[Date Index]
[Thread Index]
[Author Index]
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[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] +
1267650600228229401496703205374*binary[1]*binary[2])*
(binary[2] + binary[3] -
2*binary[2]*binary[3])
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
Prev by Date:
**Re: Bernoulli variable algebra**
Next by Date:
**Re: FW: matrix operations**
Previous by thread:
**Re: Bernoulli variable algebra**
Next by thread:
**Re: Bernoulli variable algebra**
| |