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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.
Ruben Gamboa +2 more
semanticscholar +6 more sources
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
semanticscholar +5 more sources
On automorphism group of free quadratic extensions over a ring [PDF]
International Journal of Mathematics and Mathematical Sciences, 1984 Let R be a ring with 1, ρ an automorphism of R of order 2. Then a normal extension of the free quadratic extension R[x,ρ] with a basis {1,x} over R with an R-automorphism group G is characterized in terms of the element (x−(x)α) for α in G.
George Szeto
doaj +2 more sources
Quadratic Maps and Bockstein Closed Group Extensions [PDF]
Transactions of the American Mathematical Society, 2006 We study central extensions E of elementary abelian 2-groups by elementary abelian 2-groups. Associated to such an extension is a quadratic map which determines the extension uniquely. The components of the map determine a quadratic ideal in a polynomial
Pakianathan, Jonathan, Yalcin, Ergun
core +10 more sources
Unramified Quadratic Extensions of a Quadratic Field [PDF]
Rocky Mountain Journal of Mathematics, 1995 The authors determine all quartic number fields \(L/\mathbb{Q}\) possessing a quadratic subfield \(\mathbb{Q}\subset K\subset L\) such that \(L/K\) is unramified at all finite primes. They do this by an explicit calculation of the generators and make no use of Hilbert's theory.
Blair K. Spearman, Kenneth S. Williams
openalex +3 more sources
Extensions of dissipative operators with closable imaginary part [PDF]
Opuscula Mathematica, 2021 Given a dissipative operator \(A\) on a complex Hilbert space \(\mathcal{H}\) such that the quadratic form \(f \mapsto \text{Im}\langle f, Af \rangle\) is closable, we give a necessary and sufficient condition for an extension of \(A\) to still be ...
Christoph Fischbacher
doaj +1 more source
Explicitly solvable systems of two autonomous first-order Ordinary Differential Equations with homogeneous quadratic right-hand sides [PDF]
Open Communications in Nonlinear Mathematical Physics, 2021 After tersely reviewing the various meanings that can be given to the property of a system of nonlinear ODEs to be solvable, we identify a special case of the system of two first-order ODEs with homogeneous quadratic right-hand sides which is explicitly ...
Francesco Calogero, Farrin Payandeh
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Existence of Split Property in Quaternion Algebra Over Composite of Quadratic Fields
Cauchy: Jurnal Matematika Murni dan Aplikasi, 2023 Quaternions are extensions of complex numbers that are four-dimensional objects. Quaternion consists of one real number and three complex numbers, commonly denoted by the standard vectors and .
Muhammad Faldiyan +2 more
doaj +1 more source
Coordination of Home Appliances for Demand Response: An Improved Optimization Model and Approach
IEEE Access, 2021 Home appliances constitute an interesting source of flexibility for demand response programs. However, their control and coordination are challenging, since typically a high number of such appliances has to be aggregated in order to provide a sufficient ...
Steffen Limmer +3 more
doaj +1 more source
Parallel machine arithmetic for recurrent number systems in non-quadratic fields [PDF]
Компьютерная оптика, 2020 The paper proposes a new method of synthesis of computer arithmetic systems for "error-free" parallel calculations. The difference between the proposed approach and calculations in traditional systems of Residue Number Systems for the direct sum of ...
Vladimir Chernov
doaj +1 more source