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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