2.29.2 Exact bounds for real roots of a polynomial : realroot
realroot has 2 or 4 arguments : a polynomial and a real number
є and optionnally two reals numbers α,β.
realroot returns a list of vectors.
-
If realroot has 2 arguments, the elements of each vector are
-
either a real interval containing a real root of the polynomial
and the multiplicity of this root.
Let the interval be [a1,a2] then |a1−a2|<є and
the root a verifies a1≤ a ≤ a2.
- or the value of an exact real root of the
polynomial and the multiplicity of this roots
- If realroot has 4 arguments, realroot returns a list of
vectors as above, but only for the roots inside
the interval [α,β].
To find the real roots of x3+1, input:
realroot(x^
3+1, 0.1)
Output :
[[-1,1]]
To find the real roots of x3−x2−2x+2, input:
realroot(x^
3-x^
2-2*x+2, 0.1)
Output :
[[1,1],[[(-3)/2,(-45)/32],1],[[45/32,3/2],1]]
To find the real roots of x3−x2−2x+2 in the interval [0;2], input:
realroot(x^
3-x^
2-2*x+2, 0.1,0,2)
Output :
[[1,1],[[11/8,23/16],1]]