Transporter biofilters

[Batman]

Yet crew members routinely give vaguely phrased orders like 'Tea. Earl Grey. Hot.' or 'Hot coffee. And make it extra strong', 'a bowl of chicken soup' and so on and the replicator delivers, so if nothing else they are at the very least smart enough to to match those orders with a stored pattern that likely fits the bill. People usually don't have to specify which brand of coffee, exact temperature, what size and make and model of mug and so on.
And given fashion is completely subjective the poor replicator would have to be telepathic to know what kind of sweater Worf thinks would look good on Deanna.

[SpottedKitty]

Or there may just be a finite amount of computer storage space available; the specifications for replicating a complicated object might be rather complex.

IIRC this is stated in the TNG tech manual; massive amounts of object storage capacity is saved for e.g. a plastic or ceramic cup and the hot drink inside it, by taking "average" materials and just duplicating that to fill up the volume of the object. Think of it as really fierce jpeg compression applied to a 3D object — you don't need to hold the pattern of every molecule of liquid in the cup, you just need to store enough detail to get the chemical composition right, then "flood fill" that out to the size and shape of the inside of the cup.

As long as what you get isn't something almost, but not quite, entirely unlike tea, you should be OK.

[Baffalo]

Or there may just be a finite amount of computer storage space available; the specifications for replicating a complicated object might be rather complex.

IIRC this is stated in the TNG tech manual; massive amounts of object storage capacity is saved for e.g. a plastic or ceramic cup and the hot drink inside it, by taking "average" materials and just duplicating that to fill up the volume of the object. Think of it as really fierce jpeg compression applied to a 3D object — you don't need to hold the pattern of every molecule of liquid in the cup, you just need to store enough detail to get the chemical composition right, then "flood fill" that out to the size and shape of the inside of the cup.

As long as what you get isn't something almost, but not quite, entirely unlike tea, you should be OK.

Beat me to it. Given that certain materials such as glass have a set crystal structure that repeats itself regularly, replicating a cup isn't that difficult. You're essentially telling the computer you want a container filled with a certain substance, and so the computer would first compute how to create the cup in three dimensions, which you then begin at the bottom and literally build upwards. Since the liquid will be inside the cup, you know that the hollow void left by the cup will need to be filled with a fluid, which handily will fill the volume as it's completed. So, you just literally fill the cup and build upwards. It'd be sort of the same as using a 3D printer, except it's shaping everything all at once and building on top of what's already there.

[Ted C]

Yet crew members routinely give vaguely phrased orders like 'Tea. Earl Grey. Hot.' or 'Hot coffee. And make it extra strong', 'a bowl of chicken soup' and so on and the replicator delivers, so if nothing else they are at the very least smart enough to to match those orders with a stored pattern that likely fits the bill. People usually don't have to specify which brand of coffee, exact temperature, what size and make and model of mug and so on.

Picard: Tea.
Computer: Specify variety.
Picard: Uhm... Earl Grey.
Computer: Specify temperature.
Picard. Hot.
Computer selects a temperature based on statistical analysis of what humans prefer for "hot" liquids and replicates tea.

After that, Picard remembered all the questions it asked and just answered them up front, but it's probably not necessary. The computer can surely remember your preferences as well as Google.

And given fashion is completely subjective the poor replicator would have to be telepathic to know what kind of sweater Worf thinks would look good on Deanna.

Depending on how privacy is handled in the 24th-century Federation, it may be able to reference Deanna's replicator history to select a likely item.

[Baffalo]

Yet crew members routinely give vaguely phrased orders like 'Tea. Earl Grey. Hot.' or 'Hot coffee. And make it extra strong', 'a bowl of chicken soup' and so on and the replicator delivers, so if nothing else they are at the very least smart enough to to match those orders with a stored pattern that likely fits the bill. People usually don't have to specify which brand of coffee, exact temperature, what size and make and model of mug and so on.

Picard: Tea.
Computer: Specify variety.
Picard: Uhm... Earl Grey.
Computer: Specify temperature.
Picard. Hot.
Computer selects a temperature based on statistical analysis of what humans prefer for "hot" liquids and replicates tea.

After that, Picard remembered all the questions it asked and just answered them up front, but it's probably not necessary. The computer can surely remember your preferences as well as Google.

