Set of numbers in Mma 3.0 is smaller tha

• To: mathgroup at smc.vnet.net
• Subject: [mg7555] Set of numbers in Mma 3.0 is smaller tha
• From: Ersek_Ted%PAX1A at mr.nawcad.navy.mil
• Date: Fri, 13 Jun 1997 19:38:06 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```I noticed that Mma 3.0 has two new system variables
\$MaxNumber,  and  \$MinNumber.

Suppose you need to work with numbers larger than \$MaxNumber.
or closer to zero than  \$MinNumber.  All you have to do is change the value
of
\$MaxNumber or \$MinNumber.  Sounds easy right ?

Well I tired, and couldn't.
Do I need to work with really big numbers or really tiny numbers?   No.
I was just exploring the limitations of the system.
However, I wonder if some users that are affected by this apparent
limitation.

I will point out that you can work with numbers that exceed the limitations
imposed
by \$MinNumber  and  \$MaxNumber as long as the kernal doesn't  try to
compute the numerical value.  For example you will have no trouble working
with
Exp[10^15]  even though it exceeds \$MaxNumber.
Just don't  try to do  N[Exp[10^15]].

Now does it take an awful long time to do calculations with very big
numbers?
Sometimes it does.  Consider the lines below:

In[1]:=  a=\$MaxNumber;
x1=Sqrt[a]  0.8;
x2=Sqrt[a]  0.85;

In[2]:=  (*  My 90 Mhz Pentium computes the following in a flash   *)
x1  x2;

In[2]:= (*  However it takes about 5 minutes to find the half billion digits
in the following   *)
(*  Even though I followed it with a semi-colon.    *)
Floor[a];

As I would expect it seems it is practical to work with huge numbers as long
as the amount of
Precision needed isn't huge.  I don't see why a user should be prohibited
from doing
similar calculations with numbers that are much much larger than \$MaxNumber.

It seems to me Version 2.2 had no such limitation built in.
I thought you were only limited by the storage capacity of your computer,
and the time you were willing to wait.

Questions:
-  Are there any applications that need to go outside the above limitations
?

-  Can a user increase  \$MaxNumber,  or decrease the magnitude of
\$MinNumber ?

-  Does Version 2.2  give good results when the values are outside the above
limitations ?

-  Did  WRI  impose a limitation on the range of numerical values so that
the program
could run faster?

Ted Ersek