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StandardFF

( Version 0.9.4 )

August 2022

Frank Lübeck
Email: Frank.Luebeck@Math.RWTH-Aachen.De
Homepage: https://www.math.rwth-aachen.de/~Frank.Luebeck

Copyright

This package may be distributed under the terms and conditions of the GNU Public License Version 3 or later, see https://www.gnu.org/licenses.

Colophon

WARNING: 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 standard polynomials defining finite fields and standard generators of cyclic multiplicative subgroups.

In version 1.0 and later the definitions will not be changed anymore.

1 Introduction to StandardFF package

1.1 Aim

2 Standard finite fields

2.1 Definition of standard finite fields

2.2 Creating standard finite fields

2.2-1 Constructing standard finite fields
2.2-2 Filters for standard fields

2.3 Elements in standard finite fields

2.3-1 Maps for elements of standard finite fields

2.4 Embeddings of standard finite fields

  2.4-1 SteinitzPair
  2.4-2 Embedding
  2.4-3 ZZ
  2.4-4 MoveToSmallestStandardField
  2.4-5 StandardIsomorphismGF

3 Standard generators of cyclic groups