First of all if you compute the rational fraction numerator or
denominator from their roots (and if they are complex conjugate) the
result is a complex polynomial even if the imaginary part is not shown.
Second: the simplification of numerical rational fraction is a very
difficult problem. As Tim said the roots computed by numerical
algorithm cannot be use for that purpose.
Just try:
p=poly(ones(1,n),"x","c");
r=roots(p)
plot(real(r)-1,imag(r),"+")
You will see the roots on a circle which radius is of order %eps^(1/n) !
It is not a bug just a consequence of the numerical computations.
The simplication algorithm present in Scilab tryes to find reasonable
simplification based on the bezout equation error. But it has only be
written for the real case.
The bug fixes Samuel pointed to you allow simplification for complex
polynomials having zero imaginary parts.
Serge
Le 23/11/2016 à 19:37, philippe a écrit :
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
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