Finite Fields
- Introduction
- Creation Functions
- Creation of Structures
FiniteField(q): RngIntElt → FldFinGaloisField(q): RngIntElt → FldFinGF(q): RngIntElt → FldFinFiniteField(p, n): RngIntElt, RngIntElt → FldFinGaloisField(p, n): RngIntElt, RngIntElt → FldFinGF(p, n): RngIntElt, RngIntElt → FldFinext<F | n>: FldFin, RngIntElt → FldFin, Mapext<F | P>: FldFin, RngUPolElt[FldFin] → FldFin, MapExtensionField<F, x | P>: FldFin, ... → FldFin, MapRandomExtension(F, n): FldFin, RngIntElt → FldFinSplittingField(P): RngUPolElt[FldFin] → FldFinSplittingField(S): { RngUPolElt[FldFin] } → FldFinsub<F | d>: FldFin, RngIntElt → FldFin, Mapsub<F | f>: FldFin, FldFinElt → FldFin, MapGroundField(F): FldFin → FldFinBaseField(F): FldFin → FldFinPrimeField(F): FldFin → FldFinIsPrimeField(F): Fld → BoolEltF meet G: FldFin, FldFin → FldFinCommonOverfield(K, L): FldFin, FldFin → FldFinExample: Extensions
- Creating Relations
Embed(E, F): FldFin, FldFinEmbed(E, F, x): FldFin, FldFin, FldFinEltIsIsomorphic(E, F): FldFin, FldFin → BoolElt, Map[FldFin, FldFin]
- Special Options
AssertAttribute({FldFin, }{"PowerPrinting", l}): Cat, MonStgElt, BoolEltSetPowerPrinting(F, l): FldFin, BoolEltAssertAttribute({F, }{"PowerPrinting", l}): FldFin, MonStgElt, BoolEltHasAttribute({FldFin, }{"PowerPrinting", l}): Cat, MonStgElt, BoolEltHasAttribute(F, "PowerPrinting"): FldFin, MonStgElt → BoolElt, BoolEltAssignNames(~F, [f]): FldFin, [ MonStgElt ])Name(F, 1): FldFin, RngIntElt → FldFinElt
- Homomorphisms
- Creation of Elements
- Special Elements
- Sequence Conversions
- Structure Operations
- Related Structures
Category(F): FldFin → CatParent(F): FldFin → PowerStructureCentre(F): FldFin → FldFinPrimeRing(F): FldFin → FldFinPrimeField(F): FldFin → FldFinFieldOfFractions(F): FldFin → FldFinAdditiveGroup(F): FldFin → GrpAb, MapMultiplicativeGroup(F): FldFin → GrpAb, MapUnitGroup(F): FldFin → GrpAb, MapSet(F): FldFin → SetEnumVectorSpace(F, E): FldFin, FldFin → ModTupFld, MapVectorSpace(F, E, B): FldFin, FldFin, [ FldFinElt ] → ModTupFld, MapMatrixAlgebra(F, E): FldFin, FldFin → AlgMat, MapMatrixAlgebra(A, E): AlgMat, FldFin → AlgMat, MapExample: Vector SpaceGaloisGroup(K, k): FldFin, FldFin → GrpPerm, [FldFinElt]AutomorphismGroup(K, k): FldFin, FldFin → GrpPerm, [Map], Map
- Numerical Invariants
- Defining Polynomial
- Ring Predicates and Booleans
- Roots
- Element Operations
- Arithmetic Operators
- Equality and Membership
- Parent and Category
- Predicates on Ring Elements
- Minimal and Characteristic Polynomial
- Norm, Trace and Frobenius
Norm(a): FldFinElt → FldFinEltNorm(a, E): FldFinElt, FldFin → FldFinEltAbsoluteNorm(a): FldFinElt → FldFinEltNormAbs(a): FldFinElt → FldFinEltTrace(a): FldFinElt → FldFinEltTrace(a, E): FldFinElt, FldFin → FldFinEltAbsoluteTrace(a): FldFinElt → FldFinEltTraceAbs(a): FldFinElt → FldFinEltFrobenius(a): FldFinElt → FldFinEltFrobenius(a, r): FldFinElt, RngIntElt → FldFinEltFrobenius(a, E): FldFinElt, FldFin → FldFinEltFrobenius(a, E, r): FldFinElt, FldFin, RngIntElt → FldFinEltNormEquation(K, y): FldFin, FldFin → BoolElt, FldFinEltHilbert90(a, q): FldFinElt, RngIntElt → FldFinEltAdditiveHilbert90(a, q): FldFinElt, RngIntElt → FldFinElt
- Order and Roots
- Polynomials for Finite Fields
IrreduciblePolynomial(F, n): FldFin, RngIntElt → RngUPolEltRandomIrreduciblePolynomial(F, n): FldFin, RngIntElt → RngUPolEltIrreducibleLowTermGF2Polynomial(n): RngIntElt → RngUPolEltIrreducibleSparseGF2Polynomial(n): RngIntElt → RngUPolEltPrimitivePolynomial(F, m): FldFin, RngIntElt → RngUPolEltAllIrreduciblePolynomials(F, m): FldFin, RngIntElt → { RngUPolElt }ConwayPolynomial(p, n): RngIntElt, RngIntElt → RngUPolEltExistsConwayPolynomial(p, n): RngIntElt, RngIntElt → BoolElt, RngUPolElt
- Discrete Logarithms
- Permutation Polynomials
