The most common way to represent a polynomial is writing it as a linear combination of monomials, i.e., powers of the variable. For example, the polynomial \$p(x) = x^3 + 2x^2 + x + 1\$ is a linear combination of the monomials \$x^3\$, \$x^2\$, \$x\$, and \$1\$, with coefficients \$1\$, \$2\$, \$1\$, and \$1\$ respectively. However, the monomial basis is not the only possible basis for polynomials. Another interesting basis, useful in combinatorics and some other areas of mathematics, is the ...
