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Simplify and Noncommutativity

  • To: mathgroup at
  • Subject: [mg60277] Simplify and Noncommutativity
  • From: Robert Schoefbeck <schoefbeck at>
  • Date: Fri, 9 Sep 2005 04:36:07 -0400 (EDT)
  • Sender: owner-wri-mathgroup at

I have a rather lengthy expression of abstract products of matrices
of the form


If Inv[M] denotes the inverse matrix

i have told mathematica that


and that


and a lot more things.

My Problem is:

In big expressions i have huge cancellations of the form

myDot[M1,Inv[M1+M2+M3+....]] + myDot[M2,Inv[M1+M2+M3+....]]
  + myDot[M3 ,Inv[M1+M2+M3+....]]+...

such that the summands M1,M2.... should be summed and then cancel 
against the Inv[...] part.

I have a very slow workaround,

     myDotSimp[HoldPattern[Plus[P6___, myDot[P5___, P1_, P3___], 
   myDot[P5___,P2_, P3___]]]] := P6 + myDot[P5, P1 + P2, P3];

     SetOptions[Simplify, TransformationFunctions ->

this thing, however, is immensly time consuming.

On the other hand, cancellations of the type
are extremly fast.
Is there a way to combine the power of Simplify on Rational functions 
with a noncommutative multiplication?

kind regards
robert schoefbeck

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