Gröbner basis

proper noun

A particular kind of generating set of an ideal in a polynomial ring K[x1, ..,xn] over a field K. It allows many important properties of the ideal and the associated algebraic variety to be deduced easily, such as the dimension and the number of zeros when it is finite.

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Meanings

proper nounGröbner basis (plural Gröbner bases)

plural Gröbner bases

  1. computingA particular kind of generating set of an ideal in a polynomial ring K[x1, ..,xn] over a field K. It allows many important properties of the ideal and the associated algebraic variety to be deduced easily, such as the dimension and the number of zeros when it is finite.

Origin

Introduced in 1965 by Austrian mathematician Bruno Buchberger, who named them after his academic advisor Wolfgang Gröbner.

Full word history & related roots →

Translations

Bulgarian базис на Грьобнер
  • базис на Грьобнер (bazis na Grjobner)generating set of an ideal
Russian базис Грёбнера
  • базис Грёбнера (bazis Grjóbnera)generating set of an ideal
Cite this entry
APA

Gröbner basis. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/Gr%C3%B6bner%20basis

MLA

“Gröbner basis.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Gr%C3%B6bner%20basis. Accessed November 5, 2026.

Chicago

WatkinsX Dictionary, s.v. “Gröbner basis,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/Gr%C3%B6bner%20basis.

Source: Gröbner basis on Wiktionary, CC BY-SA 4.0.