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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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