Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Suppose that we have a set of polynomials $f_1, ..., f_m \in C = k[x_1, ..., x_n]$ where $k$ is an algebraically closed field, and let $V$ denote the set on which they all simultaneously vanish. Define $I(V)$ to be the ideal of polynomials in $C$ which vanish on all of $V$.

In general, $I(V) = \text{rad}(f_1, ..., f_m)$ by Hilbert's nullstellensatz, and it is finitely generated by the Hilbert's basis theorem, but I was wondering is there a good way to find a set of generators for $I(V)$? Essentially I am asking, is there a good way to find the generators of the radical of an ideal, given that ideal's generators?

I am interested in this problem, because I am interested in solving systems of polynomial equations in several variables. I was thinking I could use Grobner bases to reduce a system of equations to a simpler system involving less variables, but as far as I'm aware in order to computer a Grobner basis one needs a generating set already. It could be that I am lucky and $I(V) = (f_1, ..., f_m)$, but that seems quite rare to me!

share|improve this question
2  
You might have a look at this book: books.google.com/books/about/… –  Dylan Moreland May 16 '12 at 14:28

1 Answer 1

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.