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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.
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
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
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