kcrisman wrote:
> Dear Devel list,
> 
> Before reading this, read the discussions at
> http://groups.google.com/group/sage-devel/browse_thread/thread/8ec32e4d895da60c
> and tracs # 1221 and # 2787.
> 
> Since nothing has been done on this in over a year, and because I feel
> fairly strongly that it is *very* important (to keep "insane ease of
> use", in wdj's words) to keep things like
> sage: integrate(sin(x),x,0,pi)
> viable, I messed around with a toy implementation of some alternate
> syntax that would preserve backward compatibility but allow for the
> Mathematica-style syntax and multiple integration.
> 
> I now have a working (still toy) implementation that keeps all current
> syntax, but adds the following possibilities giving correct answers:
> 
> sage: integrate(sin(x),[x],[var('y')]) # double integral, x first
> sage: integrate(sin(x),[x,0,pi],[y]) # one definite, one indefinite
> sage: integrate(sin(x),(x,),(x,)) # double integral, using tuples
> instead of lists if you like parentheses
> sage: integrate(sin(x),(x,),(var('y'),),(var('z'),)) # or more
> integrals
> 
> One would not (yet) be able to do something like
> sage: integrate(sin(x),[0,pi])
> though I suppose it would be easy to implement; this seems a little
> weird to me personally, though, esp. if
> sage: integrate(sin(x),0,pi)
> is already available.
> 
> Because the integration code is spread in a few places, I am sure it
> will take some work to make this work properly, but I am familiar
> enough with it from previous work that this proof of concept has
> convinced me.  (Thanks, Python, for making such things so easy!)  It
> is really just a matter of asking the right arguments to be passed at
> some point, since Maxima and the interface to it take care of the
> rest.
> 
> So I am wondering if there is any feedback from esp. William, Ondrej,
> Jason, and whomever else posted or discussed this on trac.  Certainly
> having "native" multiple integrals seems like a no-brainer to try to
> have, and enabling easy transfer from Mma is definitely useful.  But
> I'd also like to ensure that
> sage: integrate(sin(x),x,0,pi)
> and friends live happily ever after, or at least until I stop
> teaching, and I am quite happy to do all the work to make that happen
> while addressing the valid points these tickets make.


I have no opinion on the integrate(sin(x),x,0,pi), since I don't (like 
to) use that syntax and don't plan on teaching it to students.  However, 
a strong +1 to getting MMA-like syntax integrate(sin(x), (x, 0, pi)).  I 
really miss that.

Thanks,

Jason



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