| http://www.w3.org/ns/prov#value | - Basically, what you are missing is that the roots need not be algebraically independent: there could be some $F$-relation between $a_1$, $a_2$, and $a_3$, and the automorphism has to respect that relation; this is what is happening in Jack's example, where every root is a power of any other root.
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