Re: managing order of magnitude instead of numbers

*To*: mathgroup at smc.vnet.net*Subject*: [mg56819] Re: managing order of magnitude instead of numbers*From*: Paul Abbott <paul at physics.uwa.edu.au>*Date*: Sat, 7 May 2005 04:16:31 -0400 (EDT)*Organization*: The University of Western Australia*References*: <d57gvv$p8a$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

In article <d57gvv$p8a$1 at smc.vnet.net>, foice <foice@N0NSPAMMAR&tiscali.it> 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" One comment here: Mathematica does know something about objects of this type. For example, enter O[x] - O[x] and see what happens. Generally, I think you can use Series to do such calculations most efficiently. > 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? Perhaps you could use Interval arithmetic? For example, defining o[x_] := Interval[x {0.9,1.1}] to be an order of magnitude interval, then o[1] - o[0.002] returns an interval. We can use the following to check the magnitude: oCheck[int_,n_] := IntervalIntersection[int, o[n]] =!= Interval[] For example, oCheck[o[1] - o[0.002], 1] yields True, whereas oCheck[o[1] - o[0.002],0.1] and oCheck[o[1] - o[0.002], 10] do not. Cheers, Paul -- Paul Abbott Phone: +61 8 6488 2734 School of Physics, M013 Fax: +61 8 6488 1014 The University of Western Australia (CRICOS Provider No 00126G) AUSTRALIA http://physics.uwa.edu.au/~paul http://InternationalMathematicaSymposium.org/IMS2005/