Which is the preferred preposition to use after the word “augmented”, as in the sentence “A is augmented with/by B”? Does this depend on context?
For concreteness, I am interested in mathematical usage, as in the “The set is augmented with redundant vectors for greater numerical robustness”.
The usage “A is augmented by B” indicates that B is the implied subject in the passive-voice construction “A is augmented”. That is, B is doing the augmentation: “B augments A”.
The usage “A is augmented with B” implies that B is what A is augmented with, by an unspecified subject. This is a predicate adjective verb phrase.
Thus, one could write “The fruit salad is augmented with papaya by Sofia”, meaning “Sofia augments the fruit salad with papaya”.
In many cases, one could appeal to either of the two constructions – the difference is the sense of agency attributed to B.