immut Tutorial

Use immut when polynomials should behave like ordinary values. Constructors copy input arrays, updates return new values, and old values remain unchanged.

Dense Univariate DensePolynomial

let p = @immut.DensePolynomial::from_coefficients([1, 2, 3])
let q = @immut.DensePolynomial::variable()
let value = p.eval(2)
let composed = p.substitute(q + @immut.DensePolynomial::constant(1))

p represents 1 + 2x + 3x^2, so value is 17. substitute does not mutate p.

Constructors keep canonical form:

let p = @immut.DensePolynomial::from_coefficients([1, 2, 0, 0])
let coefficients = p.to_coefficients()

coefficients is [1, 2].

Exponent Vectors

let xy2 = @immut.ExponentVector::from_array([1U, 2])
let x = xy2.with_exponent(1, 0)
let degree = xy2.degree()

xy2 represents x * x_1^2; its total degree is 3. x is a new value.

Multivariate Term Arrays

let p = @immut.TermPolynomial::from_array([
  ([1U, 0], 2),
  ([1U], -2),
  ([0U, 1], 3),
])
let value = p.eval([5, 2])

The first two terms have equivalent exponents and cancel out. The remaining term is 3 * x_1, so value is 6.

Sparse Map Representation

let p = @immut.SparsePolynomial::from_array([
  ([2U], 1),
  ([1U], 2),
  ([], 1),
])
let coeff = p.get(@immut.ExponentVector::from_array([1U]))
let value = p.eval([2])

p represents x^2 + 2x + 1; coeff is Some(2) and value is 9.

Choosing A Representation

• Use DensePolynomial for dense univariate polynomials.
• Use TermPolynomial for sequential multivariate term processing.
• Use SparsePolynomial when exponent lookup matters.
• Convert between multivariate representations explicitly: SparsePolynomial::from_terms(term.to_terms()) or TermPolynomial::from_terms(sparse.to_terms()).
• Use UnivariatePolynomial, MultivariatePolynomial, ContextualPolynomial, or Type::ops() when generic code should not depend on the storage representation.