Unicode mathjs extension proposals

[gwhitney]

This is a companion discussion to #3364 collecting and adding proposals for extensions to the mathjs expression language based on the use of Unicode symbols, now that the standard is long established and it is becoming easier and easier to enter and deal with such characters.

Notation	Meaning	Issue	Comments
√x	sqrt(x)	#767	Concluded this works best as a tightly-binding unary prefix operator.
30°	30 deg	#2672	Seems uncontroversially good, simply a unit alias.
∑[2,3,4]	sum([2,3,4])	#3075	Seems like it would work well as a unary prefix operator.
∏[2,3,4]	prod([2,3,4])	#3075	Ditto.
∑_(i=1)^5 i^2	sum(range(1,5).map(_(i) = i^2)	#3075	This extension to the meaning of sum is what was specifically proposed in #3075, and as it is has a direct AsciiMath notation, it is a proposal that makes a lot of sense.
∏_(i=1)^5 i^2	product(range(1,5).map(_(i) = i^2)	#3075	Ditto.
a·b	a*b		Not clear one needs a synonym for *, but it is the standard mathematical notation.
v × w	cross(v,w)		Unicode really shines here.
v ⟂ w	v * w == 0		Not clear how "necessary" an abbreviation, but good if supporting Unicode in general.
v ⊙ w	dotMultiply(v, w)
A ⊗ B	kron(A, B)
f∘g	_(x) = f(g(x))		Function composition could actually be handy in arguments to map etc.
x ≠ y	unequal(x,y)		Seems straightforwardly good.
a ∧ b ∨ ¬c	a and b or not(c)		Again, not clear we need more synonyms, but if we are supporting Unicode in a wholehearted way, these are the standard symbols.
a ∪ b ∩ c	setUnion(a, setIntersect(b))		Would make working with sets in mathjs much easier.
a ∆ b	setSymDifference(a, b)		Ditto.
a ⊆ b	setIsSubset(a, b)		Ditto.
a ⊇ b	setIsSubset(b, a)		Ditto. (If we are supporting these, we likely should also support their strict forms and negated forms as well.)
a ∖ b	setDifference(a, b)		Ditto, but note this really has to be the Unicode setminus symbol because ascii backslash is just so overloaded already.
x ∈ S	x is an element of S		Not sure if we have a mathjs function for this: just check if x appears as an entry of S.
r ∠ t	r*(cos(t) + i*sin(t))		More of an engineer's notation than a mathematician's one, but clear and compact.
⌊x⌋	floor(x)		One of the best reasons to embrace Unicode :)
⌈x⌉	ceil(x)		Ditto.
a ≤ b	a <= b		A synonym is not needed, but clearly should be supported if mathjs embraces Unicode.
a ≥ b	a >= b		Ditto.
x ≡ y (mod m)	(x-y) % m == 0		Also similar.
a ∣ b	b % a == 0		Along the same lines. Note that this is a different vertical bar than the usual |
f′(x)	derivative(f, x)		Note this is different from any ascii quote character, so unambiguous.
Γ(x)	gamma(x)
𝒫(S)	setPowerset(S)
ζ(z)	zeta(z)
℃			That's a single Unicode character that means degree Celsius. There's one for Fahrenheit as well, not that anyone uses that unit ;-).

Unicode is so huge, it's unlikely this table is exhaustive. So feel free to recommend others or discuss any of these proposals.