Asciimath-related mathjs expression extension proposals

[gwhitney]

By now there is a fairly well established Asciimath convention for representing mathematical typography (not exactly mathematical calculation) that would suggest some further additions/features to the mathjs expression language, not to mention quite a few issues/discussions over the years for such feature. So I am creating this discussion to collect such proposals that rely only on the 7-bit ASCII character set (I will create another discussion for Unicode extensions to the mathjs expression language). This can be used to survey the possibilities and hopefully at some point select those worthy of implementation and decide against others.

Notation	Meaning	AsciiMath?	Issue	Comments
P => Q <=> R	P implies Q if_and_only_if R	yes	#2660	Note that <=> on boolean values would be identical to ==. Also if we want a simplified notation for anonymous functions (e.g., to use in map) one attractive option would be x => x+1 ala JavaScript; on the other hand, the more AsciiMath consistent notation for that would be x |-> x+1. Otherwise a perfectly sensible proposal.
$	US dollar unit	no	#2673	Currently mathjs does not have built-in currency units, and as the "conversion" between them varies over time, they seem outside the scope of mathjs
r /_ theta	r*(cos(theta) + i*sin(theta))	consistent	#2698	Apparently used by engineers; seems sensible notation for polar representation of complex numbers.
x && y || z	x and y or z	no	#2722	Not clear it adds much as a built in.
|x|	abs(x)	yes	#3044	Multiply requested; a parsing nightmare with a|b being bitwise or, and even without, is |a|b|c| parsed as abs(a)*b*abs(c) or abs(a * abs(b) *c) -- those are semantically quite different? I see two options for making this parseable: (A) Only interpret | with whitespace or string boundary immediately adjacent on exactly one side as an absolute value bar; if the whitespace or string start is on the left, then it is an "open absolute" and if whitespace or string end is on the right, it is a "close absolute". Thus the ambiguous expression above would be disambiguated as either |a| b |c| or |a |b| c|. All other | (with whitespace on both sides or neither) would be bitwise OR. (B) Use |. for open absolute and .| for close absolute, so that we would write |.x.| for abs(x). (Or possibly |:x:| if that looked better to people.) With | so common in mathematical notation, I would recommend serious consideration of one of these proposals or some other parseable scheme along these lines.
sum_(i=1)^5 i^2	sum(range(1,5).map(_(i)=i^2)	yes	#3075	Deserves another look as it exactly corresponds to an AsciiMath notation frequently used by mathematicians.
prod_(i=1)^5 i^2	product(range(1,5).map(_(i)=i^2)	yes	#3075	Ditto.
x ?? y	nullish coalesce per JavaScript	no	#3353	For more consistency with JavaScript, rather than motivated by AsciiMath.
|_ x _|	floor(x)	yes		New, for consistency with AsciiMath
|~x~|	ceil(x)	yes		Ditto.
|-x-|	round(x)	no		New but just brainstorming that it seemed to complete the trio of rounding directions.
x -= y (mod m)	(x - y) % m == 0	yes		New for consistency with AsciiMath
x |-> x+1	_(x) = x+1	yes		Ditto.
f'(x)	derivative(f, x)	yes		Ditto, but might be difficult to parse given that ' is also allowed for string quotes...
a uu b nn c	setUnion(a, setIntersect(b))	yes		New for consistency with AsciiMath. I personally haven't seen this much, but it would make working with sets in mathjs much easier.
a /_\ b	setSymDifference(a, b)	yes		Ditto, but the use of backslash here would probably be a pain and as symmetric difference is not that common an operation, perhaps not worth the trouble...
v o. w	dotMultiply(v,w)	yes
v xx w	cross(v, w)	yes		Haven't seen this much, but very handy if you are doing 3d vector calculations.
A ox B	kron(A,B)	yes		Ditto for matrix calculations.

Please feel free to propose additional possibilities for this table or discuss any of the particular proposals above. Thanks!