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[Matthew Rocklin <mrocklin AT cs.uchicago.edu>]

Thank you for the example Marc, 

I worked a bit more on my project after sending out the question. I'm posting my implementation here

https://github.com/mrocklin/matrix-algebra

-Matthew

On Fri, Apr 20, 2012 at 1:05 PM, Matthew Rocklin <mrocklin AT cs.uchicago.edu> wrote:

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

http://matthewrocklin.com

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Matthew Rocklin

University of Chicago - Computer Science PhD Student

http://matthewrocklin.com