Struct HyperrealApprox 

pub struct HyperrealApprox {
    pub seq: Vec<f64>,
    pub filter: PrincipalUltrafilter,
}

A computable hyperreal approximation via a sequence of reals modulo a principal ultrafilter.

seq[principal] gives the “value” in the ultrapower for the principal ultrafilter.

Fields

seq: Vec<f64>

The underlying sequence (length = index set size of the ultrafilter).

filter: PrincipalUltrafilter

The ultrafilter used to form the equivalence class.

Implementations

impl HyperrealApprox

pub fn constant(r: f64, n: usize, principal: usize) -> Self

Construct the constant hyperreal r (constant sequence).

pub fn from_seq(seq: Vec<f64>, principal: usize) -> Self

Construct from an explicit sequence.

pub fn value(&self) -> f64

Return the representative value for this hyperreal (value at principal element).

pub fn is_standard_zero(&self) -> bool

Check if this hyperreal is “infinitesimal” by standard: |value| < eps for small eps.

In a principal ultrafilter model, infinitesimals are just zero at the representative.

pub fn standard_part(&self) -> f64

“Standard part”: return the value at the principal element (only meaningful for finite elements).

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

Addition of two hyperreals (pointwise on sequences).

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

Multiplication of two hyperreals (pointwise on sequences).

pub fn abs(&self) -> Self

Return the absolute value hyperreal.

Trait Implementations

impl Clone for HyperrealApprox

fn clone(&self) -> HyperrealApprox

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for HyperrealApprox

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

Formats the value using the given formatter.