Enum Closed 

pub enum Closed {
    Field(Hyperreal),
    Series(Puiseux),
}

A value of the real closure in its one form: a hyperreal when it is a rational function of dt, otherwise a Puiseux series that is no such function.

Variants

Field(Hyperreal)

Series(Puiseux)

Implementations

impl Closed

pub fn from_hyperreal(h: Hyperreal) -> Closed

A hyperreal of the rational functions of dt.

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

The standard number the value is, when it has no infinitesimal part.

pub fn leading(&self) -> Option<(Rational, Algebraic)>

The exponent of the leading term in dt and its coefficient; None for zero.

pub fn is_zero(&self) -> bool

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

pub fn neg(&self) -> Closed

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

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

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

The reciprocal; None for zero. The reciprocal of a value that is no rational function of a root of dt is none either.

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

pub fn pow(&self, k: i32) -> Result<Closed, PowerRefusal>

self^k; refused for zero to a negative power and, on a rational function of a root of dt, for a power past crate::hyperreal::MAX_POWER_DEGREE in that root.

pub fn root(&self, n: u32) -> Result<Closed, String>

The real n-th root — the positive one for even n — or the reason there is none.

pub fn signum(&self) -> i32

−1, 0 or 1: the sign of the leading coefficient.

pub fn compare(&self, o: &Closed) -> Ordering

The order. The terms both expansions hold through the orders that separate their own polynomials’ roots decide it at the first place they differ; expansions that agree that far are ordered by the sign of the difference, which is the zero root of its polynomial exactly when the two are equal.

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

The exponent of the leading term in dt; None for zero.

pub fn is_infinitesimal(&self) -> bool

pub fn is_limited(&self) -> bool

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

The standard real infinitely close to a limited value; None for an infinite one.

pub fn render(&self, name: &str) -> String

The value with the infinitesimal written name.

impl Closed

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

The bytes of the value’s one form.

pub fn decode(buf: &[u8], pos: &mut usize) -> Option<Closed>

Trait Implementations

impl Clone for Closed

fn clone(&self) -> Closed

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Closed

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

Formats the value using the given formatter.

impl Hash for Closed

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

Equal values have one form, and two equal series one expansion: the field value itself, or a series by its leading term.

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 PartialEq for Closed

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 Eq for Closed