  
  
                                   [1X[5XStandardFF[105X[101X
  
  
                               ( Version 0.9.4 )
  
  
                                  August 2022
  
  
                                  Frank Lübeck
  
  
  
  Frank Lübeck
      Email:    [7Xmailto:Frank.Luebeck@Math.RWTH-Aachen.De[107X
      Homepage: [7Xhttps://www.math.rwth-aachen.de/~Frank.Luebeck[107X
  
  -------------------------------------------------------
  [1XCopyright[101X
  [33X[0;0Y© 2020- by Frank Lübeck[133X
  
  [33X[0;0YThis  package  may  be distributed under the terms and conditions of the GNU
  Public License Version 3 or later, see [7Xhttps://www.gnu.org/licenses[107X.[133X
  
  
  -------------------------------------------------------
  [1XColophon[101X
  [33X[0;0YWARNING:  This package implements the constructions in the paper [Lüb22]. As
  long as that paper is not published we reserve the right to still change the
  definition  of  [13Xstandard[113X  polynomials  defining  finite  fields and [13Xstandard[113X
  generators of cyclic multiplicative subgroups.[133X
  
  [33X[0;0YIn version 1.0 and later the definitions will not be changed anymore.[133X
  
  
  -------------------------------------------------------
  
  
  [1XContents (StandardFF)[101X
  
  1 [33X[0;0YIntroduction to [5XStandardFF[105X package[133X
    1.1 [33X[0;0YAim[133X
  2 [33X[0;0YStandard finite fields[133X
    2.1 [33X[0;0YDefinition of standard finite fields[133X
    2.2 [33X[0;0YCreating standard finite fields[133X
      2.2-1 [33X[0;0YConstructing standard finite fields[133X
      2.2-2 [33X[0;0YFilters for standard fields[133X
    2.3 [33X[0;0YElements in standard finite fields[133X
      2.3-1 [33X[0;0YMaps for elements of standard finite fields[133X
    2.4 [33X[0;0YEmbeddings of standard finite fields[133X
      2.4-1 SteinitzPair
      2.4-2 Embedding
      2.4-3 ZZ
      2.4-4 MoveToSmallestStandardField
      2.4-5 StandardIsomorphismGF
  3 [33X[0;0YStandard generators of cyclic groups[133X
    3.1 [33X[0;0YGenerators of multiplicative groups[133X
      3.1-1 StandardCyclicGenerator
  4 [33X[0;0YUtilities from the [5XStandardFF[105X package[133X
    4.1 [33X[0;0YA simple bijection on a range[133X
      4.1-1 StandardAffineShift
    4.2 [33X[0;0YFinding linear combinations[133X
      4.2-1 FindLinearCombination
    4.3 [33X[0;0YIrreducibility over finite fields[133X
      4.3-1 IsIrreducibleCoeffList
    4.4 [33X[0;0YConnection to Conway polynomials[133X
      4.4-1 FindConjugateZeroes
      4.4-2 ZeroesConway
      4.4-3 SteinitzPairConwayGenerator
    4.5 [33X[0;0YDiscrete logarithms[133X
      4.5-1 DLog
    4.6 [33X[0;0YMinimal polynomials of sequences[133X
      4.6-1 InvModCoeffs
      4.6-2 BerlekampMassey
      4.6-3 MinimalPolynomialByBerlekampMassey
    4.7 [33X[0;0YBrauer characters with respect to different lifts[133X
      4.7-1 StandardValuesBrauerCharacter
      4.7-2 [33X[0;0YFrobenius character values[133X
    4.8 [33X[0;0YKnown factorizations of multiplicative group orders[133X
      4.8-1 CANFACT
    4.9 [33X[0;0YSome loops for [5XStandardFF[105X[133X
      4.9-1 [33X[0;0YComputing all fields in various ranges[133X
    4.10 [33X[0;0YUndocumented features[133X
  
  
  [32X
