Search Results - non-commutative Gröbner basis algorithms

Nonstandard Analysis, Deformation Quantization and Some Logical Aspects of (Non)Commutative Algebraic Geometry by Kanel-Belov, Alexei, Chilikov, Alexei, Ivanov-Pogodaev, Ilya, Malev, Sergey, Plotkin, Eugeny, Yu, Jie-Tai, Zhang, Wenchao

“…This paper surveys results related to well-known works of B. Plotkin and V. Remeslennikov on the edge of algebra, logic and geometry. We start from a brief…”
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Singularly perturbed control systems using non-commutative computer algebra by Helton, J. W., Kronewitter, F. Dell, McEneaney, W. M., Stankus, Mark

“… Commutative Gröbner basis algorithms are powerful and make up the engines in symbolic algebra packages' Solve commands. Non‐commutative…”
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Feynman integral reduction using Gröbner bases by Barakat, Mohamed, Brüser, Robin, Fieker, Claus, Huber, Tobias, Piclum, Jan

“… by computing the Gröbner basis of the left ideal formed by the IBP relations. We demonstrate this explicitly for several examples…”
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A Gröbner-Shirshov basis over a special type of braid monoids by S. Cevik, Ahmet, G. Karpuz, Eylem, H. Alsulami, Hamed, K. Cetinalp, Esra

“…The aim of this paper is to present a Gröbner-Shirshov basis for a special type of braid monoids, namely the symmetric inverse monoid In, in terms of the dex-leg ordering on the related elements of monoid…”
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Why you cannot even hope to use Gröbner bases in cryptography: an eternal golden braid of failures by Barkee, Boo, Ceria, Michela, Moriarty, Theo, Visconti, Andrea

“… (and consequent uncomputability) of non-commutative Gröbner bases; unfortunately Pritchard’s algorithm for computing (finite) non-commutative…”
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Fraction-free algorithm for the computation of diagonal forms matrices over Ore domains using Gröbner bases by Levandovskyy, Viktor, Schindelar, Kristina

“…” (Levandovskyy and Schindelar, 2011). We present a new fraction-free algorithm for the computation of a diagonal form of a matrix over a certain non-commutative Euclidean domain over a computable field with the help of Gröbner bases…”
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Algorithms for checking rational roots of b-functions and their applications by Levandovskyy, V., Martín-Morales, J.

“… In this paper we propose a family of algorithms called checkRoot for optimized checking whether a given rational number is a root of Bernstein…”
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The graph of a Weyl algebra endomorphism by Lauritzen, Niels, Funch Thomsen, Jesper

“… conjecture. It is also shown how the graph construction leads to a non‐commutative Gröbner basis algorithm for detecting invertibility of an endomorphism for Weyl algebras and computing the inverse over arbitrary fields…”
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Nonstandard analysis, deformation quantization and some logical aspects of (non)commutative algebraic geometry by Kanel-Belov, Alexei, Chilikov, Alexei, Ivanov-Pogodaev, Ilya, Malev, Sergey, Plotkin, Eugeny, Jie-Tai, Yu, Zhang, Wenchao

“…This paper surveys results related to well-known works of B. Plotkin and V. Remeslennikov on the edge of algebra, logic and geometry. We start from a brief…”
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Computing diagonal form and Jacobson normal form of a matrix using Gröbner bases by Levandovskyy, Viktor, Schindelar, Kristina

“…In this paper we present an algorithm for the computation of a diagonal form of a matrix over non-commutative Euclidean domain over a field with the help of Gröbner bases…”
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Constructive D-Module Theory with Singular by Andres, Daniel, Brickenstein, Michael, Levandovskyy, Viktor, Martín-Morales, Jorge, Schönemann, Hans

“…We overview numerous algorithms in computational D -module theory together with the theoretical background as well as the implementation in the computer algebra system Singular…”
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A non-commutative F5 algorithm with an application to the computation of Loewy layers by King, Simon A.

“…We provide a non-commutative version of the F5 algorithm, namely for right-modules over path algebra quotients…”
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A non-commutative F 5 algorithm with an application to the computation of Loewy layers by King, Simon A.

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Gröbner–Shirshov basis for the Braid group in the Birman–Ko–Lee generators by Bokut, L.A.

“…In this paper, we obtain Gröbner–Shirshov (non-commutative Gröbner) bases for braid groups in the Birman–Ko…”
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Bases for projective modules in An( k) by Gago-Vargas, Jesús

“… Let M be a left submodule of a free module. In this paper we give an algorithm to compute the projective dimension of M…”
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Gröbner bases and the number of Latin squares related to autotopisms of order ≤7 by Falcón, R.M., Martín-Morales, J.

“…Latin squares can be seen as multiplication tables of quasigroups, which are, in general, non-commutative and non-associative algebraic structures…”
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Fast Kötter–Nielsen–Høholdt interpolation over skew polynomial rings and its application in coding theory by Bartz, Hannes, Jerkovits, Thomas, Rosenkilde, Johan

“…Skew polynomials are a class of non-commutative polynomials that have several applications in computer science, coding theory and cryptography…”
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Gröbner bases for special linear groups over a finite field by Ward, Meghan

“… In this thesis, we will also develop a computer program that will find the Gröbner basis for an ideal in a non-commutative algebra…”
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Rewrite Rules and Simplification of Matrix Expressions by John J Wavrik

“… The non-commutative variant of the Grobner Basis Algorithm is used to generate rewrite rules…”
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A combinatorial approach to involution and δ-regularity I: involutive bases in polynomial algebras of solvable type by Seiler, Werner M.

“… We study them for a rather general class of polynomial algebras including also non-commutative algebras like those generated by linear differential and difference operators or universal enveloping algebras of (finite-dimensional) Lie algebras…”
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