Results 1 to 10 of about 13,850 (156)
The algebraic degree of semidefinite programming [PDF]
Mathematical Programming, 2008 Given a generic semidefinite program, specified by matrices with rational entries, each coordinate of its optimal solution is an algebraic number. We study the degree of the minimal polynomials of these algebraic numbers. Geometrically, this degree counts the critical points attained by a linear functional on a fixed rank locus in a linear space of ...
Jiawang Nie +2 more
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On the Influence of the Algebraic Degree of $F^{-1}$ on the Algebraic Degree of $G \circ F$ [PDF]
IEEE Transactions on Information Theory, 2013 We present a study on the algebraic degree of iterated permutations seen as multivariate polynomials. The main result shows that this degree depends on the algebraic degree of the inverse of the permutation which is iterated. This result is also extended to non-injective balanced vectorial functions where the relevant quantity is the minimal degree of ...
Christina Boura, Anne Canteaut
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Algebraic Degree of Polynomial Optimization [PDF]
SIAM Journal on Optimization, 2009 Consider the polynomial optimization problem whose objective and constraints are all described by multivariate polynomials. Under some genericity assumptions, %% on these polynomials, we prove that the optimality conditions always hold on optimizers, and the coordinates of optimizers are algebraic functions of the coefficients of the input polynomials.
Jiawang Nie, KRISTIAN Ranestad
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ALGEBRAIC DEGREE OF SERIES OF RECIPROCAL ALGEBRAIC INTEGERS
Rocky Mountain Journal of Mathematics, 2023 15 ...
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Degree of the Product of Two Algebraic Numbers One of Which Is of Prime Degree
Mathematics, 2023 Let α and β be two algebraic numbers such that deg(α)=m and deg(β)=p, where p is a prime number not dividing m. This research is focused on the following two objectives: to discover new conditions under which deg(αβ)=mp; to determine the complete list of
Paulius Virbalas
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On the Degree of Product of Two Algebraic Numbers
Mathematics, 2023 A triplet (a,b,c) of positive integers is said to be product-feasible if there exist algebraic numbers α, β and γ of degrees (over Q) a, b and c, respectively, such that αβγ=1.
Lukas Maciulevičius
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Influence of the Linear Layer on the Algebraic Degree in SP-Networks
IACR Transactions on Symmetric Cryptology, 2022 We consider SPN schemes, i.e., schemes whose non-linear layer is defined as the parallel application of t ≥ 1 independent S-Boxes over F2n and whose linear layer is defined by the multiplication with a (n · t) × (n · t) matrix over F2.
Carlos Cid +5 more
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The Bottleneck Degree of Algebraic Varieties [PDF]
SIAM Journal on Applied Algebra and Geometry, 2020 A bottleneck of a smooth algebraic variety $X \subset \mathbb{C}^n$ is a pair of distinct points $(x,y) \in X$ such that the Euclidean normal spaces at $x$ and $y$ contain the line spanned by $x$ and $y$. The narrowness of bottlenecks is a fundamental complexity measure in the algebraic geometry of data. In this paper we study the number of bottlenecks
Sandra Di Rocco +2 more
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Parametrization of Algebraic Points of Low Degrees on the Schaeffer Curve
Journal of Mathematical Sciences and Modelling, 2021 In this paper, we give a parametrization of algebraic points of degree at most $4$ over $\mathbb{Q}$ on the schaeffer curve $\mathcal{C}$ of affine equation : $ y^{2}=x^{5}+1 $. The result extends our previous result which describes in [5] ( Afr.
Moussa Fall
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Education Sciences, 2023 To promote optimal learning in their students, mathematics teachers must be proficient in problem posing, making this skill a cornerstone in teacher training programs.
Nicolás Tizón-Escamilla, María Burgos
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