All Questions

Let $N=\{1,2,\ldots,n\}$. Suppose we are given $n$ equations, with each equation taking the form $\sum_{A\subseteq N}\left(c_A \prod_{i\in A}x_i \right) = 0$, where each $c_A$ is a real number ...

Let $I = \langle f_1, \ldots f_r \rangle$ be an ideal in $R=k[x_1,\ldots,x_n]$ where $k$ is a field, and put $A = R/I$. (If $I$ is prime then $A$ is the coordinate ring of an irreducible affine ...

There are many results about irreducible polynomials over finite fields: we know a cardinality of all irreducible polynomials with given degree, we know explicit examples of irreducible polynomials, ...

Let $R$ be a quotient of the polynomial ring $\mathbb{C}[x_1,\dots , x_n]$. We fix a $\mathbb{C}^*$ action on $R$ which preserve homogenous components and the multiplication. (The geometric analogue ...

This question must be well known but I cannot find it in the literature. Question: What is the computational complexity of the word problem in a subring of the ring of polynomials in $n\ge 1$ ...