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^*

^*Corresponding author for this work

Institute for Symbolic Artificial Intelligence

Research output: Chapter in Book/Report/Conference proceeding › Conference proceedings › peer-review

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.

Original language	English
Title of host publication	Computer Algebra in Scientific Computing
Subtitle of host publication	27th International Workshop, CASC 2025, Dubai, United Arab Emirates, November 24–28, 2025, Proceedings
Editors	François Boulier, Chenqi Mou, Timur M. Sadykov, Evgenii V. Vorozhtsov
Pages	79-97
Number of pages	19
Edition	1
DOIs	https://doi.org/10.1007/978-3-032-09645-6_5
Publication status	Published - 2026

Publication series

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

Fields of science

101013 Mathematical logic
102031 Theoretical computer science
603109 Logic
102011 Formal languages
102022 Software development
102001 Artificial intelligence
102030 Semantic technologies
102 Computer Sciences

JKU Focus areas

Digital Transformation

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

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

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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 (Eds.), Computer Algebra in Scientific Computing: 27th International Workshop, CASC 2025, Dubai, United Arab Emirates, November 24–28, 2025, Proceedings (1 ed., pp. 79-97). (Lecture Notes in Computer Science; Vol. 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. editor / François Boulier ; Chenqi Mou ; Timur M. Sadykov ; Evgenii V. Vorozhtsov. 1. ed. 2026. pp. 79-97 (Lecture Notes in Computer Science).

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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",

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Heisinger, M & Hofstadler, C 2026, f4ncgb: High Performance Gröbner Basis Computations in Free Algebras. in F Boulier, C Mou, TM Sadykov & EV Vorozhtsov (eds), Computer Algebra in Scientific Computing: 27th International Workshop, CASC 2025, Dubai, United Arab Emirates, November 24–28, 2025, Proceedings. 1 edn, Lecture Notes in Computer Science, vol. 16235 LNCS, pp. 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. ed. / François Boulier; Chenqi Mou; Timur M. Sadykov; Evgenii V. Vorozhtsov. 1. ed. 2026. p. 79-97 (Lecture Notes in Computer Science; Vol. 16235 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference proceedings › peer-review

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AU - Hofstadler, Clemens

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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.

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Heisinger M , Hofstadler C. f4ncgb: High Performance Gröbner Basis Computations in Free Algebras. In Boulier F, Mou C, Sadykov TM, Vorozhtsov EV, editors, Computer Algebra in Scientific Computing: 27th International Workshop, CASC 2025, Dubai, United Arab Emirates, November 24–28, 2025, Proceedings. 1 ed. 2026. p. 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

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f4ncgb: High Performance Gröbner Basis Computations in Free Algebras

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