Move the interpolating polynomials to a separate package

[pwl]

Remove the definitions of InterpolateAt, InterpolateDerivativeAt etc. from DASSL.jl and move them to the InterPoly.jl package (or other suitable Julia package).

[ChrisRackauckas]

I just looked in there: that's just a standard Legrangian interpolation, right? Is there really no Julia package which already does this that you can just call? How does Polynomials.jl fare for this?

If there is none, I agree this should be spawned off to another package. But it should be cleaned up a little: it should generate a polynomial type with an interpolation function on it, so that way getting more than one interpolated value is cheap (and only 1 interpolated value will be about the same cost).

[pwl]

Constructing a polynomial object every iteration would be costly and the Lagrange extrapolation can be done in place and simultaneously for the function and its derivative (currently they are computed separately, which means there is a room for improvement there). This method could be potentially used by other integrators but I think it is a little bit too small by itself to warrant a separate package. One option would be to have a general package with reusable code like that, which could be moved to a proper package once it matures, but having a helpers.jl package is not very elegant.

[ChrisRackauckas]

Ahh, I looked through the code again. I misread it the first time as you were constructing the polynomial, instead of directly doing the interpolation at the point. It think that's a useful function, but agree that I don't know where you'd put it.

[pwl]

Well, what about a single place, like wiki or docs, where we would put an info on functions that could be moved out to a separate package? This way the next person who codes a similar algorithm would just move it to a separate package instead of copying it or re-implementing it.

[ChrisRackauckas]

I plan on having a separate devdocs for explaining the interfaces and utility functions (essentially, a summary of the conclusion when we get it). This could be added as a utility function (in DiffEqBase?) and documented there.

[pwl]

That's a good idea. (although if we all start adding random functions to DiffEqBase it might end up being too cluttered)