Yet he specifies it every time. Either Picard can't figure out the Quick Select menu or the computer just can't remember, which is a major oversight in my opinion.

And given fashion is completely subjective the poor replicator would have to be telepathic to know what kind of sweater Worf thinks would look good on Deanna.

Depending on how privacy is handled in the 24th-century Federation, it may be able to reference Deanna's replicator history to select a likely item.

Don't you mean the LACK of privacy? Neelix just up and walked into a crewman's quarters and started rifling through his stuff. Medical records are laid bare. There is no privacy in the 24th century for professional busy bodies. And since the replicators should be tied together, there's probably nothing to stop Worf from browsing Deanna's history and spotting the giant 20" black rubber... nevermind.

[bilateralrope]

Yet he specifies it every time. Either Picard can't figure out the Quick Select menu or the computer just can't remember, which is a major oversight in my opinion.

I don't see the need for a quick select menu when specifying it can be done that quickly. If there was a quick select menu, I'm not sure I would even bother programming it for a cup of tea. Especially when fully specifying it will work on any Starfleet replicator, while my quick select menu would only work where I have it programmed.

Now, if I was regularly eating the same meal made up of various components, that would be a different story.

[Terralthra]

Yet crew members routinely give vaguely phrased orders like 'Tea. Earl Grey. Hot.' or 'Hot coffee. And make it extra strong', 'a bowl of chicken soup' and so on and the replicator delivers, so if nothing else they are at the very least smart enough to to match those orders with a stored pattern that likely fits the bill. People usually don't have to specify which brand of coffee, exact temperature, what size and make and model of mug and so on.

Picard: Tea.
Computer: Specify variety.
Picard: Uhm... Earl Grey.
Computer: Specify temperature.
Picard. Hot.
Computer selects a temperature based on statistical analysis of what humans prefer for "hot" liquids and replicates tea.

After that, Picard remembered all the questions it asked and just answered them up front, but it's probably not necessary. The computer can surely remember your preferences as well as Google.

Yet he specifies it every time. Either Picard can't figure out the Quick Select menu or the computer just can't remember, which is a major oversight in my opinion.

Except, thanks to "All Good Things", we know exactly how that conversation went the first time:

Captain Jean-Luc Picard: [in the past timeline] Tea, Earl Grey, hot.
Enterprise Computer: That beverage has not been programmed into the replication system.

[Ted C]

Except, thanks to "All Good Things", we know exactly how that conversation went the first time:

Captain Jean-Luc Picard: [in the past timeline] Tea, Earl Grey, hot.
Enterprise Computer: That beverage has not been programmed into the replication system.

It apparently hadn't been programmed with Earl Grey at any temperature, yet.

Of course, that Picard had all the memories of his future self and was ordering as he habitually did in his own time. It really doesn't say anything about the "real" first time Picard requested tea from the replicator.

[Elheru Aran]

Likely most ships start out with only a basic replicator menu which is then customized over time as the ship's computer learns more about its crew and their preferences. Crew and passengers can either insert their own customized programs, from which the computer can possibly extrapolate other related foods and drinks, or it picks up the occasional 'update' as time goes by.

Example: The Enterprise's replicator may not have programs for, let's say Romulan, foods. So when a Romulan visits and requests, I don't know, some kind of meat dish it says 'hold one moment, searching resources'. In this search it canvasses the shipboard version of Wikipedia, looking for the creature in question; it compares with Vulcan dishes, given that Romulans are the same people (essentially) and notes contrasts between Vulcan and Romulus; and finally checks Romulan biology in order to make sure it's not going to program any toxic spices or whatever. It then attempts to synthesize the requested dish by selecting a corresponding cut of meat from an approximately similar animal if the proper one is not programmed, 'cooked' and seasoned as needed. This is then materialized on a plate for Mr. Romulan, who takes a taste and is all 'wtf is this' (I mean, doesn't that happen half the time anyway...).

Or it just goes 'unavailable, suggest an alternative'. That has happened a time or two, too.

[Ted C]

Or it just goes 'unavailable, suggest an alternative'. That has happened a time or two, too.

It's response to Picard's "first" request for Earl Grey suggests that it will simply respond with "that dish has not been programmed".

If you give it a recipe consisting of ingredients that are in its database, it can produce the requested dish, since O'Brien was able to get it to make Irish dishes for Keiko that way.