Edit of "Output-function summary" docs from a new learner

[nathanrboyer]

This is a refactor of the helpful output summary written recently by @stevengj in #54547. I think it makes the section more digestible to move some of the information that was contained within the bullets into separate parts, so the bullet points themselves are smaller. It may need to be edited for accuracy and formality.

[LilithHafner]

Thanks for offering this edit, @nathanrboyer!

Personally I have no preference for the proposed version over the previous version or vice versa. I'd be happy to help do a final review and merge if other folks think this is an improvement, though.

[stevengj]

I think that the real reason is that convert in Julia is used for implicit conversions, e.g. when assigning an expression to an container of a different type. So it is never defined for converting between conceptually different types of objects, e.g. between numbers and strings.

[nathanrboyer]

I have now rewritten this sentence according to your explanation.

[stevengj]

Suggested change

	richer display of `x` in some interactive environments as discussed above.
	richer display of `x` in some interactive environments as discussed below.

[nathanrboyer]

Hmm, when I read this passage I thought "above" referred to the Polar example in the previous section. Now I think you may have been referring to the small explanation in the display bullet. I will rethink this.

[stevengj]

Suggested change

	it calls the 2-argument `show(io, x)`.
	`show(io, "text/plain", x)` calls the 2-argument `show(io, x)`.

[nathanrboyer]

This sentence is copied from the original text, but I am thinking now it can just be deleted?

If not deleted, then maybe moved into the display bullet like this?

In the REPL, display calls show(io, MIME"text/plain", x) (which defaults to show(io, x) if not separately defined).

[stevengj]

It’s copied from the previous text, but you edited the preceding sentence so that the new qualification is needed.

I don’t think it can be deleted. It’s important to explain how 3-arg show defaults to 2-arg show (but only for text/plain)

[stevengj]

Suggested change

	* [`show(io, mime, x)`](@ref), with three arguments,
	* [`show(io, ::MIME"text/plain", x)`](@ref), with three arguments,

[nathanrboyer]

I do not understand why you want this bullet to be specific to a text representation rather than explaining the 3-argument show generally.

[stevengj]

Because text/plain is the common case, and most of this section is about text output . Most types don’t offer output for any other mime types, which is why they are only mentioned in passing here.

Also, if you want to overload it you need to know the specific signature.

[stevengj]

Suggested change

	Multiple 3-argument `show` methods can be defined for various MIME types to enable
	Additional 3-argument `show` methods can be defined for other MIME types to enable

[nathanrboyer]

This change is contingent on the decision above: mime vs ::MIME"text/plain".

[stevengj]

Suggested change

	By default (if no 3-argument method is defined for `typeof(x)`),
	Although the underlying method is defined for a [`MIME`](@ref) argument, the caller can
	simply pass a string such as `"text/plain"`, at the expense of a dynamic dispatch.
	By default (if no 3-argument method is defined for `typeof(x)`),

[nathanrboyer]

I think this is good to explain, but it leaves me with more questions than answers. Why is the string version used most places if it is slower?
See also this related issue I created: #56768

[stevengj]

Internally, we should call the MIME version. For users, the string version is easier, and is rarely performance-critical.

[stevengj]

See also #55860 for another tweak.

[nathanrboyer]

See also #55860 for another tweak.

I added a form of that PR as below.

1612 (println and printstyled both call print,
1613 but add a newline or styling, respectively.)

[nathanrboyer]

@stevengj I took another pass at the summary. The bullets are longer now but hopefully more informative. Please review at your convenience.

My intent was to start by explaining each function/method generally and then suggest to the reader how/why they might wish to create new method definitions.

[nathanrboyer]

I'm not totally confident on why when/why to overwrite 2-arg show. Printing inside a vector is the example used above for Polar, but the show docstring maintains that the definition "should be parseable Julia code when possible" which seems to already be the default definition.