[Scilab-users] lack of simplification for rational

[philippe]

Hi,

I  have a problem  to simplify automatically rational with an imaginary 
part. In my case  I only manipulate polynomials with real coefficients 
but some imaginary part arise due to rounding errors. See this example :

-->X=poly(0,'x');

-->A=(X-1)^2;

-->B=(X-1)*(X-2);

-->R=A/B// = (X-1)/(X-2)
  R  =

   - 1 + x
     -----
   - 2 + x

-->A=clean(A+%eps*(1+%i))//  add a rounding error
  A  =

Partie réelle


               2
     1 - 2x + x
Partie imaginaire


     0

-->R=A/B// = no simplifications
  R  =

                 2
     1 - 2x +  1x
    --------------
               2
     2 - 3x + x


I can't simplify R, even using simp(R), I've found some work around 
applying clean  to numerator/denominator coefficients  TWICE (I don't 
known why twice?!?!?)  :

-->R=poly(clean(coeff(numer(R))),'x')/poly(clean(coeff(denom(R))),'x')
  R  =

              2
   - 2 + x + x
     ---------
              2
   - 6 + x + x

-->R=poly(clean(coeff(numer(R))),'x')/poly(clean(coeff(denom(R))),'x')
  R  =

     2 + x
     -----
     6 + x

but of course this doesn't work  for polynomials with complex 
coefficients like :


-->(X+%i)/(X^2+1) // = 1/(X-%i)
  ans  =


    i +  1x
    --------
          2
     1 + x

I would like to find a solution for all polynomials with real/complex 
coefficients , any idea ?

Philippe