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MathGroup Archive 2004

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Re: Bernoulli variable algebra

  • To: mathgroup at smc.vnet.net
  • Subject: [mg46530] Re: Bernoulli variable algebra
  • From: drbob at bigfoot.com (Bobby R. Treat)
  • Date: Sun, 22 Feb 2004 11:27:28 -0500 (EST)
  • References: <c16m89$5pd$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Use some special symbol (rather than x) for your Bernoulli variables.
I'll use "binary":

binary*binary ^= binary; 
Unprotect[Power]; 
binary^_ := binary
Protect[Power]; 
Expand[binary*(1 + binary)^10]
1024*binary

Bobby

jmyers6761 at aol.com (JMyers6761) wrote in message news:<c16m89$5pd$1 at smc.vnet.net>...
> I have been working on a Mathematica package used to predict the reliability of
> complex redundent systems. The calculations, which are done symboliclly, become
> quite complex. Since all of the variables used are Bernoulli variables, i.e.
> take on only values of 0 or 1, the expressions must be simplified by use of the
> rule x_^n_->x. My problem is this, the expressions are complex and large and,
> as a result the Mathematica Kernal runs out of memory trying to expand the
> expressions. I know, from other techniques, that the resulting expressions
> after application of the  x_^n_->x rule are still large (> 1000 terms) they are
> not unmanageable. (The expressions prior to applying the rule might be on the
> order of 10^6 terms) If a technique could be devised for accomplishing the
> effect of the above transformation without first requiring the full expansion
> of the expressions it would be possible to greatly simplify the required
> analysis. Is anyone aware of a technique for the simplification of algebraic
> expressions of Bernoulli variables without requiring expansion of the
> expression first?
> 
> Any hints would be greatly appreciated.
> Thankyou,
> Al Myers


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