Turn off the expansion of start solutions and make the code iterruptable

[johndcobb]

I'm running into an issue where some tasks are taking unexpectedly long. I'd like options to:

1. skip the expanding start solution steps, newton and gradient flow. I've run an example where newtons method takes 4 hours.
2. Return partial solutions on interrupt when calling critical_points.

[oskarhenriksson]

I fully agree!

There should probably be a boolean expand_start_solutions keyword in critical_points.

While waiting for somebody to add this, I think you should be able to turn off the "expansion steps" by simply setting start_grid_width = 0 when you run critical_points.

Once you've entered the monodromy phase or the subsequent parameter homotopy step, I think you should be able to interrupt it cleanly with Crtl+C.

[johndcobb]

Oh I see, monodromy_solve already has a flag catch_interrupt = true by default that does this. I'll think more about this.

[oskarhenriksson]

It would be very nice if we could also make some of our functions cleanly interruptible. In particular, this "expand_start_solutions" step, and the connection of the critical points.

[oskarhenriksson]

I'm now also having some trouble with the Newton part of the expansion step for the three-paramter cubic discriminant.

It would be great if we had a way to turn off the Newton iterations independently from the gradient flow part.