/// Traits of objecs which can form a basis.
pub trait Basis
{
  /// Iterate through the canonical basis of the space in which this object lives.
  fn canonical_basis(&fn(Self));

  /// Iterate through a basis of the subspace orthogonal to `self`.
  fn orthonormal_subspace_basis(&self, &fn(Self));

  /// Creates the canonical basis of the space in which this object lives.
  fn canonical_basis_list() -> ~[Self]
  {
    let mut res = ~[];

    do Basis::canonical_basis::<Self> |elem|
    { res.push(elem) }

    res
  }

  /// Creates a basis of the subspace orthogonal to `self`.
  fn orthonormal_subspace_basis_list(&self) -> ~[Self]
  {
    let mut res = ~[];

    do self.orthonormal_subspace_basis |elem|
    { res.push(elem) }

    res
  }
}