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MathGroup Archive 1997

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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
                         ersek_ted%pax1a at mr.nawcad.navy.mil



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