56 Finite Fields

This chapter describes the special functionality which exists in GAP for finite fields and their elements. Of course the general functionality for fields (see Chapter Fields and Division Rings) also applies to finite fields.

In the following, the term finite field element is used to denote GAP objects in the category IsFFE (see IsFFE), and finite field means a field consisting of such elements. Note that in principle we must distinguish these fields from (abstract) finite fields. For example, the image of the embedding of a finite field into a field of rational functions in the same characteristic is of course a finite field but its elements are not in IsFFE, and in fact GAP does currently not support such fields.

Special representations exist for row vectors and matrices over small finite fields (see sections Row Vectors over Finite Fields and Matrices over Finite Fields).

Sections

  1. Finite Field Elements
  2. Operations for Finite Field Elements
  3. Creating Finite Fields
  4. FrobeniusAutomorphism
  5. Conway Polynomials

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GAP 4 manual
February 2000