# Questions tagged [groebner-bases]

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### Memory usage of Gröbner basis computation

I've been calculating some Gröbner bases in preparation for finding non-commutative Hilbert series (and, once I recreate that, characters of group actions). Specifically, I've been using the ...
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### $\mathbb Z$-torsion for some quadratically presented Lie rings

$\newcommand{\Z}{\mathbb{Z}}$ I asked this question on MSE but no answer so far, so I'm also asking it here. Let $L$ be a Lie ring (a Lie algebra over $\Z$) with generators $x_1,\dots,x_n$ and ...
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### Geometric significance of Anick's resolution

Given an augmented graded associative $K$ -algebra $A$, we can construct a free resolution of $K$ given by $K_A$ modules which gives nice combinatorial informations about the homology classes of the ...
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### Size of the Groebner basis and change of coordinates

Given an ideal $I$ of $k[x,y]$, the size of the Groebner basis depends on the monomial ordering. For example, if $$I = \langle x^3y^4 , x^2 + y^2 \rangle,$$ then the Groebner basis with the ...
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### Automatic proof in Euclidean Geometry using Theory of Groebner Bases

I've done the same question in math.stackexchange here "https://math.stackexchange.com/questions/1938261/automatic-proof-in-euclidean-geometry-using-theory-of-groebner-bases?noredirect=1#...
Let $k$ be a field and let $R=k[X_1,...,X_n]$ be a polynomial ring. Let $F \subset R$ be a finite subset generating a radical ideal $I$ with precisely $e$ solutions over an algebraic closure of $k$. ...