I went with an approach mixing a few things from here
- the nice idea that defaults can basically be copied
- that the doc string is a string that is added to (for me usually 2) different functions of a solver
- reusing a few variable name explanations
an example (only of the forthcoming version) is
since this is a forthcoming version, linking the rendered string is a bit complicated, but I like the result and would like to thank everyone helping me to find that style!