Struct HeightFunction 

pub struct HeightFunction {
    pub name: String,
    pub northcott: bool,
    pub base_field: String,
}

Represents a height function on algebraic varieties.

Fields

name: String

Name of the height function.

northcott: bool

Whether the Northcott property holds (finite points of bounded height and degree).

base_field: String

Logarithmic Weil height on the base field.

Implementations

impl HeightFunction

pub fn new(name: &str, base_field: &str) -> Self

Creates a height function.

pub fn with_northcott(self) -> Self

Sets Northcott property.

pub fn weil_height_rational(p: i64, q: i64) -> f64

Weil height of a rational number p/q (in lowest terms): h(p/q) = log(max(|p|, |q|)).

pub fn projective_height(coords: &[i64]) -> f64

Naive height of (x_0 : … : x_n) in projective space: max |x_i|.

pub fn log_height(coords: &[i64]) -> f64

Logarithmic height.

pub fn northcott_bound(&self, bound: f64) -> String

Checks Northcott’s theorem consequence: there are finitely many points h(P) <= B.

Trait Implementations

impl Clone for HeightFunction

fn clone(&self) -> HeightFunction

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for HeightFunction

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

Formats the value using the given formatter.