What's the best math software if price is not a factor?

I need to get a mathematical software package to help me fiddle with a
bunch of fairly simple functions. I won't be doing anything that
complicated, but I'll be doing a lot of it, so I'd like to automate it
as much as possible. Right now, I am writing VB code to generate
tables. This is time-consuming and error prone. I downloaded a
shareware grapher, which has helped a lot, but it has no
programmability. It's time I got a real mathematical program.

I'd like to describe my needs and have some of you more experienced
users of these programs advise me on which one to get. Cost is really
not a factor as I am spending dozens of hours already and not getting
good results. Even the $1,800 for Mathematica would be paid back
fairly quickly as I have a lot of testing left to do.

I have a few requirements and then a few preferences.

First the requirements. These are things the program must do:

1. Generate graphs from both closed-form functions (y=f(x)) and from
tabular data.

2. Generate tables of X & Y values from a formula over a range.

3. Given a function that has one or more constants,

(y=100*exp((-ln(2)/h)*x))

generate either graphs or tables of values for a family of functions
for various values of h (h=10, 20, 30, 40, 50...):

y1=100*exp((-ln(2)/10)*x
y2=100*exp((-ln(2)/20)*x
y3=100*exp((-ln(2)/30)*x
y4=100*exp((-ln(2)/40)*x
y5=100*exp((-ln(2)/50)*x

4. Generate tables for the family of functions: X, Y1, Y2, Y3, Y4,
Y5.

5. Iterative capability. Given a function, y=f(x), generate a graph
or a table where y1=f(x1), y2=f(y1), y3=f(y2), etc.

6. Be able to generate tables of the above iterative functions.

7. Ability to convert date and time units. Many of my X & Y values
will be in days. A value of ".5" = 12 hours or "12:00:00". A value of
"1/24*60" = 1 minute or "00:01:00". The program needs to provide a way
for me to convert "1/24" into "01:00:00" and show that format in the
generated tables.


Now, of the programs that can do the above, which are best from the
following preferences:

a. Ease of use, intuitive and natural UI, fairly quick learning curve
b. Good support, including user groups (preferably on usenet)
c. Reliable, no bugs or gotchas
d. Documentation: clear, complete, online

As I said, price is not a concern. If Mathematica is truly the best,
I'll happily pay the $1,800. However, if something else is just as
good (for what I need), I can use the money for something else.

I appreciate any suggestions or comments.


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