On the Complexity of Linear Algebra Operations over Algebraic Extension Fields

Authors: Hashemi, Amir^{Aff12, Aff13}, Lichtblau, Daniel^Aff14

Contributors: Goos, Gerhard, Founding Editor^Aff1, Hartmanis, Juris, Founding Editor^Aff2, Bertino, Elisa, Editorial Board Member^Aff3, Gao, Wen, Editorial Board Member^Aff4, Steffen, Bernhard, Editorial Board Member^Aff5, Yung, Moti, Editorial Board Member^Aff6, Boulier, François, editor^Aff7, England, Matthew, editor^Aff8, Kotsireas, Ilias, editor^Aff9, Sadykov, Timur M., editor^Aff10, Vorozhtsov, Evgenii V., editor^Aff11

Source: Computer Algebra in Scientific Computing : 25th International Workshop, CASC 2023, Havana, Cuba, August 28 – September 1, 2023, Proceedings. 14139:141-161

On FGLM Algorithms with Tate Algebras

Authors: Caruso, Xavier, Vaccon, Tristan, Verron, Thibaut

Contributors: Verron, Thibaut, Frédéric Chyzak, George Labahn and Marc Mezzarobba

Source: Proceedings of the 2021 International Symposium on Symbolic and Algebraic Computation. :67-74

Subject Terms: Computer Science - Symbolic Computation, FOS: Computer and information sciences, [INFO.INFO-SC] Computer Science [cs]/Symbolic Computation [cs.SC], p-adic precision, Gröbner bases, FGLM algorithm, 0102 computer and information sciences, Symbolic Computation (cs.SC), 0101 mathematics, Tate algebra, 01 natural sciences, Algorithms

File Description: application/pdf

Access URL: https://hal.archives-ouvertes.fr/hal-03133590/file/tate_fglm.pdf
http://arxiv.org/abs/2102.05324
https://hal.science/hal-03133590v1
https://hal.science/hal-03133590v1/document
https://doi.org/10.1145/3452143.3465521
https://dl.acm.org/doi/pdf/10.1145/3452143.3465521
https://dblp.uni-trier.de/db/journals/corr/corr2102.html#abs-2102-05324
https://hal.archives-ouvertes.fr/hal-03133590/document
https://doi.org/10.1145/3452143.3465521

On FGLM algorithms with tropical Grbner bases

Authors: Ishihara, Yuki, Vaccon, Tristan, Yokoyama, Kazuhiro

Source: Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation. :257-264

Availability: http://dl.acm.org/doi/10.1145/3373207.3404037

In-depth comparison of the Berlekamp–Massey–Sakata and the Scalar-FGLM algorithms: The adaptive variants

Authors: Berthomieu, Jérémy, Faugère, Jean-Charles

Contributors: Berthomieu, Jérémy

Source: Journal of Symbolic Computation. 101:270-303

Subject Terms: Computer Science - Symbolic Computation, FOS: Computer and information sciences, [INFO.INFO-SC] Computer Science [cs]/Symbolic Computation [cs.SC], The Scalar-FGLM algorithm, 02 engineering and technology, Symbolic Computation (cs.SC), The BMS algorithm, 01 natural sciences, Gröbner basis computation, Multidimensional linear recurrent sequence, Algorithms comparison, 0202 electrical engineering, electronic engineering, information engineering, 0101 mathematics, Gröbner basis

File Description: application/pdf

Access URL: https://www.sciencedirect.com/science/article/am/pii/S0747717119300963
http://arxiv.org/abs/1709.07168
http://arxiv.org/abs/1806.00978
http://www.sciencedirect.com/science/article/pii/S0747717119300963
https://hal.inria.fr/hal-01516708/document
https://www.sciencedirect.com/science/article/pii/S0747717119300963
https://www.archives-ouvertes.fr/hal-01516708v1
https://ui.adsabs.harvard.edu/abs/2018arXiv180600978B/abstract
https://dblp.uni-trier.de/db/journals/corr/corr1806.html#abs-1806-00978
https://inria.hal.science/hal-01805478v3
https://doi.org/10.1016/j.jsc.2019.09.001
https://inria.hal.science/hal-01805478v3/document

Parametric FGLM algorithm

Authors: Dehghani Darmian, Mahdi ^a, Hashemi, Amir ^{b, c}

Source: In Journal of Symbolic Computation September-October 2017 82:38-56

Guessing Linear Recurrence Relations of Sequence Tuplesand P-recursive Sequences with Linear Algebra

Authors: Berthomieu, Jérémy, Faugère, Jean-Charles

Contributors: Berthomieu, Jérémy

Source: Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation. :95-102

Subject Terms: P-recursive sequences, [INFO.INFO-SC] Computer Science [cs]/Symbolic Computation [cs.SC], FGLM algorithm, Gröbner bases, 0102 computer and information sciences, 0101 mathematics, 16. Peace & justice, 01 natural sciences

