Results 61 to 70 of about 10,835,395 (273)
Journal of AlgebraIn this paper, we propose a new algebraic winding number and prove that it computes the number of complex roots of a polynomial in a rectangle, including roots on edges or vertices with appropriate counting. The definition makes sense for the algebraic closure C = R[i] of a real closed field R, and the root counting result also holds in this case.
Roy, Marie-Françoise, Perrucci, Daniel
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AIP Advances, 2021 An improved peak-selection algorithm is proposed for mesh deformation. With the use of the newly derived block-based recurrence Cholesky (BRC) decomposition scheme, the computational complexity for solving the linear algebraic system in the data reducing
Jing Liu +4 more
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Analytic curves in algebraic varieties over number fields
, 2007 We establish algebraicity criteria for formal germs of curves in algebraic varieties over number fields and apply them to derive a rationality criterion for formal germs of functions, which extends the classical rationality theorems of Borel-Dwork and P\'
A Franchetta +41 more
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Constructions of Dense Lattices of Full Diversity
Trends in Computational and Applied Mathematics, 2020 A lattice construction using Z-submodules of rings of integers of number fields is presented. The construction yields rotated versions of the laminated lattices A_n for n = 2,3,4,5,6, which are the densest lattices in their respective dimensions.
A. A. Andrade +3 more
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Analysis of Students’ Misconceptions on Solving Algebraic Contextual Problem
Risenologi, 2021 Students misconceptions in solving contextual algebraic problems is still often found in this educational world. This study aims to describe the forms of student’s misconceptions in solving algebraic contextual problems and explain the causes of these ...
Faoza Saaroh +2 more
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Ghost Numbers of Group Algebras II [PDF]
Algebras and Representation Theory, 2014 28 pages; v2 improves introduction and has many other minor changes throughout.
J. Daniel Christensen, Gaohong Wang
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Local topological algebraicity with algebraic coefficients of analytic sets or functions [PDF]
Alg. Number Th. 12 (2018) 1215-1231, 2017 We prove that any complex or real analytic set or function germ is topologically equivalent to a germ defined by polynomial equations whose coefficients are algebraic numbers.
arxiv +1 more source
Computing the First Betti Numberand Describing the Connected Components of Semi-algebraic Sets [PDF]
, 2005 In this paper we describe a singly exponential algorithm for computing the first Betti number of a given semi-algebraic set. Singly exponential algorithms for computing the zero-th Betti number, and the Euler-Poincar\'e characteristic, were known before.
Basu, Saugata +2 more
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On two notions of complexity of algebraic numbers
, 2007 we derive new, improved lower bounds for the block complexity of an irrational algebraic number and for the number of digit changes in the b-ary expansion of an irrational algebraic number.
Bugeaud, Yann, Evertse, Jan-Hendrik
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Factoring multivariate polynomials over algebraic number fields in MACSYMA
SIGS, 1975 The algorithm for factoring polynomials over the integers by Wang and Rothschild is generalized to an algorithm for the irreducible factorization of multivariate polynomials over any given algebraic number field.
Paul S. Wang
semanticscholar +1 more source