Enum Multi 

pub enum Multi {
    Standard(Algebraic),
    One(Closed, Arc<Scale>),
    Over {
        scale: Arc<Scale>,
        q: u32,
        num: PolyOver<Multi>,
        den: PolyOver<Multi>,
    },
    Alg(Arc<AlgValue>),
}

A value of several ordered infinitesimals. See the module documentation.

Variants

Standard(Algebraic)

A standard number.

One(Closed, Arc<Scale>)

A value of one infinitesimal, not standard.

Over

num/den in scale^(1/q), every coefficient a value of larger infinitesimals and at least one not standard.

Fields

scale: Arc<Scale>

q: u32

num: PolyOver<Multi>

den: PolyOver<Multi>

Alg(Arc<AlgValue>)

A value of the real closure at its smallest infinitesimal that is no rational function of a root of it (crate::closure).

Implementations

impl Multi

pub fn generator(scale: &Arc<Scale>) -> Multi

The infinitesimal itself.

pub fn of_closed(c: Closed, scale: &Arc<Scale>) -> Multi

A value of one infinitesimal, in its one form.

pub fn top(&self) -> Option<&Arc<Scale>>

The smallest infinitesimal the value involves; None for a standard number.

pub fn scales(&self) -> Vec<Arc<Scale>>

Every infinitesimal the value involves, each once, with the facts all of its parts state.

pub fn standard_part_at(&self, at: Option<&Arc<Scale>>) -> Option<Multi>

What the value is infinitely close to among the values of at and the infinitesimals larger than it, when it is limited from at’s standpoint: every infinitesimal smaller than at read at zero, the inner limit with at held fixed. With no at, the standard part. None for a value infinite from that standpoint. Every infinitesimal of the value is ordered with at.

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

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

pub fn is_infinitesimal_at(&self, at: Option<&Arc<Scale>>) -> bool

Zero, or smaller than every positive value of at and the infinitesimals larger than it (every positive standard number, with no at).

pub fn is_limited_at(&self, at: Option<&Arc<Scale>>) -> bool

Bounded by a value of at and the infinitesimals larger than it (a standard number, with no at).

pub fn is_infinitesimal(&self) -> bool

pub fn is_limited(&self) -> bool

pub fn pow(&self, k: i32) -> Result<Multi, MultiPowerError>

self^k; refused for zero to a negative power and for a degree past crate::hyperreal::MAX_POWER_DEGREE in any of the value’s infinitesimals.

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

The real n-th root, the nonnegative one for an even n: of a value of one infinitesimal in its real closure, and of a product of a power of the smallest infinitesimal and a value of the larger ones as the product of their roots.

impl Multi

pub fn render(&self) -> String

The value as an exact fraction of polynomials in its infinitesimals, as a hyperreal prints: a polynomial with its coefficients as they are, (1/2)·dt + dx, and any other value as a fraction of polynomials with coprime integer coefficients where every coefficient is rational, dx/(2·dt). An infinite integer prints as one of one infinitesimal does, a sum of reciprocals (Multi::render_reciprocals), wherever it is printed — alone, under a radical, as a coefficient.

impl Multi

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

The value’s canonical bytes: each infinitesimal it involves once, by its name, its declaration (Scale::to_bytes) and the facts about its reciprocal the value holds it with — a residue class’s, on which an infinite integer of several is one — in the order a walk of the value first meets them; then the value, each infinitesimal written by its place among them.

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

The value Multi::to_bytes wrote; None for a forged or non-canonical encoding.

Trait Implementations

impl Clone for Multi

fn clone(&self) -> Multi

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Coefficient for Multi

A value of several infinitesimals is the coefficient of an expansion in a smaller one, exactly.

fn zero() -> Self

fn one() -> Self

fn of_rational(r: Rational) -> Self

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

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

fn neg(&self) -> Result<Self, ExpansionError>

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

fn is_zero(&self) -> Result<bool, ExpansionError>

Whether the coefficient is zero; refused when that cannot be told.

fn recip(&self) -> Result<Self, ExpansionError>

fn sign(&self) -> Result<i32, ExpansionError>

−1, 0 or 1; refused when the sign cannot be told.

fn nth_root(&self, n: u32) -> Result<Self, ExpansionError>

The real n-th root, the nonnegative one for an even n.

fn exp(&self) -> Result<Self, ExpansionError>

exp, for an expansion’s exponential.

fn ln(&self) -> Result<Self, ExpansionError>

The natural logarithm of a positive coefficient, for an expansion’s logarithm.

impl Debug for Multi

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

Formats the value using the given formatter.

impl Hash for Multi

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

Equal values have one form, and one infinitesimal one name.

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 OrderedField for Multi

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 Multi

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 Multi