Struct RealRoot

pub struct RealRoot { /* private fields */ }

One real root of a square-free integer polynomial.

Either an exact dyadic point (lo == hi), or the unique root in the open interval (lo, hi) with the polynomial non-zero at both ends.

Implementations

impl RealRoot

pub fn poly(&self) -> &IntPoly

The defining square-free polynomial.

pub fn bounds(&self) -> (&Dyadic, &Dyadic)

Current isolating interval [lo, hi].

pub fn is_exact(&self) -> bool

Whether the root is a known dyadic value.

pub fn refine(&mut self)

Halve the isolating interval once (or pin the root exactly).

pub fn refine_to_width(&mut self, width: &Dyadic)

Refine until the interval is no wider than width, or the root is exact.

pub fn approx(&self) -> f64

A double near the root (for output only; never for decisions).

pub fn cmp_dyadic(&self, x: &Dyadic) -> Sign

Exact sign of root - x for a dyadic x.

pub fn sign_of(&self, q: &IntPoly) -> Sign

Exact sign of the polynomial q at this root.

Zero is decided through gcd(poly, q): q vanishes at the root iff the gcd has a root in the isolating interval, which holds no other root of poly. Otherwise the interval is refined until q has no root in it, and q’s sign there is its sign at the root.

pub fn cmp_root(&self, other: &Self) -> Sign

Exact sign of self - other.

Distinct roots are separated by refinement, which terminates because they differ. Equality is decided exactly first: g = gcd of the two polynomials. A root of g in the overlap of the two isolating intervals is a root of each polynomial in each interval, and each interval holds only one, so it is both roots. No such root means they differ.

Trait Implementations

impl Clone for RealRoot

fn clone(&self) -> RealRoot

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for RealRoot

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl PartialEq for RealRoot

fn eq(&self, other: &RealRoot) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl PartialOrd for RealRoot

fn partial_cmp(&self, other: &Self) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

fn lt(&self, other: &Rhs) -> bool

Tests less than (for self and other) and is used by the < operator.

fn le(&self, other: &Rhs) -> bool

Tests less than or equal to (for self and other) and is used by the <= operator.

fn gt(&self, other: &Rhs) -> bool

Tests greater than (for self and other) and is used by the > operator.

fn ge(&self, other: &Rhs) -> bool

Tests greater than or equal to (for self and other) and is used by the >= operator.

impl Eq for RealRoot

impl StructuralPartialEq for RealRoot