I really need to go to sleep so I won't do a top-ten, but here's a top
2:

1) Powerful substitutions and rules.  Sage does not have anything
comparable.  The .subs() function is buggy even in its limited
domain.  There have been previous posts on sage-devel that give good
examples of this.

2) Implicit variable declaration - ? I'm not sure what to call this.
Basically, mathematica assumes everything is in the equivalent of its
symbolic ring until told otherwise.  Because of problems with Sage's
symbolics, I often have to explicitly declare a ring (e.g. R.<x,y,z> =
PolynomialRing(QQ,3)), and then later when I want to do something else
declare another ring.  I often get headaches when adding or removing
variables, changing term orders, or trying to do simplifications in
which intermediate quantities don't fit the current setup (e.g. a
fraction field).  I am hoping that some of the coercion changes will
help with some of this.

Part of my problem with #2 probably doesn't make as much sense to you
because Mathematica has a bias towards working in QQ, and that is what
I usually care about.  I am sure that if you like working over more
exotic fields Sage starts to have advantages.

Hope that helps, I am too tired to explain in more detail right now.

Cheers,
M. Hampton

On Aug 20, 11:38 pm, "William Stein" <[EMAIL PROTECTED]> wrote:
> On Wed, Aug 20, 2008 at 9:37 PM, mhampton <[EMAIL PROTECTED]> wrote:
>
> > I used to really enjoy writing programs in mathematica, but maybe I'm
> > a strange person.  I only stopped in order to force myself to get
> > fluent with Sage.  I think it just depends on your background, what
> > you are used to, and what you want to do.  For symbolic calculations
> > and programming I still miss mathematica quite often.
>
> Could you remind me (yet again) of the top ten things you miss about
> mathematica for symbolic calculations?
>
>  -- William
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