f4ncgb: High Performance Gröbner Basis Computations in Free Algebras

Maximilian Heisinger; Clemens Hofstadler

doi:10.1007/978-3-032-09645-6_5

f4ncgb: High Performance Gröbner Basis Computations in Free Algebras

Maximilian Heisinger
, Clemens Hofstadler^*

^*Korrespondierende/r Autor/-in für diese Arbeit

Institut für Symbolic Artificial Intelligence

Publikation: Beitrag in Buch/Bericht/Konferenzband › Konferenzbeitrag › Begutachtung

Abstract

We present f4ncgb, a new open-source C++ library for Gröbner basis computations in free algebras, which transfers recent advancements in commutative Gröbner basis software to the noncommutative setting. As our experiments show, f4ncgb establishes a new state of the art for noncommutative Gröbner basis computations. We also discuss implementation details and design choices.

Originalsprache	Englisch
Titel	Computer Algebra in Scientific Computing
Untertitel	27th International Workshop, CASC 2025, Dubai, United Arab Emirates, November 24–28, 2025, Proceedings
Herausgeber*innen	François Boulier, Chenqi Mou, Timur M. Sadykov, Evgenii V. Vorozhtsov
Seiten	79-97
Seitenumfang	19
Auflage	1
DOIs	https://doi.org/10.1007/978-3-032-09645-6_5
Publikationsstatus	Veröffentlicht - 2026

Publikationsreihe

Name	Lecture Notes in Computer Science
Band	16235 LNCS
ISSN (Print)	0302-9743
ISSN (elektronisch)	1611-3349

Wissenschaftszweige

101013 Mathematische Logik
102031 Theoretische Informatik
603109 Logik
102011 Formale Sprachen
102022 Softwareentwicklung
102001 Artificial Intelligence
102030 Semantische Technologien
102 Informatik

JKU-Schwerpunkte

Digital Transformation

Zugriff auf Dokument

10.1007/978-3-032-09645-6_5

https://www.springerprofessional.de/f4ncgb-high-performance-groebner-basis-computations-in-free-alge/51653584

Andere Dateien und Links

Verknüpfung zur Publikation in Scopus

f4ncgb: High Performance Gröbner Basis Computations in Free Algebras
Hofstadler, C. (Vortragende*r)
27 Nov. 2025
Aktivität: Vortrag oder Präsentation › Vortrag nach Bewerbung und Auswahl › Science-to-science

Dieses zitieren

Heisinger, M., & Hofstadler, C. (2026). f4ncgb: High Performance Gröbner Basis Computations in Free Algebras. in F. Boulier, C. Mou, T. M. Sadykov, & E. V. Vorozhtsov (Hrsg.), Computer Algebra in Scientific Computing: 27th International Workshop, CASC 2025, Dubai, United Arab Emirates, November 24–28, 2025, Proceedings (1 Aufl., S. 79-97). (Lecture Notes in Computer Science; Band 16235 LNCS). https://doi.org/10.1007/978-3-032-09645-6_5

Heisinger, Maximilian ; Hofstadler, Clemens. / f4ncgb: High Performance Gröbner Basis Computations in Free Algebras. Computer Algebra in Scientific Computing: 27th International Workshop, CASC 2025, Dubai, United Arab Emirates, November 24–28, 2025, Proceedings. Hrsg. / François Boulier ; Chenqi Mou ; Timur M. Sadykov ; Evgenii V. Vorozhtsov. 1. Aufl. 2026. S. 79-97 (Lecture Notes in Computer Science).

