Inclusion-Exclusion Principle in Mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg91344] Inclusion-Exclusion Principle in Mathematica*From*: steaxauce <Trenton_Osborn at baylor.edu>*Date*: Sun, 17 Aug 2008 06:38:02 -0400 (EDT)

Hey guys, first post! I believe I've just solved a problem, and I'm trying to use mathematica to test my solution for known results, but I haven't been able to write my expression into mathematica. It looks a lot like the inclusion-exclusion principle, which is equation (3) on the following mathworld page: http://mathworld.wolfram.com/Inclusion-ExclusionPrinciple.html My expression is similar in that it contains alternating series of multiple series, where the multiple series are of increasing "depth." I hope that's clear. I can enter it in the way it's written on that page, but that wouldn't be practical for me. I can't have it in the form sum1[] - sum2[] + sum3[] - sum4[], etc. It needs to be in the form sum[-1^(j-1)sumj[]], because I'm working with a very large and varying number of sets and I can't type in all of the series manually. To do this, I need to know how to specify the "depth," or number of series in a multiple series, with a number. I've gone through the documentation, contacted mathematica tech support and posted in the student support forum, but I haven't gotten a solution yet. Can anyone who's more familiar with mathematica that me help me out? I just downloaded the program a few days ago! Thanks guys!