Re: Unprotect Plus, no automatic collection

• To: mathgroup at smc.vnet.net
• Subject: [mg39434] Re: Unprotect Plus, no automatic collection
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Sat, 15 Feb 2003 01:41:58 -0500 (EST)
• Organization: The University of Western Australia
• References: <b184d4\$kqb\$1@smc.vnet.net> <b1afsn\$ph0\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```In article <b1afsn\$ph0\$1 at smc.vnet.net>,
Friedrich Laher <mathefritz at schmieder-laher.de> wrote:

> Friedrich Laher schrieb:
> > when Unprotect[Plus]; Plus[w1,w2] = -1 is commanded
> > and then the expanding of a product gives a*w1 + a*w2 + ...
> > that is not collapsed to -a + ... automatically, even
> > if selecting that a*w1 + a*w1 and
> > the applying Simplify to it from al palette, does it.  What
> > can be done to automize it?
> >
> >
> I got a direct answer from Mihaijlo Vanevic,
> suggesting
> using a rul w2 -> -1-w2
> but
> what when there is w1+w2+w3+... = -1
> ?

PolynomialReduce is designed for this. For example,

Last[PolynomialReduce[a*w1 + a*w2, {w1 + w2 + 1},{a}]]

The generalization is clear. For example,

Simplify[Last[PolynomialReduce[a*w1 + a*w2, {w1 + w2 + w3 + 1},{a}]]]

Cheers,
Paul

```

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