Re: Q: About constants inside Distribute

• To: mathgroup at smc.vnet.net
• Subject: [mg9237] Re: [mg9187] Q: About constants inside Distribute
• From: Allan Hayes <hay at haystack.demon.co.uk>
• Date: Fri, 24 Oct 1997 01:00:51 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```sergio at scisun.sci.ccny.cuny.edu (Sergio Rojas) [mg9187] Q: About
constants inside Distribute

rule = Dot[s___,(k:(a[i_]))m___, r___]:> k Dot[s,m,r]

f = O1*a[1] + O2*a[2]
g = P1*a[3]*a[1]
h = O2*a[3]

Distribute[f.g.h]//.rule

2
a[1]  a[3] O1 . P1 . a[3] . O2 + a[1] a[2] a[3] O2 . P1 . a[3]. O2

with the a[3] not stripped out by the rule.

The problem is seems to lie in

MatchQ[a , a m___]
False

When we would expect matches like
a ~ a 1 ~ a Times[] ~ a Times[___].

I'm not clear about what is happening here but a work-around is use
default values

MatchQ[a,a m_.]	(*   note the dot m_.  *)

True

and modify the rule to

rule2 = Dot[s___,(k:a[i_])m_., r___]:> k Dot[s,m,r]

Check:

Distribute[f.g.h]//.rule2

a[1]^2*a[3]^2*O1 . P1 . O2 + a[1]*a[2]*a[3]^2*O2 . P1 . O2

Allan Hayes
hay at haystack.demon.co.uk
http://www.haystack.demon.co.uk/training.html voice:+44 (0)116 2714198
fax: +44 (0)116 2718642
Leicester,  UK

```

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