Is there any if and only if condition for checking $Q$-linear independence of given a set of numbers say $\alpha_i$ ? More precisely how to check linear independence of given $n$ algebraic numbers (algebraic numbers are given by an interval and its irreducible polynomial such that that interval does not contain any other root of that polynomial ) ? Is there any known algorithm for it?

PS : Def :- $\alpha_i$ are Q- linearly dependent iff $ \exists c_i \in \mathbb{Q} $ such that $\sum c_i\alpha_i=0$

Is there any if and only if condition for checking $\mathbb{Q}$-linear independence of given a set of numbers say $\alpha_i$ ? More precisely how to check linear independence of given $n$ algebraic numbers (algebraic numbers are given by an interval and its irreducible polynomial such that that interval does not contain any other root of that polynomial ) ? Is there any known algorithm for it?

PS : Def : $\alpha_i$ are $\mathbb{Q}$-linearly dependent iff $ \exists c_i \in \mathbb{Q} $ not all zero such that $\sum c_i\alpha_i=0$