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## Exact bounds for real roots of a polynomial : realroot

realroot has 2 or 4 arguments : a polynomial and a real number and optionnally two reals numbers ,.
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| < 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 [,].
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]]

suivant: Exact values of rational monter: Exact roots of a précédent: Exact bounds for complex   Table des matières   Index
giac documentation written by Renée De Graeve and Bernard Parisse