Questions on the use of Gröbner basis techniques in Mathematica.

learn more… | top users | synonyms

9
votes
1answer
385 views

Gröbner basis on a particular set of equations

This question is very similar in gist to equation solving with GroebnerBasis, but hopefully when I say that I make the system a little larger I mean little. I have ...
7
votes
1answer
167 views

GroebnerBasis without specifying variables

All the examples in the Mathematica documentation specify that the syntax for the GroebnerBasis command is ...
6
votes
2answers
133 views

Finding common roots of a specific system of polynomials

Some of my colleges are interested in finding common zeros of the following four polynomials: ...
6
votes
1answer
251 views

How to express the original ideal elements in the Groebner basis?

Suppose I call GroebnerBasis[{f1, f2, ...}, {x1,x2, ...}] The output is a list {g1,g2,...} For each $g_j$, there should be ...
5
votes
2answers
316 views

Equation solving with GroebnerBasis

I have a system of quadratic equations defined below ...
4
votes
2answers
137 views

Dimension of an algebraic variety

I would like to compute, using Groebner bases, the dimension of the variety defined by a set of polynomials in several variables. In the wikipedia page the method is described, and an implementation ...
1
vote
0answers
74 views

Multivariate resultant in Mathematica?

Is there any command in Mathematica 7 which can compute the (McCaulay) resultant of a parametric system of multivariate polynomial equations? In fact, it would be great if there is also a way to ...
0
votes
0answers
65 views

Finding relations between polynomials

Suppose I have a multivariate polynomial ring $A=\mathbb{R}[x_1,\ldots,x_n]$ and a set of $S=\{p_1, \ldots,p_k\}$ polynomials in $A$. Using this code (which works great) Dimension of an algebraic ...