I know I'm losing this one, but for what it's worth, I think that not
only should (1), (2), and (3) be supported, but that integrate(f)
should do what is obvious where the variable is unambiguous.  :)


>
> > While (1) and (2) syntaxes are encouraged, (3) will
> > remain valid until we sort out the coersion issue
> > and update all doctests, tutorial etc. BTW, I did update
> > some of the doctests including the docstrings that you get
> > via "integrate?"
>
> Sounds like we should throw a deprecation warning on it.
>

Yes, this would definitely require it.  There should conceivably be a
check for whether there are x, a, and b, and if a and b are both
numeric types, allowing (3) indefinitely in that case (as opposed to
integrate(f,x,a,b) where a and b are symbolic endpoints).

On the plus side, FJ is correct that it is impossible to have multiple
integration in an unambiguous way without removing (3) eventually (so
as to allow integrate(f,x,y,x) and the like).  My preference would be
to require instead integrate(f,(x,),(y,),(x,)) or integrate(f,[x],[y],
[z]), but I think that those would not prove popular.  In any case, it
should be very easy to get multiple integration working with those,
and certainly with integrate(f,(x,a,b),(y,c,d)) with the current
framework, as they pretty much work as expected if you next integrates
(I prototyped this a while ago but discarded it due to the tickets
Jason mentions not being resolved).

Your work on symbolics is impressive and valuable, Golam - keep it up!

- kcrisman
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