Localisation des zéros de polynômes par rapport au cercle unité
Localisation des zéros de polynômes réciproques
Locally bounded topologies on the rational field
Majoration de la norme des facteurs d'un polynôme
Majoration de la norme des facteurs d'un polynôme : cas où toutes les racines du polynôme sont réelles
Mémoire sur la résolution des équations algébriques les unes par les autres.
Méthode de l'élimination des intervalles pour servir à la résolution des équations algébriques et transcendantes
Minimal degree solutions for the Bezout equation
Model theory of fields: An application to positive semidefinite polynomials
Multivariate Sturm-Habicht sequences: real root counting on n-rectangles and triangles.
The main purpose of this note is to show how Sturm-Habicht Sequence can be generalized to the multivariate case and used to compute the number of real solutions of a polynomial system of equations with a finite number of complex solutions. Using the same techniques, some formulae counting the number of real solutions of such polynomial systems of equations inside n-dimensional rectangles or triangles in the plane are presented.
Natural operators lifting vector fields to bundles of Weil contact elements
Let be a Weil algebra. The bijection between all natural operators lifting vector fields from -manifolds to the bundle functor of Weil contact elements and the subalgebra of fixed elements of the Weil algebra is determined and the bijection between all natural affinors on and is deduced. Furthermore, the rigidity of the functor is proved. Requisite results about the structure of are obtained by a purely algebraic approach, namely the existence of nontrivial is discussed.
New inequalities on polynomial divisors.
Niven’s Theorem
This article formalizes the proof of Niven’s theorem [12] which states that if x/π and sin(x) are both rational, then the sine takes values 0, ±1/2, and ±1. The main part of the formalization follows the informal proof presented at Pr∞fWiki (https://proofwiki.org/wiki/Niven’s_Theorem#Source_of_Name). For this proof, we have also formalized the rational and integral root theorems setting constraints on solutions of polynomial equations with integer coefficients [8, 9].
Non-principal divisors among the values of polynomials
Norms of certain rational functions of a matrix and Schur's criterion for polynomials
Norms of factors of polynomials
Norms of matrix powers
Note sur la continuité des racines des équations algébriques
Note sur la règle des signes de Descartes
Note zu dem Aufsatze "über eine Eigenschaft von Functionaldeterminanten" Bd. 69, p. 355 dieses Journals.