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MathGroup Archive 2011

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Interval and IntervalIntersection with a List

  • To: mathgroup at smc.vnet.net
  • Subject: [mg119661] Interval and IntervalIntersection with a List
  • From: "Stan" <Cystrin at hotmail.com>
  • Date: Thu, 16 Jun 2011 04:02:24 -0400 (EDT)

What I am trying to do is to determine the existence of one interval with 
another and the existence of one interval with multiples of another.

For example, I have the following Intervals defined:
Band5=Interval[{824,849}];
Band8=Interval[{880,915}];
Band3=Interval[{1710,1785}];
Band2=Interval[{1850,1910}];

and I have a second pair of Intervals defined as:
Band38=Interval[{2570, 2620}];
Band40=Interval[{2300,2400}];

I now wish to test if my Band 38 Interval intersects with any of the Band5, 
Band8, Band3 or Band2 Intervals (clearly it does not) and then with the the 
second harmonics of the Band5/8/3/2 Intervals (i.e., 2*Band5, 2*Band8, etc.) 
and then with the third harmonic of the same Intervals. Once I have done all 
that for Band38, I want to do the same for Band40. And then, I would like to 
test the second and third harmonic of Band38 and Band40.

So the sort of test I need to do is something like:
IntervalIntersection[Band5, Band 38]
IntervalIntersection[2 Band5, Band 38]

However, as there are 2^3 * 4^3 (=512) permutations to test, there must be 
an easier thnt typing each equation separately. Can anyone suggest a way of 
doing this please?

Thanks,
Stan










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