M -> ann(x) i can find the grobner basis of kernel of ann(x) and need the final step to recover this basis to ideal as i know, eliminate is not for all cases, what is the general …

Hello, Could you help me with a reference to elementary properties of Groebner bases in rings of formal power series over a field? I am especially interested in generic initial i …

my goal is find groebner basis from data and then reverse reduce to find a monomial find groebner basis from numeric data do reverse reduce exist? any similar idea 3 how to fin …

below are maple code 3*rho1 - 2*rho2 + rho3 - rho4 = -1 4*rho1 + rho2 - rho3 = 5 original without cost function: with(Groebner): K := {y1-(x1^3)(x2^4),y2-(x2^(1+2))(w^ …

Is there an easy way to determine whether a set of elements in a field generates the whole field or only a subfield? Specifically, I have a subfield of $k(x,y)$ described in terms …

Let $A=\mathbf{Q}[x_1,\ldots,x_n]$ be the polynomial ring in $n$ variables over the rational numbers. Let $B=\mathbf{Q}[f_1,\ldots,f_r]$ and $C=\mathbf{Q}[g_1,\ldots,g_s]$ be two f …

Gröbner bases are usually considered in the ring of polynomials over a field. However, there are useful definitions and algorithms for Gröbner bases over other coefficient rings; s …

An ordering of monomials in the free associative algebra $k\langle x_1,\ldots,x_n\rangle$ is called a monomial ordering (EDIT: it seems that an equally common term used in this con …

Let $A$ and $B$ be two polynomials in $\mathbf Z[X]$ which generate $\mathbf Z[X]$, that is assume that there exist polynomials $U$ and $V$ in $\mathbf Z[X]$ such that $$ A \cdot …

Given a system of multivariate, polynomial equations, is there a way to determine if it has a solution in a given field (for instance the set of all reals). I don't care what the s …

This question comes from the explicit construction of a smooth projective model of a hyperelliptic curve. Nevertheless it is fully elementary and, to me, more interesting than hype …

Let $k$ be a commutative ring with $1$. Let $L$ be a $k$-Lie algebra, which is not necessarily free as a $k$-module. Let $S\left(L\right)$ denote the symmetric algebra of $L$ (over …

Hi all, I have a system of 6th-order polynomial equations in 4 variables $q_1, q_2, q_3, q_4$ (i.e. polynomials with all the terms such as $q_1^6, q_2^6, q_2^4 q_3^2$): $P_k(q_1, …

Are there any articles/books/examples where a non-standard monomial order is used? What are the applications of these monomial orders? In particular, uses in groebner bases and var …

Suppose we have a finite set of generators for an ideal $I \subset R := \Bbbk[x_1,\dotsc, x_n]$, where $\Bbbk$ is a field. If we choose a monomial ordering, then Buchberger's algo …