Timeline for Is there an algorithm to decide if an ideal contains monomials?
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 5, 2013 at 15:24 | vote | accept | Thomas Kahle | ||
| Apr 5, 2013 at 15:12 | answer | added | Allen Knutson | timeline score: 7 | |
| Apr 5, 2013 at 15:10 | comment | added | François Brunault | The ideal $I$ contains a monomial if and only if $x_1 \ldots x_n$ belongs to the radical of $I$. This happens if and only if $(x_1 \ldots x_n)^e \in I$, where $e$ is the Noether exponent of $I$, that is the smallest exponent such that $(\sqrt I)^e \subset I$. The effective Nullstellensatz gives you an explicit bound for $e$, see e.g. Jelonek, On the effective Nullstellensatz, Invent. Math. 2005. MR2198324 Once you know $e$, there are only a finite number of monomials to check, which you can do using Gröbner bases. | |
| Apr 5, 2013 at 14:20 | history | asked | Thomas Kahle | CC BY-SA 3.0 |