Expose domain of functions

[dpsanders]

Currently the user has no way of knowing which domain a function is defined over.

We should define e.g.

domain(sqrt) = 0..Inf

or domain_interval(sqrt).

[OlivierHnt]

I do not think we should do this. Sometimes the domain is not closed, eg for log.

However I think this should appear in the docstring of sqrt.

[dpsanders]

Good point about the domain for log.
Nonetheless I think there ideally should be some way for the user to obtain this information programatically.

[OlivierHnt]

In the end, this is truly a math question and not interval related.
How the domain relates to intervals (which is what matters for the library) depends on the function (what we do for sqrt is different than what we do for other functions).

That being said, we can leave this issue open for a little while and see if someone comes up with something.
But I suspect that this is a matter of documentation.

[dpsanders]

The reason I was thinking about this is that I wanted to do something like Piecewise(sqrt, extend=0) meaning "extend sqrt with 0 outside its domain of definition", but that requires programmatic access to the domain.

[OlivierHnt]

Oh I see, interesting!

Then Piecewise(log, extend = 0) would also work I think, or even Piecewise(asec; extend = 0).
The logic for this feature is more like a isindomain function (which resolves the issue of having to deal with non closed domains since it does not attempt to return the domain as an interval).

Something in the vein of

isindomain(::typeof(sqrt), x::Float64) = 0 <= x

isindomain(::typeof(sqrt), x::Interval) = issubset_interval(x, interval(0, Inf))