3
votes
0answers
118 views

Bound for the height of equations defining the singular locus of a variety

Fix positive integers $m, n, d$. In what follows, the height of an algebraic number will mean the absolute multiplicative height. Let $V \subset \bar{\mathbb{Q}}^n$ be an affine algebraic variety ...
0
votes
1answer
135 views

Computing toric ideals via saturation and Groebner bases of toric ideals

About a month ago I asked this question on math.stackexchange and unfortunately there was no response. Perhaps someone here knows the answer. Let $A \in \mathbb{Z}^{m \times n}$ be a matrix of full ...
2
votes
1answer
868 views

Existence of a real-valued solution to system of multivariate polynomial equations

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 solution is, I just ...
2
votes
2answers
439 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. ...
2
votes
2answers
1k 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 $q_1^6, q_2^6, q_2^4 q_3^2$): $P_k(q_1, q_2, q_3, q_4) = 0$ ...
4
votes
4answers
350 views

Lower bounds on the degrees of representatives of $u^n$ as $n \to \infty$

Let $k$ be an algebraically closed field and $A$ a finitely generated $k$-algebra, together with a specified surjective morphism $\phi \colon k[x_1, \dotsc, x_n] \to A$. For $f \in A$, define ...
1
vote
1answer
255 views

Any implemented algorithm to compute the closure of an affine variety in a product of projective spaces?

Let $I$ be an ideal of $k[x_1, \ldots, x_m, y_1, \ldots, y_n]$, $k$ being a field. Does any of the computer algebra systems implement any algorithm to calculate the generators of the ...