# Questions tagged [multivariate-polynomial]

Let $R$ be a ring. A multivariate polynomial $p(x_1,\ldots,x_n)$ over $R$ is a finite sum of powers of the $x_i$s multiplied by coefficients in $R$.

168 questions
Filter by
Sorted by
Tagged with
21 views

### Existence of constrained pairs of elements in $\mathbb{C}[x,y,z]/(x^3,y^3,z^3)$ that multiply to zero

Question: Do there exist a pair of elements $a,b\in \mathbb{C}[x,y,z]/(x^3,y^3,z^3)$, where $a\notin(x,y)\cup(y,z)$ and $b\notin (x,z)\cup (y,z)$ but $ab=0$? For context, I'm trying to show that for a ...
48 views

37 views

### Find a multivariate polynomial over finite field with given zeros (or number of zeros) with an upper bound on its degree

This is a follow-up on: Find a multivariate polynomial over finite field with given zeros (or number of zeros). I am trying to find a polynomial $f \in \mathbb{F}_q[x_1, x_2, \dots, x_m]/(x_i^q-x_i)$ ...
19 views

### Multivariable Function Approximation Review Paper

I am doing some research on function approximation for a general multivariable equation. (i.e., I have a function f that depends on $x_1, x_2, x_3, ..., x_n$. Given many data points of f at multiple ...
72 views

176 views

14 views

### Efficiently applying multinomial theorem to a large sum of terms (multivariate polynomials)

I have searched several StackExchange and StackOverflow questions and answers and have not been able to find a good solution to my problem. Ultimately, I need to be able to efficiently find the sum of ...