Let \(f(x)\) be the vector of monomials implied by the matrix basis.
Let \(P\) be the matrix generated by Legendre_P_1d. Then
\(g(x)=P^Tf(x)\) is the vector of Legendre polynomials with leading terms
corresponding to basis. e.g. the matrix \((0 1 2)^T\) implies
\(f(x)^T = (1 x x^2)\). Then \(g(x)^T = (L_0, L_1, L_2)\).
construct.P.1d(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.