Help with very very slow determinant calcuation

I think you might be right, I'm probably trying to calculate something very impractical mathematically. I was following an algorithm from a computer vision paper and was hoping to keep everything symbolic so I could write a function that calculates the result in "one shot" (albeit some monstrous equation). The 10x10 matrix that they have ends up having mostly numerical values mixed with a single polynomial symbol (z or z^2), which is probably practical to calculate. Of interest is that they note that higher order polynomial terms (> 10) end up canceling each other out, which made me optimistic that it was possible to keep it all symbolic. But I guess the intermediate steps that Maxima has to do will take an extremely long amount of time before it can do any cancellation of terms.




>________________________________
>From: Barton Willis <willisb at unk.edu>
>To: nghiaho12 at yahoo.com
>Cc: bernard at marcade.biz; cladelpino at gmail.com; maxima at math.utexas.edu
>Sent: Sunday, 7 August 2011 8:18 PM
>Subject: Re: [Maxima] Help with very very slow determinant calcuation
>
>The cost for the function determinant is comparable to the cost of a LU factorization. So, no
>computing the determinant by means of the LU factorization is unlikely to help. Nghia Ho already
>tried setting ratmx to true and newdet. And that's about all that might speed up the
>calculation. 
>
>For symbolic matrices, the standard big oh time estimates are misleading. The time for addition,
>for example, isn't constant, but the time depends on the complexity of the expressions. 
>
>It's likely that if Maxima was able to find the determinant of this 10x10 symbolic matrix, the
>result would be so huge that it wouldn't be useful. I would suggest a different approach.
>
>--Barton
>
>-----maxima-bounces at math.utexas.edu wrote: -----
>
>Can you elaborate more on how factorizing the matrix can help? My background isn't in mathematics, I only did basic engineering level maths.
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