Struct SurrealInf

pub struct SurrealInf { /* private fields */ }

A struct to represent surreal numbers with at least one infinite set.

Implementations

impl SurrealInf

pub fn new( left: Box<dyn Fn(u32) -> Option<Surreal>>, right: Box<dyn Fn(u32) -> Option<Surreal>>, ) -> SurrealInf

Creates a new surreal number with infinite sets, where these sets are described by two closures that return surreal numbers with non-infinite sets. These series can also return the same number to represent a non-infinite set, as all non-infinite sets can be reduced to a single element.

Panics

Because infinite sets can’t be fully computed, there is no guarantee that all items in the left set are less than all items in the right set. This means that, not only is comparison impossible, but arithmetic is as well.

Examples

let omega = surreal::SurrealInf::new(
    Box::new(|n: u32| Some(surreal::ftos((n + 1) as f32))),
    Box::new(|n: u32| None),
);

let epsilon = surreal::SurrealInf::new(
    Box::new(|n: u32| Some(surreal::Surreal::new(vec![], vec![]))),
    Box::new(|n: u32| Some(surreal::ftos(1.0/(2_i32.pow(n) as f32)))),
);

pub fn left(&self, index: u32) -> Option<Surreal>

Returns the left set of a surreal number (as a Vec<Surreal> instead of a Vec<&Surreal>).

Examples

let omega = surreal::SurrealInf::new(
    Box::new(|n: u32| Some(surreal::ftos((n + 1) as f32))),
    Box::new(|n: u32| None),
);

if let Some(i) = omega.left(0) {
    assert!(i == surreal::ftos(1.0));
}

pub fn right(&self, index: u32) -> Option<Surreal>

Returns the right set of a surreal number (as a Vec<Surreal> instead of a Vec<&Surreal>).

Examples

let epsilon = surreal::SurrealInf::new(
    Box::new(|n: u32| Some(surreal::Surreal::new(vec![], vec![]))),
    Box::new(|n: u32| Some(surreal::ftos(1.0/(2_i32.pow(n) as f32)))),
);

if let Some(i) = epsilon.right(0) {
    assert!(i == surreal::ftos(1.0));
}