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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.

To find the real roots of x3+1, input:

realroot(x^3+1, 0.1)

Output :

[[-1,1]]

To find the real roots of x3x2−2x+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 x3x2−2x+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]]

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