Struct Algebraic 

pub struct Algebraic { /* private fields */ }

A real algebraic number. See the module documentation.

Implementations

impl Algebraic

pub fn from_i64(n: i64) -> Algebraic

pub fn from_rational(r: Rational) -> Algebraic

pub fn from_f64(f: f64) -> Option<Algebraic>

The exact value of a finite float. None for NaN and the infinities.

pub fn root_of(p: &Poly, k: usize) -> Option<Algebraic>

The k-th real root of p (counting from 1 in increasing order, each distinct root once).

pub fn degree(&self) -> usize

pub fn minimal_polynomial(&self) -> &Poly

pub fn root_index(&self) -> usize

Which real root of the minimal polynomial this is, counting from 1 in increasing order.

pub fn to_rational(&self) -> Option<Rational>

pub fn is_zero(&self) -> bool

pub fn signum(&self) -> i32

pub fn enclosure(&self, bits: u32) -> (Rational, Rational)

A closed interval [lo, hi] holding the value, at most 2^-bits wide; a rational encloses itself exactly.

pub fn neg(&self) -> Algebraic

pub fn add(&self, o: &Algebraic) -> Algebraic

pub fn sub(&self, o: &Algebraic) -> Algebraic

pub fn mul(&self, o: &Algebraic) -> Algebraic

pub fn recip(&self) -> Option<Algebraic>

pub fn div(&self, o: &Algebraic) -> Option<Algebraic>

pub fn pow(&self, e: i32) -> Option<Algebraic>

self^e; None only for zero to a negative power.

pub fn sqrt(&self) -> Option<Algebraic>

The nonnegative square root; None for a negative number.

pub fn nth_root(&self, k: u32) -> Option<Algebraic>

The real k-th root: the nonnegative one for even k (None for a negative number), the unique one for odd k. None for k = 0.

pub fn real_roots(coeffs: &[Algebraic]) -> Vec<(Algebraic, usize)>

The distinct real roots of Σ coeffs[i]·x^i, a polynomial with real algebraic coefficients, in increasing order, each with its multiplicity; none for a constant.

Every root is a root of the polynomial’s norm over the rationals — the product of its conjugates under every embedding of its coefficients, a tower of resultants against their minimal polynomials (crate::elimination::Polynomial::resultant) — so the roots are found among the real roots of the norm’s irreducible factors, each kept when the polynomial vanishes there exactly.

pub fn floor(&self) -> BigInt

pub fn ceil(&self) -> BigInt

pub fn to_f64(&self) -> f64

The nearest f64 (ties to even): the interval is refined until both ends round alike.

Trait Implementations

impl Clone for Algebraic

fn clone(&self) -> Algebraic

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Algebraic

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

Formats the value using the given formatter.

impl Display for Algebraic

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

A rational as a rational; a quadratic irrational in simplified radical form ((1 + √5)/2, 3√2/4); anything of higher degree as root k of <minimal polynomial>.

impl ExactCodec for Algebraic

fn write(&self, out: &mut Vec<u8>)

The minimal polynomial, then which of its real roots, counting from 1.

fn read(buf: &[u8], pos: &mut usize) -> Option<Self>

Refused unless the polynomial is primitive with a positive lead, of degree at most crate::exact_codec::MAX_WIRE_DEGREE, irreducible, and has that many real roots.

fn to_bytes(&self) -> Vec<u8>

fn from_bytes(buf: &[u8]) -> Option<Self>

The value buf canonically encodes, with nothing left over.

impl Hash for Algebraic

fn hash<H: Hasher>(&self, state: &mut H)

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl Ord for Algebraic

fn cmp(&self, o: &Self) -> Ordering

This method returns an Ordering between self and other.

fn max(self, other: Self) -> Self

where Self: Sized,

Compares and returns the maximum of two values.

fn min(self, other: Self) -> Self

where Self: Sized,

Compares and returns the minimum of two values.

fn clamp(self, min: Self, max: Self) -> Self

where Self: Sized,

Restrict a value to a certain interval.

impl OrderedField for Algebraic

fn zero() -> Self

fn one() -> Self

fn from_i64(n: i64) -> Self

fn is_zero(&self) -> bool

fn add(&self, o: &Self) -> Self

fn neg(&self) -> Self

fn mul(&self, o: &Self) -> Self

fn recip(&self) -> Option<Self>

None for zero.

fn signum(&self) -> i32

−1, 0 or 1.

fn sub(&self, o: &Self) -> Self

impl PartialEq for Algebraic

fn eq(&self, o: &Self) -> 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 Algebraic

fn partial_cmp(&self, o: &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 Ring for Algebraic

fn lift(a: &Algebraic) -> Self

fn plus(&self, o: &Self) -> Result<Self, String>

fn times(&self, o: &Self) -> Result<Self, String>

impl Eq for Algebraic