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Re: [Axiom-developer] A quick question about finite fields and polynomia


From: Ralf Hemmecke
Subject: Re: [Axiom-developer] A quick question about finite fields and polynomials
Date: Tue, 17 Apr 2012 18:13:37 +0200
User-agent: Mozilla/5.0 (X11; Linux x86_64; rv:11.0) Gecko/20120329 Thunderbird/11.0.1

I'm using FriCAS here, but AXIOM should most probably be the same.

Ralf

(1) -> p := 7

   (1)  7
Type: PositiveInteger
(2) -> P := PrimeField p

   (2)  PrimeField(7)

Type: Type
(3) -> F := FiniteField(p,4)

   (3)  FiniteField(7,4)

Type: Type
(4) -> a: F := (basis()$F).2

   (4)  %A
Type: FiniteField(7,4)
(5) -> u:=5*a^3+5*a^2+a

           3      2
   (5)  5%A  + 5%A  + %A
Type: FiniteField(7,4)
(6) -> c := coordinates(u)

   (6)  [0,1,5,5]
Type: Vector(PrimeField(7))
(7) -> x:=monomial(1,1)$SparseUnivariatePolynomial(P)

   (7)  ?
Type: SparseUnivariatePolynomial(PrimeField(7))
(8) -> poly := reduce(_+, [c.i * x^i for i in 1..#c], 0)

          4     3    2
   (8)  5?  + 5?  + ?
Type: SparseUnivariatePolynomial(PrimeField(7))
(9) -> factor poly

          2  2
   (9)  5? (?  + ? + 3)
Type: Factored(SparseUnivariatePolynomial(PrimeField(7)))



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