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Results tagged with groebner-bases
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user 26700
12
votes
1
answer
2k
views
Ways to show a system of polynomial equations has no solution
I came across the following system of polynomial equations on $X_1,\dots,X_{m-2}$:
$$
\begin{cases}
2X_{2s}+\sum\limits_{t=1}^{2s-1}(-1)^tX_tX_{2s-t}=0,\quad s=1,\dots,\frac{m}{2}-1,\\
X_sX_{m-s}+(-1) …
- 767
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 …