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## Compute with the exact root of a polynomial : rootof

Let P and Q be two polynomials given by the list of their coefficients then rootof(P,Q) denotes the value P() where is the root of Q with largest real part (and largest imaginary part in case of equality).
In exact computations, Xcas will rewrite rational evaluations of rootof as a unique rootof with degree(P) <degree(Q). If the resulting rootof is the solution of a second degree equation, it will be simplified.

Example
Let be the root with largest imaginary part of Q(x) = x4 + 10x2 + 1 (all roots of Q have real part equal to 0).

• Compute . Input :
normal(1/rootof([1,0],[1,0,10,0,1]))
P(x) = x is represented by [1,0] and by rootof([1,0],[1,0,10,0,1]).
Output :
rootof([[-1,0,-10,0],[1,0,10,0,1]])
i.e. :

= - 3 - 10

• Compute 2. Input :
normal(rootof([1,0],[1,0,10,0,1])^2)
or (since P(x) = x2 is represented by [1,0,0]) input
normal(rootof([1,0,0],[1,0,10,0,1]))
Output :
-5-2*sqrt(6)

suivant: Exact roots of a monter: Polynomials précédent: Rewrite in terms of   Table des matières   Index
giac documentation written by Renée De Graeve and Bernard Parisse