**1**

vote

**0**answers

26 views

### Elimination theory for variables packaged in a matrix

I am wondering if the elimination theory in computational algebraic geometry can be more efficiently carried out if all variables lies within some given matrices.
For instance, consider the following:
...

**2**

votes

**0**answers

107 views

### Algebraic approach to showing trigonometric equations have no solution

I have very little background in algebra and algebraic geometry, so please bear with me.
I am trying to show that certain systems of trigonometric polynomial equations generally have no solution. One ...

**12**

votes

**0**answers

195 views

### Entropy in elimination theory, or a brief remark by Gelfand-Kapranov-Zelevinsky

In the introduction to their book "Discriminants, resultants and multidimensional determinant", the authors state a very intriguing observation concerning the coefficients of monomials appearing in ...

**10**

votes

**1**answer

1k views

### Why A. Weil considered elimination theory to be eliminated?

It is well known that André Weil declared, in the 1940's, that elimination theory must be eliminated from algebraic geometry. I would like to understand his mathematical reasons to adopt such an ...

**-2**

votes

**1**answer

345 views

### Why is any maximal minor of the Bezoutian matrix divisible by the resultant?

I'm referring to Emiris and Mourrain's paper "Matrices in Elimination Theory," Theorem 3.13. Toward the end of the proof, it says that, just because $(f_1,\ldots,f_{n+1})$ is dense in ${\cal Z}({\rm ...

**1**

vote

**1**answer

265 views

### Calculating the images of varieties under projections

Dear all,
I am interested in the following basic and fundamental question in elimination theory: given a variety in some product space $Z\subseteq X\times Y$, how could I explicitly calculate the ...

**1**

vote

**5**answers

308 views

### Interpolating for particular coefficients

Say $F(X) \in \mathbb{Z}[X]$ is an even degree polynomial of degree $2n$.
One needs to evaluate $F(X)$ at $O(n)$ points to interpolate and get all the coefficients of $F(X)$.
However say I need ...

**2**

votes

**3**answers

1k views

### General hyperplane sections and projection from a point

Let $k$ be an algebraically closed field, and consider some subscheme $X\subset \mathbb{P}_k^n$. Let $x$ be a closed point of $X$, and $H$ a general hyperplane containing $x$. There is a regular map ...

**5**

votes

**1**answer

2k views

### Polynomial with two repeated roots

I have a polynomial of degree 4 $f(t) \in \mathbb{C}[t]$, and I'd like to know when it has two repeated roots, in terms of its coefficients.
Phrased otherwise I'd like to find the equations of the ...