Struct ConservativeFields 

pub struct ConservativeFields;

Conservative field analysis

Implementations

impl ConservativeFields

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

Check if a vector field is conservative (curl = 0)

Examples

use mathhook_core::calculus::derivatives::ConservativeFields;
use mathhook_core::{Expression, symbol};

let x = symbol!(x);
let y = symbol!(y);
let conservative_field = vec![
    Expression::symbol(x.clone()),
    Expression::symbol(y.clone())
];
let is_conservative = ConservativeFields::is_conservative(&conservative_field, vec![x, y]);

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

Find potential function φ such that F = ∇φ

Examples

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

let x = symbol!(x);
let y = symbol!(y);
let conservative_field = vec![
    Expression::mul(vec![Expression::integer(2), Expression::symbol(x.clone())]),
    Expression::mul(vec![Expression::integer(2), Expression::symbol(y.clone())])
];
let potential = ConservativeFields::find_potential(&conservative_field, &[x, y]);

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

Check if field is irrotational (curl = 0)

Examples

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

let x = symbol!(x);
let y = symbol!(y);
let z = symbol!(z);
let irrotational_field = vec![
    Expression::symbol(x.clone()),
    Expression::symbol(y.clone()),
    Expression::symbol(z.clone())
];
let is_irrotational = ConservativeFields::is_irrotational(&irrotational_field, vec![x, y, z]);

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

Check if field is solenoidal (divergence = 0)

Examples

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

let x = symbol!(x);
let y = symbol!(y);
let solenoidal_field = vec![
    Expression::symbol(y.clone()),
    Expression::mul(vec![Expression::integer(-1), Expression::symbol(x.clone())])
];
let is_solenoidal = ConservativeFields::is_solenoidal(&solenoidal_field, vec![x, y]);