Problem with linsolve?



On 4/1/07, Kostas Oikonomou <ko at research.att.com> wrote:
> However, I don't think we have a consistency problem here

First of all, there's the issue of parameters vs. variables, which I
mentioned in a recent email (but after your last email).

Secondly, there is in fact a consistency problem here because r1..c3
have a constraint on them.

Given
   eqs:  [r(1)=r1,r(2)=r2,r(3)=r3, c(1)=c1,c(2)=c2,c(3)=c3]$

let's eliminate the x[i,j]'s:

eliminate(eqs,[x[1,1],x[1,2],x[1,3],x[2,1],x[2,2]]);
eliminate(%,[x[3,1]]);
     =>	       [ - r3 - r2 - r1 + c3 + c2 + c1 ]

(It doesn't work to combine the variable lists; I'm not sure why...)

So there is a constraint on the parameters.  Let's incorporate the constraint:

  solve(  subst( r3 =  - r2 - r1 + c3 + c2 + c1, eqs),
               [
x[1,1],x[2,1],x[3,1],x[1,2],x[2,2],x[3,2],x[1,3],x[2,3],x[3,3] ] ) =>

[[
  x[1,1] = -r2+c1+%r18-%r17+%r16,
  x[2,1] = r2-%r18-%r16,
  x[3,1] = %r17,
  x[1,2] = r2+r1-c3-c1-%r18+%r17+%r15,
  x[2,2] = %r18,
  x[3,2] = -r2-r1+c3+c2+c1-%r17-%r15,
  x[1,3] = c3-%r16-%r15,
  x[2,3] = %r16,
  x[3,3] = %r15
]]

Does that help?

           -s