Well, the design is somewhat different to start with: in Sage, you
have to declare variables explicitly (i.e. with var('x,y') or
whatever), but then symbolic variables can automatically act like
functions (as in the usage/bug above). In mathematica, anything
undefined is _assumed_ to be a new symbolic object.
Strings behave in a funny way in mathematica. They are usually
evaluated to symbolic expressions. Here is a (hopefully) relevant
example, setting the value of something to a string and then using it
in a function:
In: a = "test"
Out: test
In: f[x_] := x^2
In: f[a]
Out: test^2
The output is misleading since the returned object is really
Power["test",2] but that is displayed the same way that the symbolic
expression Power[test,2] is.
Somewhat relevant to this are the (IMHO) very nice substitutions,
rules, and patterns in mathematica (although the syntax is pretty
odd). As a very simple example, the command:
In: {x, x*y} /. {{x -> 1, y -> 2}, {x -> 2, y -> 3}}
returns
Out: {{1,2},{2,6}}
The Sage subs command is quite weak compared to such substitutions in
mathematica. One can do very complicated condition substitutions,
regular-expression like matching, etc.
Cheers,
Marshall
On May 9, 11:54 am, "William Stein" <[EMAIL PROTECTED]> wrote:
> On Fri, May 9, 2008 at 10:03 AM, Marshall Hampton <[EMAIL PROTECTED]> wrote:
>
> > Ah, ok. I am probably not the right person to weigh in on what
> > symbolics should do. I'll be happy if I can do most of what I could
> > do in mathematica - since I used it for 16 years, it defines what I
> > expect, but of course it won't always be the right design to follow
> > for Sage.
>
> > -M. Hampton
>
> Wait -- please *do* weigh in, and do explain what Mathematica would
> do in analogous situations. I do care to hear.
>
> William
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