Question:Galois group with parameters

November 12 2012
Maple

1

I consider a polynomial \$P(x)\$ such that their coefficients are in \$\mathbb{Q}(u_1,\cdots,u_k)\$ where \$u_1,\cdots,u_k\$ are complex parameters. I use in Maple the command \$galois(p(x),x)\$ and I obtain a fixed Galois group solution.  Fortunately, when I give explicit values (randomly chosen) to the \$(u_i)_i\$, I obtain always the previous group as Galois group. I think that Maple considers that the \$(u_i)_i\$ satisfy no algebraic equations, that is the \$(u_i)_i\$ are generic. Is it true and is such a result secure ?

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