changed lcm and gcd implementations for when just one arg is infinite

[Priynsh]

Fixes #56991 by adding conditions for both gcd and lcm cases. Also fixes tests for the same i.e. lot of tests regarding gcdx and lcm are removed. Two relevant tests have been added as well.

[LilithHafner]

Thanks! Looking at this I'm realizing there is another way to define lcm and gcd that allows lcm(1//1, 1//0), and possibly even lcm(0//1, 1//0) to be well-defined.

Currently, we define

a is a multiple of b if there exists an integer m such that a=mb.

If we change that to

a is a multiple of b if there exists an integer or 1//0, -1//0, or false m such that a=mb.

Then the following are correct:

julia> lcm(1//0, 1//1)
1//0 # currently 1//1

julia> lcm(1//0, 0//1)
0//1 # current behavior, only correct with #57068, otherwise error is appropriate

julia> gcd(1//0, 1//1)
1//1 # currently 1//0

julia> gcd(1//0, 0//1)
1//0 # current behavior, only correct with #57068, otherwise error is appropriate

EDITED to incorporate #57067 (comment)

[Priynsh]

since the discussion was done, this is the new implementation. Minor change -

a is a multiple of b if there exists an integer or 1//0 or -1//0 or false m such that a=mb.

[LilithHafner]

Triage wants to add the definition of multiple to gcd to match lcm (but it should be the definition of divides). Triage does not like Lilith's idea of extending integers to include 1//0, -1//0, and false in this case.

[Priynsh]

I’ve updated the implementation to throw an error when one of the arguments is infinite in gcd/lcm and fixed the related tests to reflect this change. Additionally, I’ve added a definition for 'multiple' in the docs :)

[LilithHafner]

Thanks! I've left some inline comments and this looks good; we should be able to get it merged.

[LilithHafner]

This note is already present; it previously looked like it wasn't because the base commit was out of date.

[LilithHafner]

I think this is more clear:

Suggested change

	if (isinf(x) && !isinf(y)) || (!isinf(x) && isinf(y))
	isinf(x) != isinf(y)

[LilithHafner]

Suggested change

	throw(ArgumentError("lcm is not defined"))
	throw(ArgumentError("lcm is not defined between infinite and finite numbers"))

[LilithHafner]

Suggested change

	return unsafe_rational(gcd(x.num, y.num), lcm(x.den, y.den))
	unsafe_rational(gcd(x.num, y.num), lcm(x.den, y.den))

Most of this file uses implicit return stlye

[LilithHafner]

Let's remove this unrelated whitespace change

[LilithHafner]

For tests, let's just change all the existing tests to @test_throws; that way we know we're not losing coverage. It will also make the blame/diff easier to review.