All Questions
Tagged with ac.commutative-algebra decidability
3 questions
6
votes
1
answer
635
views
Is decomposability of polynomials over a field an undecidable problem?
By a decomposition of a polynomial $F(x)$ over a field $K$ we mean writing $F(x)$ as
$$
F(x)=G(H(x)) \quad(G(x), H(x) \in K[x]),
$$
which is nontrivial if $\operatorname{deg} G(x)>1$ and $\...
2
votes
0
answers
65
views
Decidability of the solvability of quadratic systems
Let a finite collection of (complex) unknowns $\{x_1,\ldots,x_n\}$ be given, as well as an affine system $AX=B$ in the quadratic variables $X:=[x_i x_j : i\leq j]$, with entries in a computable ...
15
votes
2
answers
1k
views
Is irreducibility of polynomials $\in \mathbb{Z} [X]$ over $\mathbb{Q}$ an undecidable problem?
There are a number of criteria for determining whether a polynomial $\in \mathbb{Z} [X]$ is irreducible over $\mathbb{Q}$ (the traditional ones being Eisenstein criterion and irreducibility over a ...