Finite Fields Package

Plus, Times, D operators overloaded by the Finite Fields Package

GF represent a Galois field using its characteristic and irreducible polynomial coefficients

SetFieldFormat set the output form of elements in a field

FunctionOfCode  ▪  FunctionOfCoefficients

Characteristic prime characteristic of a field

ExtensionDegree extension degree of a field over its base field

FieldIrreducible univariate irreducible polynomial associated with a field

IrreduciblePolynomial univariate irreducible polynomial of a given degree

Element Manipulation

Successor next element in a canonical ordering of a field's elements

ReduceElement element of a field in reduced form

ToElementCode non-negative integer associated with a specified element in a field

FromElementCode element of a given field associated with a specified integer

PolynomialToElement field element corresponding to given polynomial coefficients

ElementToPolynomial univariate polynomial corresponding to a given field element

FieldExp value of the exponential function associated with a field for a given integer

FieldInd power to which the primitive element must be raised to get a specified element

PowerList data parts of nonzero elements of a field

PowerListToField field object based on a list of the type produced by PowerList

PowerListQ  ▪  PerfectPowerQ