Maxima: Transforming solutions obtained by linsolve.

On Saturday 17 November 2007 13:41, Barton Willis wrote:
> Try this:
>
>   (%i1) [x1 = -(%r1*a13+%r2*a12)/a11,x2 = %r2,x3 = %r1]$
>
>   (%i2) map('rhs,%);
>   (%o2) [(-%r1*a13-%r2*a12)/a11,%r2,%r1]
>
>   (%i3) coefmatrix(%,[%r1,%r2]);
>   (%o3) matrix([-a13/a11,-a12/a11],[0,1],[1,0])
>
> Why map rhs on to the equations?  Consider:
>
>   (%i4) coefmatrix([x+y=z, x-y=q],[x,y]);
>   (%o4) matrix([1,1],[1,-1])
>
>   (%i5) augcoefmatrix([x+y=z, x-y=q],[x,y]);
>   (%o5) matrix([1,1,-z],[1,-1,-q])
>
> BW

Thanks very much for the detailed response. This is exactly what is needed. 

I am trying to incorporate your idea in a maxima function mycoefmatrix() to 
be called as follows:

xsol1 : linsolve([a11*x1+a12*x2+a13*x3=0],[x1,x2,x3]);

(%o20) [x1 = -(%r3*a13+%r4*a12)/a11,x2 = %r4,x3 = %r3]

A1 : mycoefmatrix(xsol1);


xsol2 : linsolve([a11*x1+a12*x2+a13*x3+a14*x4=0],[x1,x2,x3,x4]);

(%o21) [x1 = -(%r5*a14+%r6*a13+%r7*a12)/a11,x2 = %r7,x3 = %r6,x4 = %r5]
(%i22) 

A2 : mycoefmatrix(xsol2);

etc............

However, I cannot find a maxima method/command  to extract the list r below.

Thanks again for the assistance.

Regards,

C. Frangos.



mycoefmatrix(listeqns) := block(

[A,B,r,....],

/*Determine if %r1, %r2.....  are present in listeqns, and if so extract and 
place in list r.*/

B : map('rhs,listeqns),
A : coefmatrix(B,r),

return(A)

);




>
> -----maxima-bounces at math.utexas.edu wrote: -----
>
> >To: maxima at math.utexas.edu
>
> From: Constantine Frangos <cfrangos at telkomsa.net>
>
> >Sent by: maxima-bounces at math.utexas.edu
> >Date: 11/17/2007 03:45AM
> >Subject: Maxima: Transforming solutions obtained by linsolve.
> >
> >I am using linsolve() for the solution of linear equations.  For example:
> >
> >
> >(%i513) ysol : linsolve([a11*x1+a12*x2+a13*x3],[x1,x2,x3]);
> >
> >(%o513) [x1 = -(%r1*a13+%r2*a12)/a11,x2 = %r2,x3 = %r1]
> >(%i514)
> >
> >I want to transform the obtained solution to the following form:
> >
> >xsol = A . r
> >
> >where r = matrix([%r1],[%r2])
> >
> >and A = matrix([-a13/a11,-a12/a11],[0,1],[1,0])
> >
> >Its not clear how to construct or extract the matrix A (and the matrix r)
> >from the list ysol.
> >
> >I could not extract the %r1 and %r2  as these seem to be different each
> >time
> >linsolve() is called, eg %r3, %r4, etc
> >
> >Any assistance would be appreciated.
> >
> >TIA
> >
> >C. Frangos.
> >_______________________________________________
> >Maxima mailing list
> >Maxima at math.utexas.edu
> >http://www.math.utexas.edu/mailman/listinfo/maxima
>
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-- 
Constantine Frangos, Pr.Eng.
Professor
Dept. of Mathematics and Statistics
University of Johannesburg
Auckland Park Kingsway Campus
P O Box 524
Auckland Park 
Johannesburg 2006
South Africa

Tel: +27-11-559-2452
Fax: +27-11-559-2832
e-mail: cfrangos at uj.ac.za , cfrangos at telkomsa.net