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ConwayPolynomials -- database of Conway polynomials for use with GF

Description

ConwayPolynomials is a package that provides a database of Conway polynomials. A Conway polynomial for a prime p and an exponent n is a particular monic polynomial whose roots are primitive elements of a finite field with p^n elements. They can take a very long time to compute, so the package comes with just a publicly available database of Conway polynomials provided by Frank Luebeck.

After the package is loaded, the function GF will return Galois fields presented by Conway polynomials, provided they are in the table. Moreover, map can be used to produce the canonical maps between Conway Galois fields.

i1 : conwayPolynomial 125

      3
o1 = a  - 2a - 2

     ZZ
o1 : --[a]
      5
i2 : GF 125

o2 = GF 125

o2 : GaloisField
i3 : ambient oo

        ZZ
        --[a]
         5
o3 = -----------
      3
     a  - 2a - 2

o3 : QuotientRing
i4 : map(GF 125^2, GF 125)

                             5    4    3    2
o4 = map(GF 15625,GF 125,{- a  + a  - a  - a  - 2a - 2})

o4 : RingMap GF 15625 <--- GF 125
i5 : isWellDefined oo

o5 = true

Author

Version

This documentation describes version 1.0 of ConwayPolynomials.

Source code

The source code from which this documentation is derived is in the file ConwayPolynomials.m2. The auxiliary files accompanying it are in the directory ConwayPolynomials/.

Exports