Struct AdvancedDifferentiation 

pub struct AdvancedDifferentiation;

Advanced differentiation methods with performance optimization

Implementations

impl AdvancedDifferentiation

pub fn implicit( equation: &Expression, x_var: Symbol, y_var: Symbol, ) -> Expression

Compute implicit derivative dy/dx for F(x,y) = 0

Uses the formula: dy/dx = -∂F/∂x / ∂F/∂y

Examples

use mathhook_core::Expression;
use mathhook_core::symbol;
use mathhook_core::calculus::derivatives::AdvancedDifferentiation;

let x = symbol!(x);
let y = symbol!(y);
let equation = Expression::add(vec![
    Expression::pow(Expression::symbol(x.clone()), Expression::integer(2)),
    Expression::pow(Expression::symbol(y.clone()), Expression::integer(2))
]);
let dy_dx = AdvancedDifferentiation::implicit(&equation, x, y);

pub fn parametric( x_param: &Expression, y_param: &Expression, parameter: Symbol, ) -> Expression

Compute parametric derivative dy/dx for x = f(t), y = g(t)

Uses formula: dy/dx = (dy/dt) / (dx/dt)

Examples

use mathhook_core::Expression;
use mathhook_core::symbol;
use mathhook_core::calculus::derivatives::AdvancedDifferentiation;

let t = symbol!(t);
let x_param = Expression::function("cos", vec![Expression::symbol(t.clone())]);
let y_param = Expression::function("sin", vec![Expression::symbol(t.clone())]);
let dy_dx = AdvancedDifferentiation::parametric(&x_param, &y_param, t);

pub fn vector_valued( components: &[Expression], parameter: Symbol, ) -> Vec<Expression>

Compute derivative of vector-valued function r’(t)

Returns velocity vector for position vector r(t) = [x(t), y(t), z(t)]

Examples

use mathhook_core::Expression;
use mathhook_core::symbol;
use mathhook_core::calculus::derivatives::AdvancedDifferentiation;

let t = symbol!(t);
let components = vec![
    Expression::function("cos", vec![Expression::symbol(t.clone())]),
    Expression::function("sin", vec![Expression::symbol(t.clone())]),
    Expression::symbol(t.clone())
];
let velocity = AdvancedDifferentiation::vector_valued(&components, t);

pub fn parametric_curvature( x_param: &Expression, y_param: &Expression, parameter: Symbol, ) -> Expression

Compute curvature for parametric curves

Uses formula: κ = |x’y’’ - y’x’’| / (x’² + y’²)^(3/2)

Examples

use mathhook_core::Expression;
use mathhook_core::symbol;
use mathhook_core::calculus::derivatives::AdvancedDifferentiation;

let t = symbol!(t);
let x_param = Expression::function("cos", vec![Expression::symbol(t.clone())]);
let y_param = Expression::function("sin", vec![Expression::symbol(t.clone())]);
let curvature = AdvancedDifferentiation::parametric_curvature(&x_param, &y_param, t);

pub fn vector_curvature( components: &[Expression], parameter: Symbol, ) -> Expression

Compute curvature for vector-valued functions (space curves)

Uses formula: κ = |r’ × r’‘| / |r’|³

Examples

use mathhook_core::Expression;
use mathhook_core::symbol;
use mathhook_core::calculus::derivatives::AdvancedDifferentiation;

let t = symbol!(t);
let components = vec![
    Expression::symbol(t.clone()),
    Expression::pow(Expression::symbol(t.clone()), Expression::integer(2)),
    Expression::pow(Expression::symbol(t.clone()), Expression::integer(3))
];
let curvature = AdvancedDifferentiation::vector_curvature(&components, t);