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Results tagged with polynomials
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user 26700
Questions in which polynomials (single or several variables) play a key role. It is typically important that this tag is combined with other tags; polynomials appear in very different contexts. Please, use at least one of the top-level tags, such as nt.number-theory, co.combinatorics, ac.commutative-algebra, in addition to it. Also, note the more specific tags for some special types of polynomials, e.g., orthogonal-polynomials, symmetric-polynomials.
7
votes
2
answers
864
views
Dimension of a homogeneous polynomial system
Let $m\geq4$ be an even integer, $V\subset\mathbb{C}^{m-1}$ be the solution set of the following polynomial equations:
\begin{cases}
&\sum\limits_{s=1}^{2t-1}z_sz_{2t-s}+\sum\limits_{s=2t+1}^{m-1}z_sz …
9
votes
0
answers
518
views
Getting a bound via polynomial equations
When studying the existence problem of power residue deference sets, I came across the following system of polynomial equations over $\mathbb{C}$,
\begin{cases}
&\sum\limits_{j=0}^{m-1}x_jx_{2k-j}=0,\ …
- 767
12
votes
1
answer
2k
views
Ways to show a system of polynomial equations has no solution
By Groebner basis computation, I verified up to $m=20$ that $1$ is in the ideal generated by the above polynomials in $\mathbb{Q}[X_1,\dots,X_{m-2}]$, whence the system has no solution in $\mathbb{C}^{ …
- 767