Struct VectorDerivative 

pub struct VectorDerivative<const P: usize, const Q: usize, const R: usize> { /* private fields */ }

Vector derivative operator ∇

The fundamental differential operator in geometric calculus that combines gradient, divergence, and curl into a single geometric operation.

Mathematical Background

The vector derivative is defined as:

∇ = e^i ∂_i  (sum over basis vectors)

When applied to fields:

• Scalar field: ∇f = gradient
• Vector field: ∇·F = divergence, ∇∧F = curl
• General: ∇F = ∇·F + ∇∧F (full geometric derivative)

Implementations

impl<const P: usize, const Q: usize, const R: usize> VectorDerivative<P, Q, R>

pub fn new(coordinates: CoordinateSystem) -> Self

Create new vector derivative operator

Arguments

• coordinates - Coordinate system (Cartesian, spherical, etc.)

Examples

use amari_calculus::{VectorDerivative, CoordinateSystem};

let nabla = VectorDerivative::<3, 0, 0>::new(CoordinateSystem::Cartesian);

pub fn with_step_size(self, h: f64) -> Self

Set step size for numerical differentiation

pub fn gradient( &self, f: &ScalarField<P, Q, R>, coords: &[f64], ) -> Multivector<P, Q, R>

Compute gradient of scalar field: ∇f

Returns a vector field representing the gradient.

pub fn divergence(&self, f: &VectorField<P, Q, R>, coords: &[f64]) -> f64

Compute divergence of vector field: ∇·F

Returns a scalar representing the divergence.

pub fn curl( &self, f: &VectorField<P, Q, R>, coords: &[f64], ) -> Multivector<P, Q, R>

Compute curl of vector field: ∇∧F

Returns a bivector representing the curl.