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Results tagged with ac.commutative-algebra
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user 2233
Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
2
votes
Maximizing and minimizing the number of positive product $k$-subsets of an $n$-set
Here are some minor remarks. Since the actual numbers do not matter, the question can be rephrased as follows. Let $\sigma: [n] \to \{-, +\}$. Say that a $k$-subset of $[n]$ is $\sigma$-positive if …
- 32.1k
8
votes
Minimal "subset" of a set of homogeneous polynomials with same solution space
The answer to the last question is no. Consider, $xy, xz, yz, x^2+y^2+z^2$ in $\mathbb{C}[x,y,z]$. The only common zero of these four polynomials is $(0,0,0)$ but removing any one of them enlarges t …
- 32.1k
23
votes
How to tell if two random polynomials are identical
If the coefficients are non-negative then you can always do it with at most two integer evaluations.
That is, $P$ and $Q$ are equal if and only if
$P(1)=Q(1)$, and
$P(P(1)+1)=Q(Q(1)+1)$.
Update. …
- 32.1k