> I think we do. Maxima sessions can have so much state that it's nice to keep
> them separate to ensure consistency of the calculus modules. Also, that
> means you won't be accidently clobbering your calculus variables, functions,
> etc.
>
I think I agree in principle, but maybe not in practice. For the user
who knows nothing about Maxima, they're definitely not going to try to
do anything via maxima("...") themselves, so I think it doesn't matter
for them. On the other hand, our use of Maxima clearly isn't perfect
-- if someone knows enough about Maxima to be able to fix the problem
they're having on the Maxima side, it would be nice if that were a
little easier. Since integrate() and friends often comes back with an
error message talking about what we need to tell Maxima first, it'd be
nice if it were easier to do that. I guess I'm saying that I think the
benefits outweigh the dangers -- someone making calls via
maxima("...") probably realizes the prospect of clobbering variables,
unless maybe they were just copy-pasting someone else's code that does
it.
> Eventually (if not already) assumptions and the like will need to be
> recorded and used at a higher level than the maxima interpreter process, so
> I don't think we could always count on the above working.
>
I agree -- ultimately the user should never need to know that we're
using Maxima, and in theory we could one day be using some completely
different backend for integrals. But right now, lots of integrals end
in tracebacks like this:
TypeError: Computation failed since Maxima requested additional
constraints (try the command 'assume(sin(x+%pi/3)>0)' before integral
or limit evaluation, for example):
Is sin(x+%pi/3) positive, negative, or zero?
Using assume or maxima.assume doesn't help, but using
sage.calculus.calculus.maxima.assume *does* fix it. I just tested, and
the first three problems on sage-support about maxima and assume I
looked at were all fixed by using sage.calculus.calculus.maxima.assume
instead. I agree that it's not the solution we want in the long term,
but either (1) unifying the two maxima sessions or (2) making the
assume() command available at top-level point to
sage.calculus.calculus.maxima.assume *would* make it so that the user
could easily compute the integral that's frustrating them. (I know
that the one time I've run into this, I tried an integral, got a
traceback about assume, tried maxima("assume(...)"), which didn't fix
it -- so I gave up and just did the integral by hand.)
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