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use alloc::vec::Vec;
use crate::{Degree, Term, TryAddError};
pub trait SizedPolynomial<N> {
/// Returns the term with the given degree from `self`.
/// If the term degree is larger than the actual degree, `ZeroTerm` will be returned.
/// However, terms which are zero will also be returned as `ZeroTerm`, so this does
/// not indicate that the final term has been reached.
fn term_with_degree(&self, degree: usize) -> Term<N>;
/// Returns a Vec containing all of the terms of `self`, where each item is
/// the coefficient and degree of each non-zero term, in order of descending degree.
///
/// # Example
///
/// ```
/// use rustnomial::{Polynomial, SizedPolynomial};
/// let polynomial = Polynomial::new(vec![1, 0, 2, 3]);
/// let terms = polynomial.terms_as_vec();
/// let mut iter = terms.into_iter();
/// assert_eq!(Some((1, 3)), iter.next());
/// assert_eq!(Some((2, 1)), iter.next());
/// assert_eq!(Some((3, 0)), iter.next());
/// assert_eq!(None, iter.next());
/// ```
fn terms_as_vec(&self) -> Vec<(N, usize)>;
/// Returns the degree of `self`.
fn degree(&self) -> Degree;
/// Returns the zero-instance of `Self`.
fn zero() -> Self
where
Self: Sized;
/// Returns true if all terms of `self` are zero, and false if a non-zero term exists.
///
/// # Example
///
/// ```
/// use rustnomial::{SizedPolynomial, Polynomial};
/// let zero = Polynomial::new(vec![0, 0]);
/// assert!(zero.is_zero());
/// let non_zero = Polynomial::new(vec![0, 1]);
/// assert!(!non_zero.is_zero());
/// ```
fn is_zero(&self) -> bool {
self.degree() == Degree::NegInf
}
/// Sets the terms of `self` to zero.
fn set_to_zero(&mut self);
}
pub trait GenericPolynomial<N>: SizedPolynomial<N> + MutablePolynomial<N> + Evaluable<N> {}
pub trait MutablePolynomial<N> {
/// Tries to add the term with given coefficient and `degree` to `self`, returning an error
/// if the particular term can not be added to self without violating constraints.
///
/// # Errors
/// Fails if the term with coefficient `coeff` and degree `degree` can not be added
/// to `self` without violating one or more of `self`'s invariants.
fn try_add_term(&mut self, coeff: N, degree: usize) -> Result<(), TryAddError>;
/// Tries to subtract the term with given coefficient and `degree` from `self`, returning
/// an error if the particular term can not be subtracted from self without violating
/// constraints.
///
/// # Errors
/// Fails if the term with coefficient `coeff` and degree `degree` can not be subtracted from
/// `self` without violating one or more of `self`'s invariants.
fn try_sub_term(&mut self, coeff: N, degree: usize) -> Result<(), TryAddError>;
}
pub trait FreeSizePolynomial<N> {
/// Creates an instance of `self` with the provided terms.
fn from_terms(terms: &[(N, usize)]) -> Self
where
Self: Sized;
/// Adds the term with given coefficient `coeff` and degree `degree` to `self`.
fn add_term(&mut self, coeff: N, degree: usize);
}
pub trait Evaluable<N> {
/// Evaluates `self` at `point`, and returns the result.
fn eval(&self, point: N) -> N;
}