Let \(f(x)\) be the vector of monomials implied by the matrix basis.
Let \(P\) be the matrix generated by Legendre_P. Then
\(g(x)=P^Tf(x)\) is the vector of Legendre polynomials with leading terms
corresponding to basis.
construct.P(basis)A matrix. Rows are taken as the degree of the associated monomial.
A matrix which functions as a change of basis from monomials to Legendre.