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geometry > algebraic geometry > Gröbner basis
algebra > commutative algebra > commutative ring > Gröbner basis
... > algebra > abstract algebra > algebraic structure > ring theory > ring > commutative ring > Gröbner basis
mathematical analysis > combinatorics > algebraic combinatorics > Gröbner basis
algebra > combinatorics > algebraic combinatorics > Gröbner basis

Preferred term

Gröbner basis  

Definition

  • In mathematics, and more specifically in computer algebra, computational algebraic geometry, and computational commutative algebra, a Gröbner basis is a particular kind of generating set of an ideal in a polynomial ring K[x1, ..., xn] over a field K. A Gröbner basis 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. Gröbner basis computation is one of the main practical tools for solving systems of polynomial equations and computing the images of algebraic varieties under projections or rational maps
    (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Gr%C3%B6bner_basis)

Broader concept

Entry terms

  • standard base

In other languages

URI

http://data.loterre.fr/ark:/67375/PSR-Q649939G-N

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RDF/XML TURTLE JSON-LD Created 8/18/23, last modified 8/18/23