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5
votes
2answers
589 views

Differential ideal membership problem

We know that in the ordinary algebra ideal case, the ideal membership problem can be solved by the Grobner Base theory, then, is there a counterpart theory in the differential ideal case? To be ...
7
votes
2answers
492 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} ...
0
votes
0answers
84 views

Maximal elements for ideals and subrings ordered by inclusion with fixed number of minimal generating polynomials

Let $R=\mathbb{R}[X_1,\dots,X_n]$, and $$\mathfrak{I}_d=\{ \text{ideals for which there is minimal generating system with $d$ elements} \}\setminus \{\text{ ideals generated by $d$ monomials}\}$$ ...