: Mathématiques: Gröbner basis

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algebra > commutative algebra > commutative ring > Gröbner basis

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mathematical analysis > combinatorics > algebraic combinatorics > Gröbner basis

algebra > combinatorics > algebraic combinatorics > Gröbner basis

Gröbner basis

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 $K [x 1, ..., x n]$ 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)

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