       Re: Bernoulli variable algebra

• To: mathgroup at smc.vnet.net
• Subject: [mg46532] Re: Bernoulli variable algebra
• From: drbob at bigfoot.com (Bobby R. Treat)
• Date: Sun, 22 Feb 2004 11:27:30 -0500 (EST)
• References: <c16m89\$5pd\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```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]
synonymous.

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

Then enter

subFunction[binary]
binary[i_]*binary[i_] ^= binary[i];
Unprotect[Power];
binary[i_]^(n_)?Positive := binary[i]
Protect[Power];

Expand[(binary + binary)^10]
binary + binary + 1022*binary*binary

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

Expand[(binary + binary)^100]*
Expand[(binary - binary)^100]

(binary + binary +
1267650600228229401496703205374*binary*binary)*
(binary + binary -
2*binary*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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