.. _sphx_glr_api_gallery_abstract_algebra_groebner:

Gröbner bases
---------------

Multivariate division and Buchberger's algorithm.


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    <div class="sphx-glr-thumbcontainer" tooltip="Gaussian elimination solves linear systems by making them triangular. Buchberger&#x27;s 1965 thesis did the same for systems of polynomial equations: complete the generators to a Gröbner basis, adding the remainder of every S-polynomial (a combination in which two leading terms cancel) until all of them reduce to zero. With a lexicographic order the basis is triangular: its last element involves only the last variable, so the system is solved by one-variable root finding and back substitution.">

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  :doc:`/api/gallery/abstract_algebra/groebner/plot_01_buchberger_groebner_basis`

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   /api/gallery/abstract_algebra/groebner/plot_01_buchberger_groebner_basis