Re: Symbolic replacement of scalar products

• To: mathgroup at smc.vnet.net
• Subject: [mg120046] Re: Symbolic replacement of scalar products
• From: DrMajorBob <btreat1 at austin.rr.com>
• Date: Thu, 7 Jul 2011 07:28:56 -0400 (EDT)
• References: <201107060940.FAA29437@smc.vnet.net>

```This might do it:

Simplify[#, {a1*b1 + a2*b2 + a3*b3 == pAB}] & /@ {a1*b1 + a2*b2 +
a3*b3, -a1*b1 - a2*b2 - a3*b3, 2 a1*b1 + 2 a2*b2 + 2 a3*b3}

{pAB, -pAB, 2 pAB}

Bobby

On Wed, 06 Jul 2011 04:40:38 -0500, Giuseppe <juseppe78 at gmail.com> wrote:

> Hello,
>
> I have very complicated expressions containing scalar products like
>
> a1*b1 + a2*b2 + a3*b3
>
> In order to reduce the complexity, I would like to establish a set of
> rules like
>
> rule={a1*b1 + a2*b2 + a3*b3 -> pAB, ...}
>
> in order to replace each time the scalar product by an appropriate new
> symbol (pAB in the example).
> The problem is that, apparently, Mathematica does not perform the
> substitution if in the expression the scalar products appear together
> with some multiplying factor; for example Mathematica fails to apply the
> previous rule if the expression is
>
> -a1*b1 - a2*b2 - a3*b3
>
> or
>
> 2a1*b1 + 2a2*b2 + 2a3*b3
>
> How could solve this problem?
>

--
DrMajorBob at yahoo.com

```

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