The irreeducibility of a polynomial $f\!\in\!K[x_1,\ldots,x_n]$ in general depends on what the field $K$ is (for example, if $K=\mathbb{R}$, then $f=x_1^2+1$ is irreducible, but if $K=\mathbb{C}$, it is not).
However, when $n\geq2$, there exist polynomials that are irreducible no matter what $K$ is (for example $x_i-x_j^d$ where $d\in\mathbb{N}$ is arbitrary and $i\neq j$, is always irreducible).
Question: Is there a command in any computer algebra system (preferably SINGULAR), that could (in some cases) confirm if a polynomial is irreducible over any field?
For example, in A Singular Introduction to Commutative Algebra, page 222, there is written: Since there is mention of the quotient field $Q(A)$, this means $A$ is a domain, i.e. $x^4+6x^2y-y^3$ is irreducible.
Question: How can I show that $x^4+6x^2y-y^3$ is irreducible over any $K$?