WI: Anna Komnene Inherits Without Incident

Let's posit a scenario in which Anna Komnene is the only surviving child of Alexios at the time of his death and is thus the undoubted heir apparent. Do we know enough about her to make some predictions about how her reign would have differed from her brother's? Obviously she would have to share a certain amount of power with her spouse, but how much might she retain personally? I've read a couple of casual discussions of her life on other websites recently that suggest she was something of a prodigy, is that at all true?
 
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