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- From: Matthew Rocklin <mrocklin AT cs.uchicago.edu>
- To: maude-help AT cs.uiuc.edu
- Subject: [Maude-help] Guidance on symbolic matrix algebra expressions
- Date: Fri, 20 Apr 2012 13:05:20 -0500
- List-archive: <http://lists.cs.uiuc.edu/pipermail/maude-help>
- List-id: <maude-help.cs.uiuc.edu>
Hi Everyone,
I'm trying to simplify expressions in matrix algebra using known facts about the matrices in the _expression_.
I.e. supplied with the following
_expression_: transpose(B*Q*transpose(B*Q) )
facts: Q is orthogonal, B is symmetric
can we simplify to the following _expression_
B*B
by going through the following states
transpose(B*Q*transpose(Q)*transpose(B)) *** because transpose(XY) == transpose(X)*transpose(Y)
transpose(B*transpose(B)) *** because X*transpose(X) == identity if X is orthogonal and Q is orthogonal
B*transpose(B) *** because transpose(X) == X if X is symmetric and X*transpose(X) is symmetric for any X
B * B *** because transpose(X) == X if X is symmetric and B is symmetric
I know/can write down all of the equations and rules that appear on the right. I need to organize a system that handles both the known facts and the _expression_ at once. My experience with Maude is quite limitied. Mostly I've just played with the primer and manual. I'm ok playing with the small examples in the manual but it isn't clear to me how best to structure a program to solve this problem cleanly. I would appreciate any suggestions from the community or pointers to examples that come close to this problem.
Best,
Matthew Rocklin
University of Chicago - Computer Science PhD Student
- [Maude-help] Guidance on symbolic matrix algebra expressions, Matthew Rocklin, 04/20/2012
- Re: [Maude-help] Guidance on symbolic matrix algebra expressions, Marc Boyer, 04/26/2012
- Re: [Maude-help] Guidance on symbolic matrix algebra expressions, Matthew Rocklin, 04/26/2012
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