File Description: application/pdf

Access URL: https://hal.inria.fr/hal-01314266/file/main_HAL.pdf
https://dl.acm.org/doi/10.1145/2930889.2930926
https://hal.inria.fr/hal-01314266/document
https://doi.org/10.1145/2930889.2930926
https://hal.archives-ouvertes.fr/hal-01314266
https://doi.acm.org/10.1145/2930889.2930926
https://dl.acm.org/citation.cfm?id=2930926

Linear algebra for computing Gröbner bases of linear recursive multidimensional sequences

Authors: Berthomieu, Jérémy ¹, Boyer, Brice, Faugère, Jean-Charles

Source: In Journal of Symbolic Computation November-December 2017 83:36-67

Linear Algebra for Computing Gröbner Bases of Linear Recursive Multidimensional Sequences

Authors: Berthomieu, Jérémy, Boyer, Brice, Faugère, Jean-Charles

Contributors: Berthomieu, Jérémy

Source: Proceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation. :61-68

Subject Terms: Gröbner basis computation, Berlekamp - Massey - Sakata algorithm, 13. Climate action, [INFO.INFO-SC] Computer Science [cs]/Symbolic Computation [cs.SC], multidimensional linear recursive sequence, FGLM algorithm, BMS and FGLM algorithms, $0$-dimensional ideal, multidimensional linear recurrent sequence, 0101 mathematics, 01 natural sciences

File Description: application/pdf

Access URL: https://hal.inria.fr/hal-01237861/file/BMS-HAL.pdf
https://inria.hal.science/hal-01237861v1/document
https://inria.hal.science/hal-01237861v1
https://doi.org/10.1145/2755996.2756673
https://inria.hal.science/hal-01253934v3
https://doi.org/10.1016/j.jsc.2016.11.005
https://inria.hal.science/hal-01253934v3/document
https://www.infona.pl/resource/bwmeta1.element.elsevier-cfdcd9e5-569f-32bb-8906-e9f6c9667ff1
https://doi.org/10.1016/j.jsc.2016.11.005
https://dblp.uni-trier.de/db/journals/jsc/jsc83.html#BerthomieuBF17
https://hal.inria.fr/hal-01253934
http://www.sciencedirect.com/science/article/pii/S0747717116301249
https://www.sciencedirect.com/science/article/pii/S0747717116301249

Fast algorithm for change of ordering of zero-dimensional Gröbner bases with sparse multiplication matrices

Authors: Faugère, Jean-Charles, Mou, Chenqi

Source: Proceedings of the 36th international symposium on Symbolic and algebraic computation. :115-122

Availability: http://dl.acm.org/doi/10.1145/1993886.1993908

Gröbner Bases over Commutative Rings and Applications to Coding Theory

Authors: Byrne, Eimear^Aff6, Mora, Teo^Aff7

Contributors: Sala, Massimiliano, editor^Aff1, Sakata, Shojiro, editor^Aff2, Mora, Teo, editor^Aff3, Traverso, Carlo, editor^Aff4, Perret, Ludovic, editor^Aff5

Source: Gröbner Bases, Coding, and Cryptography. :239-261

Efficient Forney functions for decoding AG codes

Authors: Douglas A. Leonard

Source: IEEE Transactions on Information Theory. 45:260-265

Subject Terms: Decoding, Forney formula, 0202 electrical engineering, electronic engineering, information engineering, FGLM algorithm, 02 engineering and technology, 0101 mathematics, algebraic geometric codes, 01 natural sciences, Geometric methods (including applications of algebraic geometry) applied to coding theory

File Description: application/xml

Access URL: https://zbmath.org/1365186
https://doi.org/10.1109/18.746805
http://dblp.uni-trier.de/db/journals/tit/tit45.html#Leonard99
https://ieeexplore.ieee.org/document/746805/
http://ieeexplore.ieee.org/document/746805/
https://dblp.uni-trier.de/db/journals/tit/tit45.html#Leonard99

In-depth comparison of the Berlekamp – Massey – Sakata and the Scalar-FGLM algorithms: the non adaptive variants

Authors: Berthomieu, Jérémy, Faugère, Jean-Charles

Contributors: Polynomial Systems (PolSys), Laboratoire d'Informatique de Paris 6 (LIP6), Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)-Centre Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Source: https://inria.hal.science/hal-01516708 ; 2017.

Subject Terms: the Scalar-FGLM algorithm, The BMS algorithm, Gröbner basis computation, multidimensional linear recurrent sequence, algorithms comparison, [INFO.INFO-SC]Computer Science [cs]/Symbolic Computation [cs.SC]

Relation: info:eu-repo/semantics/altIdentifier/arxiv/1709.07168; ARXIV: 1709.07168

Availability: https://inria.hal.science/hal-01516708
https://inria.hal.science/hal-01516708v2/document
https://inria.hal.science/hal-01516708v2/file/main_part1.pdf

On the p-adic stability of the FGLM algorithm

Authors: Renault, Guénaël, Vaccon, Tristan

Contributors: Polynomial Systems (PolSys), Laboratoire d'Informatique de Paris 6 (LIP6), Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)-Centre Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Rikkyo University Tokyo, Université européenne de Bretagne, Ecole doctorale Matisse, Japanese Society for the Promotion of Science, ANR-12-BS01-0010,PEACE,Espaces de paramètres pour une arithmétique efficace et une évaluation de la sécurité des courbes(2012)

Source: https://hal.science/hal-01266071 ; 2016.

