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** monter:** Exact roots and poles
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##

Roots and poles of a rational function : `froot`

`froot` takes a rational function *F*(*x*) as argument.

`froot` returns a vector whose components are the roots and the poles
of *F*[*x*], each one followed by it's multiplicity.

If `Xcas` can not find the exact values of the roots or poles,
it tries to find approximate values if *F*(*x*) has numeric coefficients.

Input :
`froot((x``^`

5-2*x`^`

4+x`^`

3)/(x-2))

Output :
`[1,2,0,3,2,-1]`

Hence, for
*F*(*x*) = :
- 1 is a root of multiplicity 2,
- 0 is a root of multiplicity 3,
- 2 is a pole of order 1.

Input :
`froot((x``^`

3-2*x`^`

2+1)/(x-2))

Output :
`[1,1,(1+sqrt(5))/2,1,(1-sqrt(5))/2,1,2,-1]`

**Remark** : to have the complex roots and the poles, check `Complex` in
the `cas` configuration (red button giving the state line).

Input :
`froot((x``^`

2+1)/(x-2))

Output :
`[-i,1,i,1,2,-1]`

giac documentation written by Renée De Graeve and Bernard Parisse