Algorithm to check whether rational polynomial is irreducible over $\mathbb{C}$?

Question

Let $F\in\mathbb{Q}[x_1,\ldots,x_n]$ a multivariate polynomial. Is there an algorithm for checking whether $F$ is irreducible over $\mathbb{C}$? Is this implemented somewhere?

Answer 1

You can use GIAC to factorize a multivariate polynomial over $\mathbb{R}$ or $\mathbb{C}$:

complex_mode = 1
p = 3/2*x^2*y^2+x^2+3*x*y^3/2+x*y
factor(p)

output: (3*y^2+2)*x*(x+y)/2.