Help with very very slow determinant calcuation

Without additional manual labor, I'm not sure that nullspace will do what you need; example:

 (%i2) nullspace(matrix([a,b],[c,d]));
 "Proviso: "notequal(a,0) and notequal(a*d-b*c,0)
 (%o2) span()

Assuming a # 0 and ad-bc # 0, the nullspace is empty. You'll need to investigate
the cases a=0, ad-bc=0 manually. Maybe you should try triangularize?


--Barton (author of nullspace)

-----maxima-bounces at math.utexas.edu wrote: -----

>To: Richard Fateman <fateman at eecs.berkeley.edu>
>From: Nghia Ho 
>Sent by: maxima-bounces at math.utexas.edu
>Date: 08/09/2011 02:33AM
>Cc: "maxima at math.utexas.edu" <maxima at math.utexas.edu>, Barton Willis
><willisb at unk.edu>
>Subject: Re: [Maxima] Help with very very slow determinant calcuation
>
>There should be newline characters, at least on Linux. Thanks for the
>suggestion about using only one coeff call.    After much re-reading of
>the paper, I think I might have misinterpreted the paper (doh!). The
>problem boils down to solving a linear system of this form:  C(z) * X(x,y)
>= 0  where C(z) is the 10x10 symbolic matrix of constants and 'z' and
>X(x,y) a 10x1 matrix comprised of combinations of 'x' and 'y'. This looks
>like a typical nullspace problem (Ax = 0), where I have to find a
>non-trivial solution. The paper says there is a non-trivial solution if
>and only if det(C(z)) = 0, which I think I misinterpreted as the equation
>to solve. I now believe the correct solution is to call nullspace(Cz),
>then solve a polynomial equation. I've tried the nullspace function on a
>mock 10x10 symbolic/numerical matrix and it returns a result almost
>immediately.    ----- Original Message ----- > From: Richard Fateman
><fateman at eecs.berkeley.edu> > To: Nghia Ho <nghiaho12 at yahoo.com> > Cc:
>Barton Willis <willisb at unk.edu>; "maxima at math.utexas.edu"
><maxima at math.utexas.edu> > Sent: Tuesday, 9 August 2011 8:41 AM > Subject:
>Re: [Maxima] Help with very very slow determinant calcuation >  > On
>8/8/2011 7:50 AM, Nghia Ho wrote: >>  My maxima script can be downloaded
>here > It would be nice to put newlines in your script. >  >  > There
>seems to be at least 39 variables, just looking at the first few lines of
>> the script. >  > there are many redundancies in your code. for example,
>expand() could be called > once instead of 100 times. and
>coeff(coeff(E,x,2),y,2)? ? is?  coeff(E,x^2*y^2). >  > Unless there is
>something more that you know about the determinant, calculating  > it > by
>brute force seems unreasonable.? Can you do a 3X3 case? >
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