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Re: managing order of magnitude instead of numbers

  • To: mathgroup at
  • Subject: [mg56685] Re: managing order of magnitude instead of numbers
  • From: dh <dh at>
  • Date: Wed, 4 May 2005 00:32:50 -0400 (EDT)
  • References: <d57gvv$p8a$>
  • Sender: owner-wri-mathgroup at

Hi Roberto,
you could define a new data type that encapsulates the order of 
magnitude. From your example I take it, that by order of magnitude you 
do not mean powers of a variable, but powers of 10.
Therefore we may define a new type called e.g. ord and inside ord we 
specify the power of 10:
ord[n] where n must ne an integer.
We must now give the rules for ord, e.g.:

ord /: ord[x_Integer] + ord[y_Integer] := ord[Round[Log[10, 10^x + 10^y]]];
ord /: ord[x_Integer] - ord[y_Integer] :=
           ord[Round[Log[10, Abs[10^x - 10^y]]]];
ord /: ord[x_Integer]*ord[y_Integer] := ord[x + y];
ord /: ord[x_Integer]/ord[y_Integer] := ord[x - y];

we are now ready to calculate. E.g.
a=ord[0];  (*this specifies an number of the order 1*)
b=ord[1];  (*this specifies an number of the order 10*)
and we get:

a+b  --> ord[1]
a-b  --> ord[1]
a*b  --> ord[1]
a/b  --> ord[-1]

Sincerely, Daniel

foice wrote:
> i need to make calculation without specifing the exact values of my
> parameters, i want only to specify their order of magnitude.
> obviously i need only order of magnitudes as result.
> now the problem is that 
> O(1) - O(1) = O(1)
> while
> 1-1 = 0
> so it's clear i cannot use numbers to make this "order of magintude
> calculation"
> at the present stage i let mathematica do the calculation in a fully
> simbolic way and then, by hand calculation, i get my result by
> susbstitution of the order of magnitudes in place of the symobls used.
> making a very simple example:
> i ask to mathematica to do
> a - b
> and then i substitute 
> a=O(1)
> b=O(0.002)
> and calculate
> a - b = O(1)
> in this way i'm  making operation between magnitues not values, but i
> have to do it on my own, while doing calculation with mathematica will
> be much better.
> is there any way to make calculation betwwen order of magnitues
> instead of between numbers?
> thanks.
> roberto.

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