@inproceedings{44804dd3383e450aa6c8ad5dbbbad9a1,

title = "f4ncgb: High Performance Gr{\"o}bner Basis Computations in Free Algebras",

abstract = "We present f4ncgb, a new open-source C++ library for Gr{\"o}bner basis computations in free algebras, which transfers recent advancements in commutative Gr{\"o}bner basis software to the noncommutative setting. As our experiments show, f4ncgb establishes a new state of the art for noncommutative Gr{\"o}bner basis computations. We also discuss implementation details and design choices.",

author = "Maximilian Heisinger and Clemens Hofstadler",

year = "2026",

doi = "10.1007/978-3-032-09645-6\_5",

language = "English",

isbn = "9783032096449",

series = "Lecture Notes in Computer Science",

pages = "79--97",

editor = "Fran{\c c}ois Boulier and Chenqi Mou and Sadykov, \{Timur M.\} and Vorozhtsov, \{Evgenii V.\}",

booktitle = "Computer Algebra in Scientific Computing",

edition = "1",

}

Heisinger, M & Hofstadler, C 2026, f4ncgb: High Performance Gröbner Basis Computations in Free Algebras. in F Boulier, C Mou, TM Sadykov & EV Vorozhtsov (Hrsg.), Computer Algebra in Scientific Computing: 27th International Workshop, CASC 2025, Dubai, United Arab Emirates, November 24–28, 2025, Proceedings. 1 Aufl., Lecture Notes in Computer Science, Bd. 16235 LNCS, S. 79-97. https://doi.org/10.1007/978-3-032-09645-6_5

f4ncgb: High Performance Gröbner Basis Computations in Free Algebras. / Heisinger, Maximilian ; Hofstadler, Clemens.
Computer Algebra in Scientific Computing: 27th International Workshop, CASC 2025, Dubai, United Arab Emirates, November 24–28, 2025, Proceedings. Hrsg. / François Boulier; Chenqi Mou; Timur M. Sadykov; Evgenii V. Vorozhtsov. 1. Aufl. 2026. S. 79-97 (Lecture Notes in Computer Science; Band 16235 LNCS).

Publikation: Beitrag in Buch/Bericht/Konferenzband › Konferenzbeitrag › Begutachtung

TY - GEN

T1 - f4ncgb: High Performance Gröbner Basis Computations in Free Algebras

AU - Heisinger, Maximilian

AU - Hofstadler, Clemens

PY - 2026

Y1 - 2026

N2 - We present f4ncgb, a new open-source C++ library for Gröbner basis computations in free algebras, which transfers recent advancements in commutative Gröbner basis software to the noncommutative setting. As our experiments show, f4ncgb establishes a new state of the art for noncommutative Gröbner basis computations. We also discuss implementation details and design choices.

AB - We present f4ncgb, a new open-source C++ library for Gröbner basis computations in free algebras, which transfers recent advancements in commutative Gröbner basis software to the noncommutative setting. As our experiments show, f4ncgb establishes a new state of the art for noncommutative Gröbner basis computations. We also discuss implementation details and design choices.

UR - https://www.scopus.com/pages/publications/105021819864

U2 - 10.1007/978-3-032-09645-6_5

DO - 10.1007/978-3-032-09645-6_5

M3 - Conference proceedings

SN - 9783032096449

T3 - Lecture Notes in Computer Science

SP - 79

EP - 97

BT - Computer Algebra in Scientific Computing

A2 - Boulier, François

A2 - Mou, Chenqi

A2 - Sadykov, Timur M.

A2 - Vorozhtsov, Evgenii V.

ER -

Heisinger M , Hofstadler C. f4ncgb: High Performance Gröbner Basis Computations in Free Algebras. in Boulier F, Mou C, Sadykov TM, Vorozhtsov EV, Hrsg., Computer Algebra in Scientific Computing: 27th International Workshop, CASC 2025, Dubai, United Arab Emirates, November 24–28, 2025, Proceedings. 1 Aufl. 2026. S. 79-97. (Lecture Notes in Computer Science). doi: 10.1007/978-3-032-09645-6_5

f4ncgb: High Performance Gröbner Basis Computations in Free Algebras

Abstract

Publikationsreihe

Wissenschaftszweige

JKU-Schwerpunkte

Zugriff auf Dokument

Andere Dateien und Links

Aktivitäten

f4ncgb: High Performance Gröbner Basis Computations in Free Algebras

Dieses zitieren