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nzmath.finitefield.FinitePrimeFieldElement Class Reference
Inheritance diagram for nzmath.finitefield.FinitePrimeFieldElement:
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Collaboration diagram for nzmath.finitefield.FinitePrimeFieldElement:
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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)

◆ __str__()

def nzmath.finitefield.FinitePrimeFieldElement.__str__ (   self)

◆ 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

◆ orderfactor

nzmath.finitefield.FinitePrimeFieldElement.orderfactor

Definition at line 195 of file finitefield.py.

◆ ring


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