Last Updated
：2025/12/05
Gröbner basis
Proper noun
Japanese Meaning
Gröbner基底とは、計算機理論において、多項式環K[x1, ..., xn]上のイデアルに対して考えられる特定の生成集合のことである。この生成集合を用いると、イデアルおよびそれに関連する代数多様体の次元や有限な場合の零点の数といった重要な性質を容易に導出することができる。
（ plural ）
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(computing theory) 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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Gröbner basis
To solve systems of polynomial equations efficiently, researchers often compute a Gröbner basis of the ideal and then analyze its structure to determine the number of solutions.
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To solve systems of polynomial equations efficiently, researchers often compute a Gröbner basis of the ideal and then analyze its structure to determine the number of solutions.
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