Trait ComplexAnalysis 

pub trait ComplexAnalysis {
    // Required methods
    fn is_analytic_at(&self, variable: &Symbol, point: &Expression) -> bool;
    fn pole_order(&self, variable: &Symbol, pole: &Expression) -> u32;
    fn is_removable_singularity(
        &self,
        variable: &Symbol,
        point: &Expression,
    ) -> bool;
    fn is_essential_singularity(
        &self,
        variable: &Symbol,
        point: &Expression,
    ) -> bool;
}

Trait for complex analysis operations related to singularities

Required Methods

fn is_analytic_at(&self, variable: &Symbol, point: &Expression) -> bool

Check if function is analytic at a point

Examples

use mathhook_core::{Expression, symbol};
use mathhook_core::calculus::ComplexAnalysis;

let z = symbol!(z);
let expr = Expression::pow(Expression::symbol(z.clone()), Expression::integer(2));
let point = Expression::integer(1);
let is_analytic = expr.is_analytic_at(&z, &point);

fn pole_order(&self, variable: &Symbol, pole: &Expression) -> u32

Determine the order of a pole

Examples

use mathhook_core::{Expression, symbol};
use mathhook_core::calculus::ComplexAnalysis;

let z = symbol!(z);
let expr = Expression::pow(
    Expression::pow(
        Expression::add(vec![Expression::symbol(z.clone()), Expression::integer(-1)]),
        Expression::integer(2)
    ),
    Expression::integer(-1)
);
let pole = Expression::integer(1);
let order = expr.pole_order(&z, &pole);

fn is_removable_singularity( &self, variable: &Symbol, point: &Expression, ) -> bool

Check if point is a removable singularity

Examples

use mathhook_core::{Expression, symbol};
use mathhook_core::calculus::ComplexAnalysis;

let z = symbol!(z);
let expr = Expression::mul(vec![
    Expression::function("sin", vec![Expression::symbol(z.clone())]),
    Expression::pow(Expression::symbol(z.clone()), Expression::integer(-1))
]);
let point = Expression::integer(0);
let is_removable = expr.is_removable_singularity(&z, &point);

fn is_essential_singularity( &self, variable: &Symbol, point: &Expression, ) -> bool

Check if point is an essential singularity

Examples

use mathhook_core::{Expression, symbol};
use mathhook_core::calculus::ComplexAnalysis;

let z = symbol!(z);
let expr = Expression::function(
    "exp",
    vec![Expression::pow(Expression::symbol(z.clone()), Expression::integer(-1))]
);
let point = Expression::integer(0);
let is_essential = expr.is_essential_singularity(&z, &point);

Implementors

impl ComplexAnalysis for Expression