# Questions tagged [groebner-bases]

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59 questions
742 views

### PBW theorem over a Q-algebra, without freeness or flatness

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 $k$), constructed ...
507 views

### Nonstandard monomial orders?

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 variable elimination. (...
2k views

### Numerical solution for a system of multivariate polynomial equations

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 $q_1^6, q_2^6, q_2^4 q_3^2$): $P_k(q_1, q_2, q_3, q_4) = 0$ ...
363 views

### Is the first part of Eisenbud's Proposition 15.15's proof o.k?

In the chapter on Gröbner bases from Eisenbud's "Commutative Algebra" the following statement appears as Proposition 15.15 (page 344): Let $F$ be a free $S$ module with basis and monomial order ...
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### Systems of polynomial equations

Hi all, I'm an engineer assigned to determine some parameters of a manipulator (ie., calibration). It has a number of parameters, but after some manipulations of its dynamic equations, I can have the ...