Unfortunately, the live demo is no longer up, but I think the solution
you are getting at is basically the one at
http://code.google.com/p/sympy/issues/detail?id=2871.

The way that worked was, in the docs, for every example, if you hover
over it, it would show you two words, "Copy," and "Execute".  On the
bottom right of the screen, there would be a little box with a copy of
SymPy Live (it would be minimized by default).  Clicking on one of
these words would copy the expression to the box, and, for "Execute,"
it would execute it.  Since this was just a SymPy Live session, this
would just work like you had copied the expression into a Python
session.  You could then type arbitrary commands into the shell to
play around with the code.  Or you could just execute the rest of the
examples.

Having played around with it when it worked, I truly think that this
is the way to go for interactive documentation.  It hopefully
shouldn't be hard to get this up and running again, and can easily be
part of a GSoC project on SymPy Live.

Aaron Meurer

On Thu, Mar 8, 2012 at 4:02 AM, Sergiu Ivanov
<unlimitedscol...@gmail.com> wrote:
> On Thu, Mar 8, 2012 at 12:28 PM, Sergiu Ivanov
> <unlimitedscol...@gmail.com> wrote:
>>
>> https://docs.google.com/file/d/0B8pXy4LH0sF0SjNtNlRiRzlRZ1dkQjdfR3N2ZlVKdw/edit
>
> Right now the interface looks a lot more like SymPy Quick Reference
> than SymPy Quick Guide: the user can choose any module, see the
> documentation of any function of that module, and also test it a
> little bit.
>
> However, I am not yet sure this is much better than
> http://docs.sympy.org/dev/modules/ .  Of course, the new interface
> makes it possible to read the documentation *and* test the functions
> at the same time; what I'm not really enthusiastic about is the fact
> that the interface rigidly fixes the use of a function.  Considering
> the abs() function, the user wouldn't be able to test what 3*abs(-1)
> would be.  While this is not really relevant for abs(), this may be a
> show stopper for other functions.  Moreover, this makes it hard to
> work with methods: how do you plan to make it possible to test
> something like this: exp(x).series()?
>
> Also, as I said, I think it would be very nice to have something
> guide-like.  A couple years ago, the software for the J programming
> language provided a nice getting-started practical guide.  It
> consisted of a series of lessons, which you could take sequentially.
> The application would show the user a description of some feature and
> then allow them to play around with it until they felt comfortable
> with it and were ready to go to the next lesson.
>
> These lessons were, however, executed within a text-based environment.
> I believe, you could make use of the benefits of a graphical user
> interface.
>
> On the other hand, in a guide-like environment, you could mimic the
> behaviour of gamma.sympy.org (
> http://gamma.sympy.org/input/?i=integrate%28sin%28x%29%29 ) or Wolfram
> Alpha ( http://www.wolframalpha.com/input/?i=integrate%28sin%28x%29%29
> ).  However, besides showing additional information about the input,
> you may also show *how* the user could obtain that additional
> information.
>
> In case you find this direction worth exploring, you may consider
> starting from the already existing gamma.sympy.org and live.sympy.org
> interfaces and extend them with the new features.  I believe this is
> going to be among the most time-efficient approaches.
>
> Sergiu
>
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