FiniteField(p, n)ΒΆ

ffp.spad line 283

FiniteField(p, n) implements finite fields with p^n elements. This packages checks that p is prime. For a non-checking version, see InnerFiniteField.

0: %
from AbelianMonoid
1: %
from MagmaWithUnit
*: (%, %) -> %
from Magma
*: (%, Fraction Integer) -> %
from RightModule Fraction Integer
*: (%, PrimeField p) -> %
from RightModule PrimeField p
*: (Fraction Integer, %) -> %
from LeftModule Fraction Integer
*: (Integer, %) -> %
from AbelianGroup
*: (NonNegativeInteger, %) -> %
from AbelianMonoid
*: (PositiveInteger, %) -> %
from AbelianSemiGroup
*: (PrimeField p, %) -> %
from LeftModule PrimeField p
+: (%, %) -> %
from AbelianSemiGroup
-: % -> %
from AbelianGroup
-: (%, %) -> %
from AbelianGroup
/: (%, %) -> %
from Field
/: (%, PrimeField p) -> %
from VectorSpace PrimeField p
=: (%, %) -> Boolean
from BasicType
^: (%, Integer) -> %
from DivisionRing
^: (%, NonNegativeInteger) -> %
from MagmaWithUnit
^: (%, PositiveInteger) -> %
from Magma
~=: (%, %) -> Boolean
from BasicType
algebraic?: % -> Boolean
from ExtensionField PrimeField p
annihilate?: (%, %) -> Boolean
from Rng
antiCommutator: (%, %) -> %
from NonAssociativeSemiRng
associates?: (%, %) -> Boolean
from EntireRing
associator: (%, %, %) -> %
from NonAssociativeRng
basis: () -> Vector %
from FiniteAlgebraicExtensionField PrimeField p
basis: PositiveInteger -> Vector %
from FiniteAlgebraicExtensionField PrimeField p
characteristic: () -> NonNegativeInteger
from NonAssociativeRing
charthRoot: % -> %
from FiniteFieldCategory
charthRoot: % -> Union(%, failed)
from CharacteristicNonZero
coerce: % -> %
from Algebra %
coerce: % -> OutputForm
from CoercibleTo OutputForm
coerce: Fraction Integer -> %
from Algebra Fraction Integer
coerce: Integer -> %
from NonAssociativeRing
coerce: PrimeField p -> %
from RetractableTo PrimeField p
commutator: (%, %) -> %
from NonAssociativeRng
conditionP: Matrix % -> Union(Vector %, failed)
from FiniteFieldCategory
convert: % -> InputForm
from ConvertibleTo InputForm
coordinates: % -> Vector PrimeField p
from FiniteAlgebraicExtensionField PrimeField p
coordinates: Vector % -> Matrix PrimeField p
from FiniteAlgebraicExtensionField PrimeField p
createNormalElement: () -> %
from FiniteAlgebraicExtensionField PrimeField p
createPrimitiveElement: () -> %
from FiniteFieldCategory
D: % -> %
from DifferentialRing
D: (%, NonNegativeInteger) -> %
from DifferentialRing
definingPolynomial: () -> SparseUnivariatePolynomial PrimeField p
from FiniteAlgebraicExtensionField PrimeField p
degree: % -> OnePointCompletion PositiveInteger
from ExtensionField PrimeField p
degree: % -> PositiveInteger
from FiniteAlgebraicExtensionField PrimeField p
differentiate: % -> %
from DifferentialRing
differentiate: (%, NonNegativeInteger) -> %
from DifferentialRing
dimension: () -> CardinalNumber
from VectorSpace PrimeField p
discreteLog: % -> NonNegativeInteger
from FiniteFieldCategory
discreteLog: (%, %) -> Union(NonNegativeInteger, failed)
from FieldOfPrimeCharacteristic
divide: (%, %) -> Record(quotient: %, remainder: %)
from EuclideanDomain
enumerate: () -> List %
from Finite
euclideanSize: % -> NonNegativeInteger
from EuclideanDomain
expressIdealMember: (List %, %) -> Union(List %, failed)
from PrincipalIdealDomain
exquo: (%, %) -> Union(%, failed)
from EntireRing
extendedEuclidean: (%, %) -> Record(coef1: %, coef2: %, generator: %)
from EuclideanDomain
extendedEuclidean: (%, %, %) -> Union(Record(coef1: %, coef2: %), failed)
from EuclideanDomain
extensionDegree: () -> OnePointCompletion PositiveInteger
from ExtensionField PrimeField p
extensionDegree: () -> PositiveInteger
from FiniteAlgebraicExtensionField PrimeField p
factor: % -> Factored %
from UniqueFactorizationDomain
factorsOfCyclicGroupSize: () -> List Record(factor: Integer, exponent: Integer)
from FiniteFieldCategory
Frobenius: % -> %
from ExtensionField PrimeField p
Frobenius: (%, NonNegativeInteger) -> %
from ExtensionField PrimeField p
gcd: (%, %) -> %
from GcdDomain
gcd: List % -> %
from GcdDomain
gcdPolynomial: (SparseUnivariatePolynomial %, SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial %
from GcdDomain
generator: () -> %
from FiniteAlgebraicExtensionField PrimeField p
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
index: PositiveInteger -> %
from Finite
inGroundField?: % -> Boolean
from ExtensionField PrimeField p
init: %
from StepThrough
inv: % -> %
from DivisionRing
latex: % -> String
from SetCategory
lcm: (%, %) -> %
from GcdDomain
lcm: List % -> %
from GcdDomain
lcmCoef: (%, %) -> Record(llcm_res: %, coeff1: %, coeff2: %)
from LeftOreRing
leftPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
leftPower: (%, PositiveInteger) -> %
from Magma
leftRecip: % -> Union(%, failed)
from MagmaWithUnit
linearAssociatedExp: (%, SparseUnivariatePolynomial PrimeField p) -> %
from FiniteAlgebraicExtensionField PrimeField p
linearAssociatedLog: % -> SparseUnivariatePolynomial PrimeField p
from FiniteAlgebraicExtensionField PrimeField p
linearAssociatedLog: (%, %) -> Union(SparseUnivariatePolynomial PrimeField p, failed)
from FiniteAlgebraicExtensionField PrimeField p
linearAssociatedOrder: % -> SparseUnivariatePolynomial PrimeField p
from FiniteAlgebraicExtensionField PrimeField p
lookup: % -> PositiveInteger
from Finite
minimalPolynomial: % -> SparseUnivariatePolynomial PrimeField p
from FiniteAlgebraicExtensionField PrimeField p
minimalPolynomial: (%, PositiveInteger) -> SparseUnivariatePolynomial %
from FiniteAlgebraicExtensionField PrimeField p
multiEuclidean: (List %, %) -> Union(List %, failed)
from EuclideanDomain
nextItem: % -> Union(%, failed)
from StepThrough
norm: % -> PrimeField p
from FiniteAlgebraicExtensionField PrimeField p
norm: (%, PositiveInteger) -> %
from FiniteAlgebraicExtensionField PrimeField p
normal?: % -> Boolean
from FiniteAlgebraicExtensionField PrimeField p
normalElement: () -> %
from FiniteAlgebraicExtensionField PrimeField p
one?: % -> Boolean
from MagmaWithUnit
opposite?: (%, %) -> Boolean
from AbelianMonoid
order: % -> OnePointCompletion PositiveInteger
from FieldOfPrimeCharacteristic
order: % -> PositiveInteger
from FiniteFieldCategory
prime?: % -> Boolean
from UniqueFactorizationDomain
primeFrobenius: % -> %
from FieldOfPrimeCharacteristic
primeFrobenius: (%, NonNegativeInteger) -> %
from FieldOfPrimeCharacteristic
primitive?: % -> Boolean
from FiniteFieldCategory
primitiveElement: () -> %
from FiniteFieldCategory
principalIdeal: List % -> Record(coef: List %, generator: %)
from PrincipalIdealDomain
quo: (%, %) -> %
from EuclideanDomain
random: () -> %
from Finite
recip: % -> Union(%, failed)
from MagmaWithUnit
rem: (%, %) -> %
from EuclideanDomain
representationType: () -> Union(prime, polynomial, normal, cyclic)
from FiniteFieldCategory
represents: Vector PrimeField p -> %
from FiniteAlgebraicExtensionField PrimeField p
retract: % -> PrimeField p
from RetractableTo PrimeField p
retractIfCan: % -> Union(PrimeField p, failed)
from RetractableTo PrimeField p
rightPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
rightPower: (%, PositiveInteger) -> %
from Magma
rightRecip: % -> Union(%, failed)
from MagmaWithUnit
sample: %
from AbelianMonoid
size: () -> NonNegativeInteger
from Finite
sizeLess?: (%, %) -> Boolean
from EuclideanDomain
smaller?: (%, %) -> Boolean
from Comparable
squareFree: % -> Factored %
from UniqueFactorizationDomain
squareFreePart: % -> %
from UniqueFactorizationDomain
subtractIfCan: (%, %) -> Union(%, failed)
from CancellationAbelianMonoid
tableForDiscreteLogarithm: Integer -> Table(PositiveInteger, NonNegativeInteger)
from FiniteFieldCategory
trace: % -> PrimeField p
from FiniteAlgebraicExtensionField PrimeField p
trace: (%, PositiveInteger) -> %
from FiniteAlgebraicExtensionField PrimeField p
transcendenceDegree: () -> NonNegativeInteger
from ExtensionField PrimeField p
transcendent?: % -> Boolean
from ExtensionField PrimeField p
unit?: % -> Boolean
from EntireRing
unitCanonical: % -> %
from EntireRing
unitNormal: % -> Record(unit: %, canonical: %, associate: %)
from EntireRing
zero?: % -> Boolean
from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

Algebra %

Algebra Fraction Integer

BasicType

BiModule(%, %)

BiModule(Fraction Integer, Fraction Integer)

BiModule(PrimeField p, PrimeField p)

CancellationAbelianMonoid

canonicalsClosed

canonicalUnitNormal

CharacteristicNonZero

CharacteristicZero if PrimeField p has CharacteristicZero

CoercibleTo OutputForm

CommutativeRing

CommutativeStar

Comparable

ConvertibleTo InputForm

DifferentialRing

DivisionRing

EntireRing

EuclideanDomain

ExtensionField PrimeField p

Field

FieldOfPrimeCharacteristic

Finite

FiniteAlgebraicExtensionField PrimeField p

FiniteFieldCategory

GcdDomain

IntegralDomain

LeftModule %

LeftModule Fraction Integer

LeftModule PrimeField p

LeftOreRing

Magma

MagmaWithUnit

Module %

Module Fraction Integer

Module PrimeField p

Monoid

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors

PrincipalIdealDomain

RetractableTo PrimeField p

RightModule %

RightModule Fraction Integer

RightModule PrimeField p

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

StepThrough

UniqueFactorizationDomain

unitsKnown

VectorSpace PrimeField p