منابع مشابه
Arithmetic Multivariate Descartes' Rule Arithmetic Multivariate Descartes' Rule
Let L be any number field or p-adic field and consider F := (f1, . . . , fk) where fi∈L[x ±1 1 , . . . , x ±1 n ]\{0} for all i and there are exactlym distinct exponent vectors appearing in f1, . . . , fk. We prove that F has no more than 1+ ( σm(m− 1)2n2 logm )n geometrically isolated roots in Ln, where σ is an explicit and effectively computable constant depending only on L. This gives a sign...
متن کاملArithmetic Multivariate Descartes ’ Rule
Let L be any number field or p-adic field and consider F := (f1, . . . , fk) where fi∈L[x 1 , . . . , x±1 n ]\{0} for all i and there are exactly μ distinct exponent vectors appearing in f1, . . . , fk. We prove that F has no more than 1+ ( ln(μ− n+ 1)min{1,n−1}(μ− n)2 log μ )n geometrically isolated roots in Ln, where l is an explicit and effectively computable constant depending only on L. Th...
متن کاملArithmetic Multivariate Descartes ’ Rule 1
Let L be any number field or p-adic field and consider F := (f1, . . . , fk) where f1, . . . , fk ∈ L[x1, . . . , xn] and no more than μ distinct exponent vectors occur in the monomial term expansions of the fi. We prove that F has no more than 1 + ( Cn(μ− n)3 log(μ− n) )n geometrically isolated roots in Ln, where C is an explicit and effectively computable constant depending only on L. This gi...
متن کاملDescartes' 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 the number of sign changes in its coefficient list. Our proof follows the simple inductive proof given by Arthan [1], which was also used by John Harrison in his HOL Light formalisation. We proved most of the lemmas for arbitrary linearly-ordered integrity domains (e.g....
متن کاملThe Descartes Rule of Sweeps and the Descartes Signature
The Descartes Rule of Signs, which establishes a bound on the number of positive roots of a polynomial with real coefficients, is extended to polynomials with complex coefficients. The extension is modified to bound the number of complex roots in a given direction on the complex plane, giving rise to the Descartes Signature of a polynomial. The search for the roots of a polynomial is sometimes ...
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ژورنال
عنوان ژورنال: American Journal of Mathematics
سال: 2004
ISSN: 1080-6377
DOI: 10.1353/ajm.2004.0005