Is there a general algorithm to find a primitive element of a given finite extension (with a finite number of intermediate fields)?)

I just want to know if there is an algorithm to find the primitive element of a given finite extension $F/k$ if the intermediate fields are given. I know how to approach it in particular examples picking linear combinations (the case $\mathbb{Q}(\sqrt{2}, \sqrt{3})/\mathbb{Q}$ for instance). If it does not exists, is there, then, an algorithm for the finite separable extension case or for extensions of $\mathbb{Q}$?

Thanks in advance.

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