Function scalar_potential 

pub fn scalar_potential(
    field: &Matrix,
    vars: &[&Ex],
) -> Result<Ex, SymplexError>

Scalar potential φ with ∇φ = F for a conservative Cartesian field.

Works in any dimension. The potential is built by successive integration: φ = ∫F₁ dx₁ + ∫(F₂ − ∂φ₁/∂x₂) dx₂ + …, and the result is verified by re-differentiation. The additive constant is zero.

Errors

• SymplexError::InvalidArgument if field is not an n×1 column vector with n == vars.len().
• SymplexError::ComputationFailed if the field is not conservative or an antiderivative could not be found in closed form.

Examples

use symplex::prelude::*;
use symplex::vector::{gradient, scalar_potential};

let ctx = Context::new();
let (x, y, z) = (ctx.symbol("x"), ctx.symbol("y"), ctx.symbol("z"));
let phi = &(&x * &y) * &z + &x.powi(2);
let f = gradient(&phi, &[&x, &y, &z]);
let recovered = scalar_potential(&f, &[&x, &y, &z]).unwrap();
assert!((&recovered - &phi).expand().is_zero_structural());

// y x̂ − x ŷ is rotational: no potential
let rot = Matrix::col_vector(vec![y.clone(), -&x, ctx.int(0)]);
assert!(scalar_potential(&rot, &[&x, &y, &z]).is_err());