Monomial alternant
= Monomial alternant
{title2=$A_\ell(x)=\det(x_i^{\ell_j})$}
= Alternant
{synonym}
A monomial alternant is the <determinant> formed from powers with an integer exponent tuple $\ell$. It is a <polynomial> when the exponents are nonnegative, and otherwise a <Laurent polynomial>. Equal exponents give equal columns and zero <determinant>; interchanging exponents changes its sign. Ordered strictly decreasing nonnegative exponents give a <basis> of alternating <polynomials>, by grouping monomials into permutation orbits.