Thank you thank you thank you!
I've been stuck on this for two weeks.
I had the same input, but got the matrix([]) business. I looked
carefully again at my input and removed a statement (at the
beginning) declaring x to be non-scalar. reran it, and bingo.
Subsequent stuff works, too, now - it had been crashing when I tried
to compute the matrix d/dx of (xprime/sqrt(mm)); presumably because
it didn't think xprime/sqrt(mm) was a 3-vector. Not sure what was
wrong with declaring x to be non-scalar, but as I say it works now.
On Jan 6, 2007, at 10:49 AM, Barton Willis wrote:
> This is what I got:
>
> (%i1) P1:matrix([(-sigma) * x[1]+sigma * x[2]],[rho * x[1]-x[2]],[(-
> beta)
> *
> x[3]])$
>
> P2:matrix([0],[(-x[1]) * x[3]],[x[1] * x[2]])$
>
> SQ: matrix([x[1]],[x[2]],[x[3]]) . matrix([sigma * x[1]],[x[2]],[beta
> * x[3]]) - (rho+sigma) * x[1] * x[2]$
>
> RR:matrix([x[1]],[x[2]],[x[3]]) . matrix([x[1]],[x[2]],[x[3]]);
>
> xprime:(1+RR) * (1-RR) * P1 + (1+RR) * P2 + 2 * (1-RR) * SQ * matrix
> ([x[1]],[x[2]],[x[3]])$
>
> mm: xprime . xprime$
>
> x[1]:1;x[2]:2;x[3]:.5$
> expand(''mm);
> (%i2)
> (%i3)
> (%i4)
> (%o4) x[3]^2+x[2]^2+x[1]^2
> (%i5)
> (%i6)
> (%i7)
> (%o7) 1
> (%o8) 2
> (%i10)
> (%o10)
> 633.31640625*sigma^2-289.0*rho*sigma+36.125*beta*sigma+578.0*sigma
> +416.56640625*rho^2+72.25*beta*rho-1500.25*rho+
> 171.8759765625*beta^2+187.53125*beta+1500.25
> (%i11) sigma:5;rho:25;beta:3$
> expand(''mm);
> (%o11) 5
> (%o12) 25
> (%i14)
> (%o14) 215016.0166015625
>
> Notice that (%o10) and (%o14) are not 1 x 1 matrices. In the
> expression
> for xprime, did you change
> three dot operators to star operators?
>
> Barton
>
> maxima-bounces at math.utexas.edu wrote on 01/06/2007 08:55:18 AM:
>
>> sorry. I used :
>>
>> x[1]:1;x[2]:2;x[3]:.5; expand(''mm);
>> the result of which was
>> matrix([a polynomial in the parameters sigma, rho, beta])
>> It's correct that it's a polynomial, but weird that it's a one by one
>> matrix
>>
>> then picking values for the parameters
>> sigma:5;rho:25;beta:3; expand(''mm);
>> gives a pure number inside [ ], and it's not a matrix
>>
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