6.29.1 Exact bounds for real roots of a polynomial:
realroot
The
realroot
command finds bounds for the real roots of a polynomial.
realroot
takes two mandatory arguments and two optional arguments:
P
, a polynomial.
є, a postive real number.
Optionally,
a
,
b
, two complex numbers.
realroot(
P
,є
)
returns a list of vectors, where the elements of each vector are a list containing one of:
an interval of length less than є containing a real root of the polynomial and the multiplicity of this root.
the value of an exact real root of the polynomial and the multiplicity of this root.
realroot(
P
,є,
a
,
b
)
returns a list of vectors as above, but only for the roots lying in the interval [
a
,
b
].
Examples.
Find the real roots of
x
3
+1.
Input:
realroot(x^3+1, 0.1)
Output:
⎡
⎣
−1
1
⎤
⎦
Find the real roots of
x
3
−
x
2
−2
x
+2.
Input:
realroot(x^3-x^2-2*x+2, 0.1)
Output:
⎡
⎢
⎢
⎣
−[1.40624999999999..1.50000000000001]
1
1
1
[1.37499999999999..1.43750000000001]
1
⎤
⎥
⎥
⎦
Find the real roots of
x
3
−
x
2
−2
x
+2 in the interval [0;2].
Input:
realroot(x^3-x^2-2*x+2, 0.1,0,2)
Output:
⎡
⎢
⎣
1
1
[1.37499999999999..1.43750000000001]
1
⎤
⎥
⎦