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Results tagged with groebner-bases
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user 38468
4
votes
Dimension of a homogeneous polynomial system
I don't have a complete solution, but the following may be helpful.
Change variables by $z_i = \sum_j y_j \xi^{ij}$ where $\xi$ is $m$-th primitive root of $1$.
Then the first line equations (I am us …
- 5,186
2
votes
Fast computation of a Groebner basis. What is possible?
Assume for simplicity that your polynomials are homogeneous of degree three.
If you have a complete intersection, it has Hilbert series
$$
(1-t^3)^{18}/(1-t)^{19} = (1+t+t^2)^{18}/(1-t)
$$
It is conc …
- 5,186