Finding all solutions

[Torkel Loman]

Is there a good way to find all solutions to a system.

E.g. this simple 1d case:

function ff!(F,x)
    F[1] = x[1]^2  - 9
end
@time nlsolve(ff!, [x0.])

has solutions x=3 and x=-3. If x0 is set to 1 the former is found, if x0=-1 the later is found. Is there some good way of finding both these solutions without simply trying several different initial conditions and see what turns up?

(For this system it is quite easy, but given a much larger system with many dimensions it might be harder)

[Patrick Kofod Mogensen]

Depends on what you mean by large. There’s intervalrootfinding.jl that’ll do that for you, but you need to define large for anyone to give you any guidance.

[Torkel Loman]

Large would be about 10-15 variables.

[Patrick Kofod Mogensen]

Try IntervalRootFinding.jl, it might work!

[Torkel Loman]

Thanks, another question: Say that I want to find a solution, but with certain restrictions (that all variable values are non-negative). Is there a good way to do this?

[Patrick Kofod Mogensen]

Hadn't noticed your last question. We don't allow for restrictions like that.