Results 11 to 20 of about 167,419 (271)
Formalized Mathematics, 2021 Summary In this article we further develop field theory [6], [7], [12] in Mizar [1], [2], [3]: we deal with quadratic polynomials and quadratic extensions [5], [4]. First we introduce quadratic polynomials, their discriminants and prove the midnight formula. Then we show that - in case the discriminant of p being non square - adjoining a
Schwarzweller, Christoph +1 more
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Quadratic Extensions in ACL2 [PDF]
Electronic Proceedings in Theoretical Computer Science, 2020 Given a field K, a quadratic extension field L is an extension of K that can be generated from K by adding a root of a quadratic polynomial with coefficients in K. This paper shows how ACL2(r) can be used to reason about chains of quadratic extension fields Q = K_0, K_1, K_2, ..., where each K_i+1 is a quadratic extension field of K_i.
Gamboa, Ruben +2 more
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The quadratic Graver cone, quadratic integer minimization, and extensions [PDF]
Mathematical Programming, 2012 We consider the nonlinear integer programming problem of minimizing a quadratic function over the integer points in variable dimension satisfying a system of linear inequalities. We show that when the Graver basis of the matrix defining the system is given, and the quadratic function lies in a suitable {\em dual Graver cone}, the problem can be solved ...
Lee, Jon +3 more
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Supersimplicity and quadratic extensions [PDF]
Archive for Mathematical Logic, 2008 The paper deals with the algebraic characterization of supersimple fields. Pillay conjectured that such a field \(K\) is perfect, bounded and pseudo algebraically closed, and with Poizat proved both perfection and boundedness. Thus it remains to prove or disprove pseudo algebraic closedness, in other words that every absolutely irreducible plane curve ...
Martin-Pizarro, Amador +1 more
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Quadratic Extensions of Linearly Compact Fields [PDF]
Transactions of the American Mathematical Society, 1972 A group valuation is constructed on the norm factor group of a quadratic extension of a linearly compact field, and the norm factor group is explicitly computed as a valued group. Generalizations and applications of this structure theory are made to cyclic extensions of prime degree, to square (and pth power) factor groups, to generalized quaternion ...
Brown, Ron, Warner, Hoyt D.
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Nonlinear evolution of water waves and their dispersion relation in coastal waters [PDF]
Theoretical and Applied Mechanics, 2023 Preliminary results of the derivation of a new phase-resolving (deterministic) spatio-temporal nonlinear model of water wave evolution in nondeep waters with constant bathymetry are presented in this paper. The model is the first of its kind to include a
Vrećica Teodor, Toledo Yaron
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Heights and quadratic forms: on Cassels' theorem and its generalizations [PDF]
, 2012 In this survey paper, we discuss the classical Cassels' theorem on existence of small-height zeros of quadratic forms over Q and its many extensions, to different fields and rings, as well as to more general situations, such as existence of totally ...
Fukshansky, Lenny
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Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2014 Soient ℓ et ℓ' deux nombres premiers distincts, k = Q(√ℓℓ') et k∞ la Z2-extension cyclotomique de k. Soient L∞ la 2-extension maximale non ramifiée sur k∞ et L∞ la sous-extension abélienne maximale de L∞/k∞.
Mouhib Ali
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On the Content Bound for Real Quadratic Field Extensions
Axioms, 2012 Let K be a finite extension of Q and let S = {ν} denote the collection of K normalized absolute values on K. Let V+K denote the additive group of adeles over K and let K ≥0 c : V + → R denote the content map defined as c({aν }) = Q K ν ∈S ν (aν ) for
Robert G. Underwood
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First-Degree Prime Ideals of Biquadratic Fields Dividing Prescribed Principal Ideals
Mathematics, 2020 We describe first-degree prime ideals of biquadratic extensions in terms of the first-degree prime ideals of two underlying quadratic fields. The identification of the prime divisors is given by numerical conditions involving their ideal norms.
Giordano Santilli, Daniele Taufer
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