Struct Germ 

pub struct Germ { /* private fields */ }

A germ at dt = 0. See the module documentation.

Implementations

impl Germ

pub fn is_transmissible(&self) -> bool

Whether the germ can travel as data: one holding a real built from a function a program defines cannot, that function staying with the program.

pub fn from_hyperreal(h: &Hyperreal) -> Germ

The series of a hyperreal.

pub fn from_puiseux(p: &Puiseux) -> Germ

The expansion of a value of the real closure, on its branch’s grid.

pub fn from_i64(n: i64) -> Germ

pub fn constant(x: &ExactReal) -> Germ

A computable real, constant in dt.

pub fn as_hyperreal(&self) -> Option<&Hyperreal>

The rational function this germ is the series of, when it was built as one.

pub fn flow(flow: &Arc<Flow>, i: usize) -> Germ

Component i of a flow’s state.

pub fn standard(x: &ExactReal) -> Germ

A limited value known by its standard part alone; every higher order is GermError::StandardOnly.

pub fn unlimited(sign: i32) -> Germ

A value beyond every bound with the sign of sign.

pub fn ramification(&self) -> u32

The ramification q: order k is the coefficient of dt^(k/q).

pub fn unlimited_sign(&self) -> Option<i32>

The sign of an unlimited germ; None for a limited one and for one whose order is not known.

pub fn floor(&self) -> i64

The lowest order whose coefficient may be nonzero, in units of dt^(1/q).

pub fn coefficient(&self, k: i64) -> Result<ExactReal, GermError>

The coefficient of dt^(k/q), q the Germ::ramification.

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

pub fn neg(&self) -> Germ

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

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

pub fn leading(&self) -> Result<(i64, ExactReal), GermError>

The order, in units of dt^(1/q), and the coefficient of the first nonzero term.

pub fn recip(&self) -> Result<Germ, GermError>

pub fn root(&self, n: u32) -> Result<Germ, GermError>

The real n-th root (n ≥ 1), the nonnegative one for an even n; refused for a negative germ and an even n.

pub fn exp(&self) -> Result<Germ, GermError>

exp(self), refused for an infinite value, whose exponential lies beyond every power of dt.

pub fn ln(&self) -> Result<Germ, GermError>

The natural logarithm of a value whose standard part is positive; one that is negative has none, and one that is a positive infinitesimal or infinite carries the logarithm of dt.

pub fn div(&self, o: &Germ) -> Result<Germ, GermError>

pub fn signum(&self) -> Result<i32, GermError>

−1, 0 (only for a germ that is exactly a zero rational function) or 1.

pub fn standard_part(&self) -> Result<Option<ExactReal>, GermError>

The standard part of a limited germ; None for an infinite one.

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

The two leading orders and, from the order after the last one shown on the germ’s grid, what is left, the infinitesimal written name: e - (1/2)·e·dt + O(dt^2), 1 + √dt + O(dt).

Trait Implementations

impl Clone for Germ

fn clone(&self) -> Germ

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Germ

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

Formats the value using the given formatter.

impl ExactCodec for Germ

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

A node tag, then the node: 0 the series of a hyperreal; 1 a sum and 2 a product of two germs; 3 a negation; 4 a reciprocal, whose leading term is found again on reading; 5 a component of a flow — its width n, the number of update terms and each as n × n rationals, T, δ, the n start germs and the component; 6 a computable real constant in dt; 7 a value known by its standard part; 8 an unlimited value by its sign; 10 a value of the real closure; 11 an exponential, 12 a logarithm and 13 an n-th root, n after the germ; 14 a component of a flow whose update is a polynomial in a root of dt, its grid and then the fields of 5. A germ refined to a finer grid is written as itself: every node that meets two grids meets them again as it is read.

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

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

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

The value buf canonically encodes, with nothing left over.