Minilib.Math.Polynomial
Defined in minilib-math@0.6.1
Polynomial of one variable, for example x^2 + 2x + 1. The coefficients can be any ring.
Values
namespace Minilib.Math.Polynomial
at_degree
Type: [a : Minilib.Math.Types::Ring] Std::I64 -> a -> Minilib.Math.Polynomial::Polynomial a
a.at_degree(n) creates a polynomial a * x ^ n.
generate
Type: Std::I64 -> Std::I64 -> Std::Iterator::DynIterator (Minilib.Math.Polynomial::Polynomial (Minilib.Math.Modular::Modular Std::I64))
generate(p,m) generates polynomials of degree m or lower in GF(p).
generate_primitive_polynomials
Type: Std::I64 -> Std::I64 -> Std::Iterator::DynIterator (Minilib.Math.Polynomial::Polynomial (Minilib.Math.Modular::Modular Std::I64))
generate_primitive_polynomials(p, m) generates primitive polynomials of degree m in GF(p).
get
Type: [a : Minilib.Math.Types::Ring] Std::I64 -> Minilib.Math.Polynomial::Polynomial a -> a
f.get(i) returns the coefficient of degree i.
get_degree
Type: Minilib.Math.Polynomial::Polynomial a -> Std::I64
f.get_degree returns the degree of a polynomial f.
is_primitive
Type: Minilib.Math.Polynomial::Polynomial (Minilib.Math.Modular::Modular Std::I64) -> Std::Bool
Checks whether it is a primitive polynomial.
make
Type: [a : Minilib.Math.Types::Ring] Std::Array a -> Minilib.Math.Polynomial::Polynomial a
Polynomial::make(coeff) creates a polynomial from coefficients.
For example, Polynomial::make([1,2,3]) makes a polynomial 3x^2 + 2x + 1.
For polynomials with degree greater than zero, the coefficient array is
truncated so that the coefficient of highest degree is not zero.
polynomial
Type: [a : Minilib.Math.Types::Ring] Std::Array a -> Minilib.Math.Polynomial::Polynomial a
Synonym for Polynomial::make.
set
Type: [a : Minilib.Math.Types::Ring] Std::I64 -> a -> Minilib.Math.Polynomial::Polynomial a -> Minilib.Math.Polynomial::Polynomial a
f.set(i, a) sets the coefficient of degree i.
subst
Type: [a : Minilib.Math.Types::Ring] a -> Minilib.Math.Polynomial::Polynomial a -> a
f.subst(x) substitutes the indeterminate of a polynomial with x.
subst0
Type: [a : Minilib.Math.Types::Ring] a -> (c -> a -> a) -> Minilib.Math.Polynomial::Polynomial c -> a
f.subst0(x, mul_coeff) substitutes the indeterminate of a polynomial with x.
mul_coeff is a function that multiplies a value of type a by a coefficient of type c.
Types and aliases
namespace Minilib.Math.Polynomial
Polynomial
Defined as: type Polynomial a = unbox struct { ...fields... }
A structure that represents a polynomial over a ring.
The coefficient array is ascending order of degree.
For example, [1,2,3] means a polynomial 3x^2 + 2x + 1.
field coeff
Type: Std::Array a
Traits and aliases
Trait implementations
impl Minilib.Math.Polynomial::Polynomial : Std::Functor
impl [a : Minilib.Math.Types::Field] Minilib.Math.Polynomial::Polynomial a : Minilib.Math.Types::DivMod
divmod(num, den) calculates a quotient quo = num / den
and a reminder rem = num % den.
Returns (quo, rem).
The type of coefficients must be a field.
If the division of the field does not fulfill the requirement
(ie. forall a b, a == a / b * b),
this function may return an incorrect result.