Virtual Roots of Real Polynomials
Résumé
The fact that a real univariate polynomial misses some real roots is usually over-
came by considering complex roots, but the price to pay for, is a complete lost of
the sign structure that a set of real roots is endowed with (mutual position on the
line, signs of the derivatives, etc...). In this paper we present real substitutes for
these missing roots which keep sign properties and which extend of course the exist-
ing roots. Moreover these "virtual roots" are the values of semialgebraic continuous
{ rather uniformly { functions dened on the set of monic polynomials. We present
some applications.
Domaines
Algèbre commutative [math.AC]
Fichier principal
virtrootfinal-cor2017.pdf (344.35 Ko)
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EnglishTheorems.tex (2.19 Ko)
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cubica.pdf (43.78 Ko)
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gr3.pdf (9.07 Ko)
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psfig.tex (8.85 Ko)
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