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conwayPolynomial -- provide a Conway polynomial

Description

Synopsis

  • Usage:
    conwayPolynomial(q,Variable=>a)
  • Inputs:
    • q, an integer, a power of a prime number
    • a, a symbol, an optional input, the symbol served as variable, default a
  • Outputs:
    • a Conway polynomial whose roots generate a field with q elements
i1 : conwayPolynomial 125

      3
o1 = a  - 2a - 2

     ZZ
o1 : --[a]
      5

Synopsis

  • Usage:
    conwayPolynomial(p,n,Variable=>a)
  • Inputs:
    • p, an integer, a prime number
    • n, an integer
    • a, a symbol, an optional input, the symbol served as variable, default a
  • Outputs:
    • a Conway polynomial whose roots generate a field with p^n elements
i2 : conwayPolynomial(2,20,Variable=>"b")

      20    10    9    7    6    5    4
o2 = b   + b   + b  + b  + b  + b  + b  + b + 1

     ZZ
o2 : --[b]
      2

Ways to use conwayPolynomial:

  • conwayPolynomial(ZZ)
  • conwayPolynomial(ZZ,ZZ)

For the programmer

The object conwayPolynomial is a method function with options.

The source of this document is in ConwayPolynomials.m2:102:0.