Re: ReplaceAll

• To: mathgroup at smc.vnet.net
• Subject: [mg90426] Re: ReplaceAll
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Wed, 9 Jul 2008 04:52:47 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <g4v2u3\$idv\$1@smc.vnet.net>

```Bruce Colletti wrote:

> Re Mathematica 6.0.2 under WinXP.
>
> Why doesn't the following substitute x for b'**b (appears in the third, fourth, sixth and seventh summands)?  (a**b')**b/.b'**b->x does.

Note that

(-a ** b') ** b /. b' ** b -> x

(-a ** b') ** b

does not work either.

A quick glance at the TreeForm (or FullForm) of the expressions will
reveal why.

TreeForm[(a ** b') ** b]

TreeForm[(-a ** b') ** b]

The following pattern handles correctly the negative case:

(-a ** b') ** b /. ((f_) a ** b') ** b -> f a ** x

-a ** x

> In[1]:= M=b**a'-a**b';
> Distribute[M**M**M,Plus]/.b'**b->x
>
> Out[2]= (-a**b^\[Prime])**(-a**b^\[Prime])**(-a**b^\[Prime])+b**a^\[Prime]**(-a**b^\[Prime])**(-a**b^\[Prime])+(-a**b^\[Prime])**b**a^\[Prime]**(-a**b^\[Prime])+(-a**b^\[Prime])**(-a**b^\[Prime])**b**a^\[Prime]+b**a^\[Prime]**b**a^\[Prime]**(-a**b^\[Prime])+b**a^\[Prime]**(-a**b^\[Prime])**b**a^\[Prime]+(-a**b^\[Prime])**b**a^\[Prime]**b**a^\[Prime]+b**a^\[Prime]**b**a^\[Prime]**b**a^\[Prime]
>

In[31]:= M = b ** a' - a ** b';
Distribute[M ** M ** M, Plus] /. ((f_) a ** b') ** b -> f a ** x

Out[32]= (-a ** x) ** a' ** (-a ** b') + (-a ** b') ** (-a ** x) ** a' +

(-a ** b') ** (-a ** b') ** (-a ** b') + b ** a' ** (-a ** x) ** a' +

b ** a' ** (-a ** b') ** (-a ** b') + (-a ** x) ** a' ** b ** a' +

b ** a' ** b ** a' ** (-a ** b') + b ** a' ** b ** a' ** b ** a'

Regards,
-- Jean-Marc

```

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