Simplify and Noncommutativity
- To: mathgroup at smc.vnet.net
- Subject: [mg60277] Simplify and Noncommutativity
- From: Robert Schoefbeck <schoefbeck at hep.itp.tuwien.ac.at>
- Date: Fri, 9 Sep 2005 04:36:07 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
I have a rather lengthy expression of abstract products of matrices
of the form
myDot[M1,M2,...]
If Inv[M] denotes the inverse matrix
i have told mathematica that
myDot[P1___,P2_,Inv[P2_],P3___]:=myDot[P1,P3];
myDot[P1___,Inv[P2_],P2_,P3___]:=myDot[P1,P3];
myDot[]=Unity;
and that
myDot[P1___,P2_+P3_,P4___]:=myDot[P1,P2,P4]+myDot[P1,P3,P4];
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 ->
{Automatic,myDotSimp}];
this thing, however, is immensly time consuming.
On the other hand, cancellations of the type
Simplify[b/(b+c)+c/(b+c)]
are extremly fast.
Is there a way to combine the power of Simplify on Rational functions
with a noncommutative multiplication?
kind regards
robert schoefbeck