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Relevant bibliographies by topics / Base du Gröbner

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Journal articles

Academic literature on the topic 'Base du Gröbner'

Author: Grafiati

Published: 25 May 2024

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Journal articles on the topic "Base du Gröbner"

1

Bokut, L. A., Yuqun Chen, and Zerui Zhang. "Gröbner–Shirshov bases method for Gelfand–Dorfman–Novikov algebras." Journal of Algebra and Its Applications 16, no. 01 (2017): 1750001. http://dx.doi.org/10.1142/s0219498817500013.

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We establish Gröbner–Shirshov base theory for Gelfand–Dorfman–Novikov algebras over a field of characteristic [Formula: see text]. As applications, a PBW type theorem in Shirshov form is given and we provide an algorithm for solving the word problem of Gelfand–Dorfman–Novikov algebras with finite homogeneous relations. We also construct a subalgebra of one generated free Gelfand–Dorfman–Novikov algebra which is not free.

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2

Steiner, Matthias Johann. "Solving Degree Bounds for Iterated Polynomial Systems." IACR Transactions on Symmetric Cryptology 2024, no. 1 (2024): 357–411. http://dx.doi.org/10.46586/tosc.v2024.i1.357-411.

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For Arithmetization-Oriented ciphers and hash functions Gröbner basis attacks are generally considered as the most competitive attack vector. Unfortunately, the complexity of Gröbner basis algorithms is only understood for special cases, and it is needless to say that these cases do not apply to most cryptographic polynomial systems. Therefore, cryptographers have to resort to experiments, extrapolations and hypotheses to assess the security of their designs. One established measure to quantify the complexity of linear algebra-based Gröbner basis algorithms is the so-called solving degree. Cam

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3

Jha, Ranjan, Damien Chablat, and Luc Baron. "Influence of design parameters on the singularities and workspace of a 3-RPS parallel robot." Transactions of the Canadian Society for Mechanical Engineering 42, no. 1 (2018): 30–37. http://dx.doi.org/10.1139/tcsme-2017-0011.

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This paper presents variations in the workspace, singularities, and joint space with respect to design parameter k, which is the ratio of the dimensions of the mobile platform to the dimensions of the base of a 3-RPS parallel manipulator. The influence of the design parameters on parasitic motion, which is important when selecting a manipulator for a desired task, is also studied. The cylindrical algebraic decomposition method and Gröbner-based computations are used to model the workspace and joint space with parallel singularities in 2R1T (two rotational and one translational) and 3T (three t

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4

Yoshida, Hiroshi. "A model for analyzing phenomena in multicellular organisms with multivariable polynomials: Polynomial life." International Journal of Biomathematics 11, no. 01 (2018): 1850007. http://dx.doi.org/10.1142/s1793524518500079.

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Most of life maintains itself through turnover, namely cell proliferation, movement and elimination. Hydra’s cells, for example, disappear continuously from the ends of tentacles, but these cells are replenished by cell proliferation within the body. Inspired by such a biological fact, and together with various operations of polynomials, I here propose polynomial-life model toward analysis of some phenomena in multicellular organisms. Polynomial life consists of multicells that are expressed as multivariable polynomials. A cell is expressed as a term of polynomial, in which point [Formula: see

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5

Gräbe, Hans-Gert, and Franz Pauer. "A remark on Hodge algebras and Gröbner bases." Czechoslovak Mathematical Journal 42, no. 2 (1992): 331–38. http://dx.doi.org/10.21136/cmj.1992.128327.

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6

Bellini, Emanuele, Massimiliano Sala, and Ilaria Simonetti. "Nonlinearity of Boolean Functions: An Algorithmic Approach Based on Multivariate Polynomials." Symmetry 14, no. 2 (2022): 213. http://dx.doi.org/10.3390/sym14020213.

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We review and compare three algebraic methods to compute the nonlinearity of Boolean functions. Two of them are based on Gröbner basis techniques: the first one is defined over the binary field, while the second one over the rationals. The third method improves the second one by avoiding the Gröbner basis computation. We also estimate the complexity of the algorithms, and, in particular, we show that the third method reaches an asymptotic worst-case complexity of O(n2n) operations over the integers, that is, sums and doublings. This way, with a different approach, the same asymptotic complexit

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7

Eder, Christian. "Improving incremental signature-based Gröbner basis algorithms." ACM Communications in Computer Algebra 47, no. 1/2 (2013): 1–13. http://dx.doi.org/10.1145/2503697.2503699.

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8

Eder, Christian, and Jean-Charles Faugère. "A survey on signature-based Gröbner basis computations." ACM Communications in Computer Algebra 49, no. 2 (2015): 61. http://dx.doi.org/10.1145/2815111.2815156.

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9

Francis, Maria, and Thibaut Verron. "A Signature-Based Algorithm for Computing Gröbner Bases over Principal Ideal Domains." Mathematics in Computer Science 14, no. 2 (2019): 515–30. http://dx.doi.org/10.1007/s11786-019-00432-5.

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AbstractSignature-based algorithms have become a standard approach for Gröbner basis computations for polynomial systems over fields, but how to extend these techniques to coefficients in general rings is not yet as well understood. In this paper, we present a proof-of-concept signature-based algorithm for computing Gröbner bases over commutative integral domains. It is adapted from a general version of Möller’s algorithm (J Symb Comput 6(2–3), 345–359, 1988) which considers reductions by multiple polynomials at each step. This algorithm performs reductions with non-decreasing signatures, and

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10

Eder, Christian. "An analysis of inhomogeneous signature-based Gröbner basis computations." Journal of Symbolic Computation 59 (December 2013): 21–35. http://dx.doi.org/10.1016/j.jsc.2013.08.001.

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