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Re: Bernoulli variable algebra

  • To: mathgroup at
  • Subject: [mg46532] Re: Bernoulli variable algebra
  • From: drbob at (Bobby R. Treat)
  • Date: Sun, 22 Feb 2004 11:27:30 -0500 (EST)
  • References: <c16m89$5pd$>
  • Sender: owner-wri-mathgroup at

Oops, I just posted a very incomplete answer; here's a better one.

Each Bernoulli variable could be bernoulli[i]. First of all, here's a
function that may help, It allows you to make a[i] and Subscript[a,i]

subFunction[a_Symbol] := 
  Block[{aa = ToString[a]}, 
       i_], f_] := MakeExpression[
      RowBox[{ToString[a], "[", i, "]"}]]; 
    MakeBoxes[a[i_], f_] := SubscriptBox[
      MakeBoxes[a, f], MakeBoxes[i, f]]]

Then enter

binary[i_]*binary[i_] ^= binary[i]; 
binary[i_]^(n_)?Positive := binary[i]
Expand[(binary[1] + binary[2])^10]
binary[1] + binary[2] + 1022*binary[1]*binary[2]

You may need to compute intermediate expressions, so that full
expansion doesn't occur before any simplifications. For instance:

Expand[(binary[1] + binary[2])^100]*
  Expand[(binary[2] - binary[3])^100]

(binary[1] + binary[2] + 
  (binary[2] + binary[3] - 


jmyers6761 at (JMyers6761) wrote in message news:<c16m89$5pd$1 at>...
> 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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