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##

Becoming Familiar with Maxima, Maple, and Mathematica

But let us return to Maxima.

The Maxima
command `limit` can be used
to evaluate limits
of various real-variable expressions. For example

limit (x - 7, x, 3); produces - 4

This stands for

In Maple
the synopsis
for `limit` is a little different. There you have to say
limit (x-7, x=3);

Whereas in Mathematica,
the corresponding phrase would be:
Limit [x-7, x->3]

In Mathematica we don't use semicolons
to terminate expressions. In
Maxima and in Maple we do. In Mathematica, as in Fortran, the command
terminator is a new-line. But when you work with a Mathematica
worksheet, a newline merely transfers you to another line. In this
case you must either type the `Enter` key, on the far right of your
keyboard, or `Shift-Return` in order to terminate a Mathematica
command.

Unlike Mathematica's and Maple's own worksheet interfaces, the
Bill Schelter's book-mode does not have
*section boxes* .
When you work with the book-mode, you must remember
the scope of anything you send to Maxima or to Maple. You get more
freedom, but you also have to think more about what you do. This is
usually the case with freedom anyway.

You
can also work with Maxima, Maple and Mathematica directly, without
worksheets or the book-mode, that, sometimes, do tend to get in the
way . Here is a Maxima
example:

Here is how you'd do the same
with Maple:

And here is the same
with Mathematica:

`Ctrl-D`, which means ``End-of-Text''
will get you safely out of all three.
Maple and Maxima share a number of similarly named functions with quite
similar syntax. For example,
both can `expand` expressions. This is
Maxima:

And here is Maple
doing the same:

Both
can also `solve` algebraic equations, assuming that they are
easily solvable. Maxima:

and Maple:

In Mathematica all predefined functions have names that begin with
capital letters, square brackets are used for function arguments and
commands themselves are terminated with a newline:

We can see more differences between Mathematica and the other two
when we invoke its function `Solve`:

In summary, here the differences between
Mathematica on one side and Maple
and Maxima on the other are as follows:
- 1.
- the function name begins with the capital ``S''
- 2.
- square brackets are used to enclose function arguments
- 3.
- there is no
`*` between `a` and `x^2`

: Mathematica tries to
immitate a standard mathematical notation. When two
algebraic symbols are put together, as in *ab*, it is understood
as ``*a* times *b*''
- 4.
- logical
`==` is used instead of `=`, which in Mathematica is
used for a value assignment only.

Mathematica is an odd-man-out in this company.

** Next:** Simple Plots
** Up:** The Playsome Threesome: Maxima,
** Previous:** The Book Mode
*Zdzislaw Meglicki*

*2001-02-26*