On the seperation of basic semialgebraic sets by polynomials.
Ludwig Bröcker (1988)
Manuscripta mathematica
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Ludwig Bröcker (1988)
Manuscripta mathematica
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Roffelsen, Pieter (2010)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Andrzej Schinzel (1995)
Banach Center Publications
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Adam Parusinski, Zbigniew Szafraniec (1997)
Manuscripta mathematica
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Christoph Schwarzweller (2017)
Formalized Mathematics
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In this article we further extend the algebraic theory of polynomial rings in Mizar [1, 2, 3]. We deal with roots and multiple roots of polynomials and show that both the real numbers and finite domains are not algebraically closed [5, 7]. We also prove the identity theorem for polynomials and that the number of multiple roots is bounded by the polynomial’s degree [4, 6].
Keijo Väänänen (1977)
Manuscripta mathematica
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M.D. Presic (1979)
Publications de l'Institut Mathématique [Elektronische Ressource]
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Rafał Pierzchała (2003)
Annales Polonici Mathematici
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We give a deepened version of a lemma of Gabrielov and then use it to prove the following fact: if h ∈ 𝕂[[X]] (𝕂 = ℝ or ℂ) is a root of a non-zero polynomial with convergent power series coefficients, then h is convergent.
Souad El Otmani, Armand Maul, Georges Rhin, Jean-Marc Sac-Épée (2013)
Journal de Théorie des Nombres de Bordeaux
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In this work, we propose a new method to find monic irreducible polynomials with integer coefficients, only real roots, and span less than 4. The main idea is to reduce the search of such polynomials to the solution of Integer Linear Programming problems. In this frame, the coefficients of the polynomials we are looking for are the integer unknowns. We give inequality constraints specified by the properties that the polynomials should have, such as the typical distribution of their roots....
Marcellán, F., Alfaro, M. (1983-1984)
Portugaliae mathematica
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Yann Bugeaud, Andrej Dujella (2014)
Acta Arithmetica
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We construct parametric families of (monic) reducible polynomials having two roots very close to each other.
Thomas Ernst (2014)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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We study q-analogues of three Appell polynomials, the H-polynomials, the Apostol–Bernoulli and Apostol–Euler polynomials, whereby two new q-difference operators and the NOVA q-addition play key roles. The definitions of the new polynomials are by the generating function; like in our book, two forms, NWA and JHC are always given together with tables, symmetry relations and recurrence formulas. It is shown that the complementary argument theorems can be extended to the new polynomials...
Thomas Ernst (2015)
Annales UMCS, Mathematica
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We study q-analogues of three Appell polynomials, the H-polynomials, the Apostol-Bernoulli and Apostol-Euler polynomials, whereby two new q-difference operators and the NOVA q-addition play key roles. The definitions of the new polynomials are by the generating function; like in our book, two forms, NWA and JHC are always given together with tables, symmetry relations and recurrence formulas. It is shown that the complementary argument theorems can be extended to the new polynomials...
Joseph Maurer (1980)
Manuscripta mathematica
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