Improve show and string

[Joel-Dahne]

This PR makes several updates to the show and string methods for Mag, Arf, Arb and Acb. Some of them are strict improvements, some of them are more opinionated. We can see which one we keep in the end.

After:

julia> Mag(1)
1.0
julia> Mag(1)
1.0
julia> Mag(π)
3.14159266
julia> show(IOContext(stdout, :compact => true), Mag(π))
3.14159
julia> Arf(1)
1.0
julia> Arf(1 // 3)
0.33333333333333333333333333333333333333333333333333333333333333333333333333333
julia> show(IOContext(stdout, :compact => true), Arf(1 // 3))
0.333333
julia> Arb(1)
1.0
julia> Arb(π)
[3.1415926535897932384626433832795028841971693993751058209749445923078164062862 +/- 1.93e-77]
julia> show(IOContext(stdout, :compact => true), Arb(π))
[3.14{…72 digits…}62 ± 1.93e-77]

Before:

julia> Mag(1)
(536870912 * 2^-29)
julia> Mag(π)
(843314857 * 2^-28)
julia> show(IOContext(stdout, :compact => true), Mag(π))
(843314857 * 2^-28)
julia> Arf(1)
1.0
julia> Arf(1 // 3)
0.3333333333333333333333333333333333333333333333333333333333333333333333333333348
julia> show(IOContext(stdout, :compact => true), Arf(1 // 3))
0.3333333333333333333333333333333333333333333333333333333333333333333333333333348
julia> Arb(1)
1.0000000000000000000000000000000000000000000000000000000000000000000000000000
julia> Arb(π)
[3.1415926535897932384626433832795028841971693993751058209749445923078164062862 +/- 1.93e-77]
julia> show(IOContext(stdout, :compact => true), Arb(π))
[3.1415926535897932384626433832795028841971693993751058209749445923078164062862 +/- 1.93e-77]

(Acb just prints the real and imaginary parts using the Arb version)

The first commit is an update to the interface and the remaining 5 make changes to the output format.

The string_nice method is removed, it never actually worked for Mag and Arf and was not particularly easy to use for Arb and Acb since you had to contruct the flag argument yourself. The interface is now based on Base.string, with flags for the various options. In addition to this we now use the arf_get_str function, which didn't exist when this code was first written. Before we converted Arf to BigFloat for printing, which is slightly problematic since Arf can represent more values than BigFloat.

The changes to the output format are (in the same order as the commits):

1. Print Mag by converting to Arf. I think this is to prefer as the old output format is not particularly informative.
2. Add compact show to Mag and Arf which only prints 6 digits. This is similar to how Float64 and BigFloat works.
3. Add unicode argument to Base.string for Arb and Acb. This does replace(str, "+/-" => "±", "..." => "…") on the output.
4. Add compact show for Arb and Acb. This sets the arguments condense = 2 and unicode = true for constructing the string.
5. Remove trailing zeros for decimal numbers. This is similar to what the Base._prettify_bigfloat method does. I find this very convenient when the values are small integers, as 1.0 is significantly easier to read than 1.0000000000000000000000000000000000000000000000000000000000000000000000000000.

Some issues/possible improvements:

1. The documentation for Base.string says that one should usually not define string directly, but this was the most natural way I found to be able to give formatting arguments when constructing strings. But Base does define it directly for e.g. Integer and BigFloat.
2. I have not added any docstring for Base.string. Since the methods do accept a fairly large number of arguments this would maybe be reasonable to do.
3. The decimal representation for Mag does round upwards. The printed result is hence not guaranteed to be an upper bound. I think it would be a nice improvement if it did round upwards. I thought I would add an issue in Flint about this (note that there is not even any mag_get_str function in Flint).

[Joel-Dahne]

Oh, and maybe this is also a good time to publish 1.2.0?

[kalmarek]

we could just replace this with

Suggested change

	function Base.string(
	x::MagOrRef;
	digits::Integer = digits_prec(30),
	remove_trailing_zeros::Bool = true,
	)
	cstr = ccall(@libflint(arf_get_str), Ptr{UInt8}, (Ref{arf_struct}, Int), Arf(x), digits)
	str = unsafe_string(cstr)
	ccall(@libflint(flint_free), Nothing, (Ptr{UInt8},), cstr)
	return remove_trailing_zeros ? _remove_trailing_zeros(str) : str
	end
	function Base.string(
	x::MagOrRef;
	digits::Integer = digits_prec(30),
	remove_trailing_zeros::Bool = true,
	)
	return string(Arf(x); digits, remove_trailing_zeros)
	end

I actually didn't know that one can pass kwargs without explicitly writing them! when was it introduced?!

[kalmarek]

Suggested change

	str = string(
	realref(z);
	digits,
	more,
	no_radius,
	condense,
	unicode,
	remove_trailing_zeros,
	)
	if !iszero(imagref(z))
	str *=
	" + " *
	string(
	imagref(z);
	digits,
	more,
	no_radius,
	condense,
	unicode,
	remove_trailing_zeros,
	) *
	"im"
	end
	kwargs = (
	:digits => digits,
	:more => more,
	:no_radius => no_radius,
	:condense => condense,
	:unicode => unicode,
	:remove_trailing_zeros => remove_trailing_zeros
	)
	str = string(realref(z); kwargs...)
	if !iszero(imagref(z))
	str *= " + " * string(imagref(z); kwargs...) * "im"
	end
	return str

seems a bit more readable for me

[kalmarek]

sure, we can release 1.2.0.

I see all of those changes as clear improvements!

I wouldn't add any docstring to string -- nobody does so and lets keep it this way ;)

[Joel-Dahne]

I have made changes according to your comments and set the version to 1.2.

Regarding the kwargs I believe you already learned about this once before #152 (review).

[kalmarek]

well clearly I forgot again 🤣