A. Alkiviadis and G. , Reflections on an pair of theorems by Budan and Fourier, Mathematics Magazine, vol.55, issue.5, pp.292-298, 1982.

G. Alonso-garcia, A : Real roots isolation for sparse polynomials, Proceedings ISSAC'2012, ACM, pp.35-42, 2012.

K. Atkinson and . Sharma, A Partial Characterization of Poised Hermite???Birkhoff Interpolation Problems, SIAM Journal on Numerical Analysis, vol.6, issue.2, pp.230-236, 1969.
DOI : 10.1137/0706021

J. C. Butcher, R. Corless, L. Vega, and S. , Polynomial algebra for Birkhoff interpolants, Numerical Algorithms, vol.206, issue.1, pp.319-347, 2011.
DOI : 10.1007/s11075-010-9385-x

D. Bembé, An algebraic certificate for Budan???s theorem, Journal of Pure and Applied Algebra, vol.215, issue.6, 2011.
DOI : 10.1016/j.jpaa.2010.08.016

D. Bembé and G. , Virtual roots of a real polynomial and fractional derivatives, Proceedings of the 36th international symposium on Symbolic and algebraic computation, ISSAC '11, 2011.
DOI : 10.1145/1993886.1993897

J. Bochnack, M. Coste, and M. Roy, Real Algebraic Geometry, 1998.
DOI : 10.1007/978-3-662-03718-8

. Budan-de-boislaurent, Nouvelle méthode pour la résolution deséquationsdeséquations numériques d'un degré quelconque. Paris (1822) Contains in the appendix a proof of Budan's theorem presented at the Académie des, Sciences, 1811.

M. Coste, . Lajous, R. Lombardi, and M. , Generalized Budan???Fourier theorem and virtual roots, Journal of Complexity, vol.21, issue.4, pp.478-486, 2005.
DOI : 10.1016/j.jco.2004.11.003

N. Dyn, G. G. Lorentz, and S. D. Riemenschneider, Continuity of the Birkhoff Interpolation, SIAM Journal on Numerical Analysis, vol.19, issue.3, pp.507-509, 1982.
DOI : 10.1137/0719032

. Gonzalez-vega, H. Lombardi, and M. , Virtual roots of real polynomials, Journal of Pure and Applied Algebra, vol.124, issue.1-3, pp.147-166, 1998.
DOI : 10.1016/S0022-4049(96)00102-8

. Galligo, Roots of the derivatives of some random polynomials, Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation, SNC '11, 2011.
DOI : 10.1145/2331684.2331703
URL : https://hal.archives-ouvertes.fr/inria-00552081

. Galligo, A: Deformation of Roots of Polynomials via Fractional Derivatives. Accepted for publication in JSC, 2012.

. Galligo, A: Improved Budan-Fourier Count for Root Finding, Preprint, 2011.

V. P. Kostov, Root arrangements of hyperbolic polynomial-like functions, Rev. Mat. Complut, vol.19, issue.1, pp.197-225, 2006.

V. P. Kostov, On root arrangements for hyperbolic polynomial-like functions and their derivatives, Bulletin des Sciences Math??matiques, vol.131, issue.5, pp.201-216, 2005.
DOI : 10.1016/j.bulsci.2006.12.004

V. P. Kostov, On root arrangements for hyperbolic polynomial-like functions and their derivatives, Bulletin des Sciences Math??matiques, vol.131, issue.5, pp.477-492, 2007.
DOI : 10.1016/j.bulsci.2006.12.004

V. P. Kostov, A realization theorem about D-sequences, Comptes Rendus de l'Academie Bulgare Des Sciences, vol.60, p.12, 2007.

V. P. Kostov, On hyperbolic polynomial-like functions and their derivatives, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol.137, issue.04, pp.819-8452, 2007.
DOI : 10.1017/S0308210506000023

G. G. Lorentz and K. Zeller, Birkhoff Interpolation, SIAM Journal on Numerical Analysis, vol.8, issue.1, pp.43-48, 1971.
DOI : 10.1137/0708006

G. Muhlbach, An algorithmic approach to Hermite-Birkhoff-interpolation, Numerische Mathematik, vol.14, issue.3, pp.339-347, 1981.
DOI : 10.1007/BF01400313

G. Peyser, On the Roots of the Derivative of a Polynomial With Real Roots, The American Mathematical Monthly, vol.74, issue.9, pp.1102-1104, 1967.
DOI : 10.2307/2313625

Q. I. Rahman and G. Schmeisser, Analytic theory of polynomials, 2002.

B. Shapiro and M. Shapiro, This strange and mysterious Rolle's theorem. submitted to Amer. math. Monthly, arXiv: math CA, 302215.

M. Vincent, Sur la résolution deséquationsdeséquations numériques, Journal de mathématiques pures et appliquées, vol.44, pp.235-372, 1836.