmath.ring.Ideal.__mul__(), nzmath.poly.ring.PolynomialIdeal.__nonzero__(), nzmath.poly.multiutil.PolynomialIdeal.__nonzero__(), nzmath.poly.ring.PolynomialIdeal.__repr__(), nzmath.poly.multiutil.PolynomialIdeal.__repr__(), nzmath.poly.ring.PolynomialIdeal.__str__(), nzmath.poly.multiutil.PolynomialIdeal.__str__(), nzmath.poly.ring.PolynomialIdeal._euclidean_reduce(), nzmath.ring.ResidueClassRing._getOne(), nzmath.ring.ResidueClassRing._getZero(), nzmath.poly.ring.PolynomialIdeal._normalize_generators(), nzmath.finitefield.FinitePrimeFieldElement.getRing(), and nzmath.poly.ring.PolynomialIdeal.reduce().

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

• nzmath/finitefield.py