Module Pari.Polynomial

create a returns a_{n-1} X^{n-1} + ... + a_0 for array a of length n.

# let q = Polynomial.create
  [|
    Integer.of_int 1;
    Integer.of_int (-111);
    Integer.of_int 6064;
    Integer.of_int (-189804);
  |];;
val q : Integer.t Polynomial.t = <abstr>
# Polynomial.to_string q;;
- : string = "x^3 - 111*x^2 + 6064*x - 189804"
# let zero = Polynomial.create [| Integer.of_int 0 |];;
val zero : Integer.t Polynomial.t = <abstr>
# let qq = Polynomial.create [| q; q; zero; zero |];;
val qq : Integer.t Polynomial.t Polynomial.t = <abstr>
# Polynomial.to_string qq;;
- : string =
"(x^3 - 111*x^2 + 6064*x - 189804)*y^3 + (x^3 - 111*x^2 + 6064*x - 189804)*y^2"

minimal p reduces p to be the minimal polynomial of the roots of p over the field of the rational numbers.

# let q = Polynomial.create
  [|
    (Rational.of_int 1);
    (Rational.of_int (-111));
    (Rational.of_int 6064);
    (Rational.of_int (-189804));
  |];;
val q : Rational.t Polynomial.t = <abstr>
# Polynomial.to_string q;;
- : string = "x^3 - 111*x^2 + 6064*x - 189804"
# let qmin = Polynomial.minimal q;;
val qmin : Rational.t Polynomial.t = <abstr>
# Polynomial.to_string qmin;;
- : string = "x^3 - x^2 - 60*x - 364"
# Number_field.(are_isomorphic (create q) (create qmin));
- : bool = true