Does this CPEX propose a quick way to define Legendre and Lagrange polynomials ?
Yes and no.
Yes. We need to come up with a consistent notation for standard parametrised functions such as Legendre (and by extension the Jacobi polynomials).
No. Lagrange polynomials are different, since determined by the control points and therefore we would need to add those in the notation. The Lagrange polynomials are moreover already covered in cpex0045. Related to that, we still have to come up with a more compact way to store splines (nurbs, ...). I think therefore b-splines, nurbs should be an extension to cpex0045, in which we allow to specify how to interpolate the solution starting from the control points.