Allow keywords arguments for roots

[Kolaru]

I new issue found while writing the documentation. The current situation is awkward.

I think we could go with the following scheme:

Positional arguments

1. The function.
2. The search region.
3. The method.

Optionally for Krawczyk and Newton:

1. The function.
2. Its derivative.
3. The search region.
4. The method.

Keyword arguments

• The type of search (once #97 is merged).
• The tolerance (both absolute and relative once #66 is fixed).
• The maximum number of intervals considered (once #59 is implemented).
• The linear equation solver to be used by the contractor (see #86).

Maybe the method should be both a keyword and an optional argument, not sure about this one.

[dpsanders]

Since there are ever more parameters to control the search, I think it is time to introduce a RootsProblem type, similar to ODEProblem in DifferentialEquations.

This would contain all of the parameters of the search etc. There could still be a convenience roots function for quick usage, or just create the RootsProblem object and call roots (or maybe solve) on that.

[Kolaru]

Indeed, as I add things to the list, the more I agree with the idea of a RootsProblem, this will probably simplify passing around the parameters internally.

It may also be good to force keywords parameters to be passed through such object and have roots with only positional arguments (i.e. have it as a convenient function for simple cases).

[dpsanders]

Eg. See how it's done in MDBP.jl:

https://discourse.julialang.org/t/ann-mdbm-jl-a-root-finding-package-for-system-of-non-linear-equations/22141

It would maybe be useful to be able to use either package with the same or similar syntax.

[Kolaru]

It would be good to follow the common interface from https://github.com/SciML/CommonSolve.jl

Edit : It is also used by Roots.jl and may allow to drop it as a dependency

[lucaferranti]

I use that in IntervalLinearAlgebra.jl. it's very nice