Struct VectorFieldOperations 

pub struct VectorFieldOperations;

Vector field operations for divergence, curl, and Laplacian

Implementations

impl VectorFieldOperations

pub fn divergence( vector_field: &[Expression], variables: Vec<Symbol>, ) -> Expression

Compute divergence ∇ · F for vector field F = [P, Q, R, …]

Examples

use mathhook_core::simplify::Simplify;
use mathhook_core::calculus::derivatives::Derivative;
use mathhook_core::calculus::derivatives::PartialUtils;
use mathhook_core::calculus::derivatives::VectorFieldOperations;
use mathhook_core::calculus::derivatives::ConservativeFields;
use mathhook_core::calculus::derivatives::FluidDynamicsOperations;
use mathhook_core::{Expression};
use mathhook_core::symbol;

let x = symbol!(x);
let y = symbol!(y);
let z = symbol!(z);
let vector_field = vec![
    Expression::symbol(x.clone()),
    Expression::symbol(y.clone()),
    Expression::symbol(z.clone())
];
let div = VectorFieldOperations::divergence(&vector_field, vec![x, y, z]);

pub fn curl( vector_field: &[Expression], variables: &[Symbol], ) -> Vec<Expression>

Compute curl ∇ × F for 3D vector field F = [P, Q, R]

Examples

use mathhook_core::calculus::derivatives::VectorFieldOperations;
use mathhook_core::{Expression};
use mathhook_core::symbol;

let x = symbol!(x);
let y = symbol!(y);
let z = symbol!(z);
let vector_field = vec![
    Expression::symbol(y.clone()),
    Expression::symbol(x.clone()),
    Expression::integer(0)
];
let curl = VectorFieldOperations::curl(&vector_field, &[x, y, z]);

pub fn laplacian(expr: &Expression, variables: Vec<Symbol>) -> Expression

Compute Laplacian ∇²f = ∂²f/∂x² + ∂²f/∂y² + … for scalar field f

Examples

use mathhook_core::simplify::Simplify;
use mathhook_core::calculus::derivatives::Derivative;
use mathhook_core::calculus::derivatives::VectorFieldOperations;
use mathhook_core::{Expression};
use mathhook_core::symbol;

let x = symbol!(x);
let y = symbol!(y);
let f = Expression::add(vec![
    Expression::pow(Expression::symbol(x.clone()), Expression::integer(2)),
    Expression::pow(Expression::symbol(y.clone()), Expression::integer(2))
]);
let laplacian = VectorFieldOperations::laplacian(&f, vec![x, y]);

pub fn gradient_magnitude( expr: &Expression, variables: Vec<Symbol>, ) -> Expression

Compute gradient magnitude |∇f| = √(∂f/∂x)² + (∂f/∂y)² + …

Examples

use mathhook_core::calculus::derivatives::VectorFieldOperations;
use mathhook_core::{Expression};
use mathhook_core::symbol;

let x = symbol!(x);
let y = symbol!(y);
let f = Expression::pow(Expression::symbol(x.clone()), Expression::integer(2));
let grad_mag = VectorFieldOperations::gradient_magnitude(&f, vec![x, y]);