The auxiliary verb (using in perfect tenses) in sentences with 2 or more notional verbs

There is an example:

Today I have written a letter and done my homework.

Or is it necessarily to put the auxiliary verb before done? Somebody has told me that we can ommit the auxiliary verb in such cases when we use perfect continious tenses...Is it correct? (Would you give me some links where I can learn about the rules if they exist)

A single auxiliary before the first in a series of coordinated verbs applies to all in the series. If the infinitive marker to is required, it can also be omitted after the first instance.

She wants to fly to Paris and take a boat ride on the Seine.

You have to sift the flour, measure it, then pour it into the bowl.

I've been to that restaurant several times but only ordered the fish.