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GBLA: Gröbner Basis Linear Algebra Package [PDF]
Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation, 2016 This is a system paper about a new GPLv2 open source C library GBLA implementing and improving the idea [8] of Faugère and Lachartre (GB reduction).
Brice Boyer +4 more
semanticscholar +7 more sources
Triangular x-basis decompositions and derandomization of linear algebra algorithms over K[x]
Journal of Symbolic Computation, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Somi Gupta +3 more
semanticscholar +6 more sources
Regions of Linearity, Lusztig Cones, and Canonical Basis Elements for the Quantized Enveloping Algebra of Type A4 [PDF]
Journal of Algebra, 2000 Let U_q be the quantum group associated to a Lie algebra g of rank n. The negative part U^- of U has a canonical basis B with favourable properties, introduced by Kashiwara and Lusztig. The approaches of Kashiwara and Lusztig lead to a set of alternative parametrizations of the canonical basis, one for each reduced expression for the longest word in ...
Carter, Roger, Marsh, Robert
+6 more sources
DUAL PRESENTATION AND LINEAR BASIS OF THE TEMPERLEY-LIEB ALGEBRAS [PDF]
Journal of the Korean Mathematical Society, 2010 The braid group $B_n$ maps homomorphically into the Temperley-Lieb algebra $\TL_n$. It was shown by Zinno that the homomorphic images of simple elements arising from the dual presentation of the braid group $B_n$ form a basis for the vector space underlying the Temperley-Lieb algebra $\TL_n$.
Lee, Eon-Kyung, Lee, Sang Jin
+7 more sources
Recent progress in linear algebra and lattice basis reduction [PDF]
Proceedings of the 36th international symposium on Symbolic and algebraic computation, 2011 A general goal concerning fundamental linear algebra problems is to reduce the complexity estimates to essentially the same as that of multiplying two matrices (plus possibly a cost related to the input and output sizes). Among the bottlenecks one usually finds the questions of designing a recursive approach and mastering the sizes of the ...
Gilles Villard
openaire +3 more sources
Linear forms at a basis of an algebraic number field
Journal of Number Theory, 2012 For a real number \(x\), let us denote \(\|x\|\) the distance between \(x\) and the nearest integer. \textit{Littlewood conjecture} asserts that: \textit{for any real numbers \(\alpha\) and \(\beta\), one has \[ \inf_{q>0} q\|q\alpha\|\|q\beta\|=0, \] where \(q\) runs through the positive integers.} The \textit{dual form} of Littlewood conjecture is : \
Bernard de Mathan
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The Universal Askey-Wilson Algebra [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2011 In 1992 A. Zhedanov introduced the Askey-Wilson algebra AW=AW(3) and used it to describe the Askey-Wilson polynomials. In this paper we introduce a central extension Δ of AW, obtained from AW by reinterpreting certain parameters as central elements in ...
Paul Terwilliger
doaj +6 more sources
On unique parametrization of the linear group GL(4.C) and its subgroups by using the Dirac matrix algebra basis [PDF]
, 2006 23 pages, submitted to Nonlinear Phenomena in Complex ...
Bogush, A. A., Red'kov, V. M.
+5 more sources
Operators for generic effective field theory at any dimension: on-shell amplitude basis construction [PDF]
Journal of High Energy Physics, 2022 We describe a general procedure to construct the independent and complete operator bases for generic Lorentz invariant effective field theories, given any kind of gauge symmetry and field content, up to any mass dimension.
Hao-Lin Li +4 more
doaj +2 more sources
Linear Algebra Provides a Basis for Elasticity without Stress or Strain
Soft, 2015 Linear algebra provides insights into the description of elasticity without stress or strain. Classical descriptions of elasticity usually begin with defining stress and strain and the constitutive equations of the material that relate these to each other.
H. H. Hardy
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