Descartes' rule of signs

Known as: Descartes' sign rule, Rule of signs, Descartes rule of sign 
In mathematics, Descartes' rule of signs, first described by René Descartes in his work La Géométrie, is a technique for determining an upper bound… (More)
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10 relations
CoefficientGauss–Lucas theoremPolynomialProperties of polynomial roots
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Papers overview

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2017
2017
Some remarks about Descartes ’ rule of signs
What can we deduce about the roots of a real polynomial in one variable by simply considering the signs of its coefficients? On… (More)
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2016
2016
Descartes' Rule of Signs for Polynomial Systems supported on Circuits
We give the first multivariate version of Descartes’ rule of signs to bound the number of positive real roots of a system of… (More)
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2015
2015
Descartes' Rule of Signs
In this work, we formally proved Descartes Rule of Signs, which relates the number of positive real roots of a polynomial with… (More)
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2013
2013
Computing Real Roots of Real Polynomials - An Efficient Method Based on Descartes' Rule of Signs and Newton Iteration
Computing the real roots of a polynomial is a fundamental problem of computational algebra. We describe a variant of the… (More)
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2010
2010
Counting zeros of generalized polynomials : Descartes ’ rule of signs and Laguerre ’ s extensions
A slightly different question is how many positive zeros a polynomial has. Here the basic result is known as “Descartes’ rule of… (More)
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2004
2004
New Designs for the Descartes Rule of Signs
The question of how to construct polynomials having as many roots as allowed by the Descartes rule of signs has been the focus of… (More)
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2004
2004
Polynomials that Sign Represent Parity and Descartes’ Rule of Signs
A real polynomial P(X 1, ... , X n ) sign represents f : A n → {0, 1} if for every (a 1, ... , a n ) ∈ A n , the sign of P(a 1… (More)
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2002
2002
Descartes' Rule of Signs for Radial Basis Function Neural Networks
We establish versions of Descartes' rule of signs for radial basis function (RBF) neural networks. The RBF rules of signs provide… (More)
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2002
2002
RBF Neural Networks and Descartes' Rule of Signs
We establish versions of Descartes' rule of signs for radial basis function (RBF) neural networks. These RBF rules of signs… (More)
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Highly Cited
1976
Highly Cited
1976
Polynomial real root isolation using Descarte's rule of signs
Uspensky's 1948 book on the theory of equations presents an algorithm, based on Descartes' rule of signs, for isolating the real… (More)
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