Subject Terms: p-adic precision, Gröbner bases, FGLM algorithm, p-adic algorithm, Smith Normal Form, [INFO.INFO-SC]Computer Science [cs]/Symbolic Computation [cs.SC], [MATH.MATH-AC]Mathematics [math]/Commutative Algebra [math.AC]

Relation: info:eu-repo/semantics/altIdentifier/arxiv/1602.00848; ARXIV: 1602.00848

Availability: https://hal.science/hal-01266071
https://hal.science/hal-01266071v1/document
https://hal.science/hal-01266071v1/file/fglmp.pdf

Solving a Multivariable Congruence By Change of Term Order

Authors: Patrick Fitzpatrick

Contributors: The Pennsylvania State University CiteSeerX Archives

Source: http://euclid.ucc.ie/pages/staff/fitzpatrick/Papers/cb.ps.

Subject Terms: Grobner basis, multivariable congruence, FGLM algorithm, Euclidean algorithm, Berlekamp-Massey algorithm

File Description: application/postscript

Relation: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.20.2565; http://euclid.ucc.ie/pages/staff/fitzpatrick/Papers/cb.ps

Availability: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.20.2565
http://euclid.ucc.ie/pages/staff/fitzpatrick/Papers/cb.ps

Solving a Multivariable Congruence By Change of Term Order

Authors: Patrick Fitzpatrick

Contributors: The Pennsylvania State University CiteSeerX Archives

Source: http://ogham.ucc.ie/~fitzpat/papers/cb.ps.

Subject Terms: Grobner basis, multivariable congruence, FGLM algorithm, Euclidean algorithm, Berlekamp-Massey algorithm

File Description: application/postscript

Relation: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.55.3076; http://ogham.ucc.ie/~fitzpat/papers/cb.ps

Availability: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.55.3076
http://ogham.ucc.ie/~fitzpat/papers/cb.ps

最尤復号に対する池上楫アルゴリズムの計算量を減らすための試み ; 最尤復号に対する池上・楫アルゴリズムの計算量を減らすための試み ; サイユウ フクゴウ ニタイスル イケガミ・カジ アルゴリズム ノ ケイサンリョウ オ ヘラス タメノ ココロミ ; An attempt to reduce the computational complexity in the Ikegami-Kaji algorithm for maximum likelihood decoding

Authors: 辻, 雄太, 19362, ツジ, ユウタ, 9000240183867, Tsuji, Yuta, 吉水, 敏郎, 19363, ヨシミズ, トシロウ, 9000240183868, Yoshimizu, Toshirou, 渡辺, 扇之介, ワタナベ, センノスケ, 1000080735316, Watanabe, Sennosuke, 80735316, 渡邊, 芳英, 15621, ワタナベ, ヨシヒデ, 1000050127742, Watanabe, Yoshihide, 50127742, DA13048779

Subject Terms: 411.8, グレブナー基底, 最尤復号, 池上・楫アルゴリズム, FGLMアルゴリズム, Gröbner basis, maximum likelihood decoding, Ikegami-Kaji Algorithm, FGLM Algorithm

File Description: application/pdf

Relation: 掲載刊行物所蔵情報へのリンク ／ Link to Contents; https://doors.doshisha.ac.jp/opac/opac_link/bibid/SB00960326/?lang=0; 同志社大学理工学研究報告; 54; 171; 177; The Science and Engineering Review of Doshisha University; AN00165868; https://doshisha.repo.nii.ac.jp/record/22424/files/023054020010.pdf; https://doi.org/10.14988/pa.2017.0000013295; https://doshisha.repo.nii.ac.jp/records/22424

Availability: https://doshisha.repo.nii.ac.jp/record/22424/files/023054020010.pdf
https://doi.org/10.14988/pa.2017.0000013295
https://doshisha.repo.nii.ac.jp/records/22424

Additional Titles: An attempt to reduce the computational complexity in the Ikegami-Kaji algorithm for maximum likelihood decoding

Authors: Tsuji, Yuta, Yoshimizu, Toshirou, 80735316, Watanabe, Sennosuke, 50127742, DA13048779, Watanabe, Yoshihide

Index Terms: 411.8, Gröbner basis, maximum likelihood decoding, Ikegami-Kaji Algorithm, FGLM Algorithm, Departmental Bulletin Paper., VoR.

URL: https://doi.org/10.14988/pa.2017.0000013295
https://doshisha.repo.nii.ac.jp/records/22424
https://doors.doshisha.ac.jp/opac/opac_link/bibid/SB00960326/?lang=0
https://doshisha.repo.nii.ac.jp/record/22424/files/023054020010.pdf