- Introduction
- Creation Functions
- Creation of Structures
- FiniteField(q) : RngIntElt -> FldFin
- FiniteField(p, n) : RngIntElt, RngIntElt -> FldFin
- ext<F | n> : FldFin, RngIntElt -> FldFin, Map
- ext<F | P> : FldFin, RngUPolElt[FldFin] -> FldFin, Map
- ExtensionField<F, x | P> : FldFin, ... -> FldFin, Map
- RandomExtension(F, n) : FldFin, RngIntElt -> FldFin
- SplittingField(P) : RngUPolElt[FldFin] -> FldFin
- SplittingField(S) : RngUPolElt[FldFin] -> FldFin
- sub<F | d> : FldFin, RngIntElt -> FldFin, Map
- sub<F | f> : FldFin, FldFinElt -> FldFin, Map
- GroundField(F) : FldFin -> FldFin
- PrimeField(F) : FldFin -> FldFin
- IsPrimeField(F) : Fld -> BoolElt
- F meet G : FldFin, FldFin -> FldFin
- CommonOverfield(K, L) : FldFin, FldFin -> FldFin
- Example FldFin_Extensions (H22E1)
- Creating Relations
- Embed(E, F) : FldFin, FldFin ->
- Embed(E, F, x) : FldFin, FldFin, FldFinElt ->
- IsIsomorphic(E, F) : FldFin, FldFin -> BoolElt, Map[FldFin, FldFin]
- Special Options
- AssertAttribute(FldFin, "PowerPrinting", l) : Cat, MonStgElt, BoolElt ->
- SetPowerPrinting(F, l) : FldFin, BoolElt ->
- HasAttribute(FldFin, "PowerPrinting", l) : Cat, MonStgElt, BoolElt ->
- HasAttribute(F, "PowerPrinting") : FldFin, MonStgElt -> BoolElt, BoolElt
- AssignNames(~F, [f]) : FldFin, [ MonStgElt ]) ->
- Name(F, 1) : FldFin, RngIntElt -> FldFinElt
- Homomorphisms
- Creation of Elements
- Special Elements
- Sequence Conversions
- Structure Operations
- Related Structures
- AdditiveGroup(F) : FldFin -> GrpAb, Map
- MultiplicativeGroup(F) : FldFin -> GrpAb, Map
- Set(F) : FldFin -> SetEnum
- VectorSpace(F, E) : FldFin, FldFin -> ModTupFld, Map
- VectorSpace(F, E, B) : FldFin, FldFin, [ FldFinElt ] -> ModTupFld, Map
- MatrixAlgebra(F, E) : FldFin, FldFin -> AlgMat, Map
- MatrixAlgebra(A, E) : AlgMat, FldFin -> AlgMat, Map
- Example FldFin_VectorSpace (H22E2)
- GaloisGroup(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 -> FldFinElt
- Norm(a, E) : FldFinElt, FldFin -> FldFinElt
- AbsoluteNorm(a) : FldFinElt -> FldFinElt
- Trace(a) : FldFinElt -> FldFinElt
- Trace(a, E) : FldFinElt, FldFin -> FldFinElt
- AbsoluteTrace(a) : FldFinElt -> FldFinElt
- Frobenius(a) : FldFinElt -> FldFinElt
- Frobenius(a, r) : FldFinElt, RngIntElt -> FldFinElt
- Frobenius(a, E) : FldFinElt, FldFin -> FldFinElt
- Frobenius(a, E, r) : FldFinElt, FldFin, RngIntElt -> FldFinElt
- NormEquation(K, y) : FldFin, FldFin -> BoolElt, FldFinElt
- Hilbert90(a, q) : FldFinElt, RngIntElt -> FldFinElt
- AdditiveHilbert90(a, q) : FldFinElt, RngIntElt -> FldFinElt
- Order and Roots
- Polynomials for Finite Fields
- IrreduciblePolynomial(F, n) : FldFin, RngIntElt -> RngUPolElt
- RandomIrreduciblePolynomial(F, n) : FldFin, RngIntElt -> RngUPolElt
- IrreducibleLowTermGF2Polynomial(n) : RngIntElt -> RngUPolElt
- IrreducibleSparseGF2Polynomial(n) : RngIntElt -> RngUPolElt
- PrimitivePolynomial(F, m) : FldFin, RngIntElt -> RngUPolElt
- AllIrreduciblePolynomials(F, m) : FldFin, RngIntElt -> { RngUPolElt }
- ConwayPolynomial(p, n) : RngIntElt, RngIntElt -> RngUPolElt
- ExistsConwayPolynomial(p, n) : RngIntElt, RngIntElt -> BoolElt, RngUPolElt
- Discrete Logarithms
- Permutation Polynomials
- Bibliography
V2.29, 3 August 2026