Binding strength in traditional mathematical notation

Conversation started Jul 17, 2019 at 19:32.

Adám

Jul 17, 2019 19:32

Another fun one is 4/2/2

flawr

I'd say that is pretty much always evaluated left to right, isn't it?

Adám

@flawr Except in TMN, where it really should be right-to-left.

flawr

what is TMN?

Adám

@flawr Traditional Mathematical Notation.

flawr

@Adám Even then I'd say it is (4/2)/2, but really it is just a bad idea to use an inline / in such a case

Adám

Jul 17, 2019 19:37

@flawr Precedence is evil.

flawr

oh matlab has a fun one: what is 2\4/2 ? :)

Adám

Ah, a\b is b/a, right?

flawr

right, except when the operands are not commutative

DJMcMayhem

@flawr It evaluates to the sound of a programmer quietly sobbing

flawr

Well actually the one I posted was kinda obvious

try 2/4\3 instead:)

Adám

Jul 17, 2019 19:41

What is 4 ÷ 2 × a ?

flawr

(4/2)*a

Adám

@flawr What is 4 ÷ 2 a ?

flawr

@Adám 4 / (2a) :)

Adám

@flawr Precedence is evil.

dzaima

@Adám Error: ambiguous expression

Adám

Jul 17, 2019 19:43

What is sin a × b ?

flawr

It's a sin.

Adám

@dzaima Interestingly, a few (but very few) language have that.

dzaima

@Adám once i wanted to get an answer to something like that from my math teacher. didn't get a conclusive one :D

flawr

What I do like in haskell is that you can define the precedence as well as the associativity of binary operators.

Adám

@dzaima Right, it is because it (officially?) depends on the goodwill of the reader.

flawr

Jul 17, 2019 19:44

Caused by the incompetence of the writer

In math one should really try to avoid expressions like these, even if not everyone is doing so.

Adám

sin a cos a is "obviously" (sin a)(cos a), but sin 2 a is "obviously sin(2 a) so there is no blanket precedence of sin vs (implied) ×.

dzaima

@flawr even more evil, sin 2a × a

Adám

@dzaima lol

flawr

@Adám the latter depends on how much space there is between the consecutive symbols :D

dzaima

i wonder if there'd a big difference from interpreting sin 2a × a and sin 2a×a

John Dvorak

Jul 17, 2019 19:47

Bob eying quilts, quietly sobbing

flawr

but really the unclear conventions caused us to use monstrosities like ⫋

Adám

@flawr Well, I does that.

DJMcMayhem

@Adám funnily enough, I tried to see what google thought was more 'obvious'. sin 2 pi is sin(2 * pi) but sin pi 2 just doesn't get evaluated by the calculator haha

dzaima

sin 2a*b vs sin 2a * b

Adám

@dzaima Wow!

John Dvorak

Jul 17, 2019 19:48

That's because 2 is actually a monadic function that multiplies its argument by two

while pi is a mathematical constant

Adám

‽‽‽ \○/

DJMcMayhem

@JohnDvorak I can't tell if that's a joke or not

flawr

@JohnDvorak and in this context I use unary because monadic has other meanings in programming and math:)

John Dvorak

ah, yes, unary.

Adám

@dzaima But sin 2a × b and sin 2a×b are both sin(2a)b!!!

Erik the Outgolfer

Jul 17, 2019 19:51

@DJMcMayhem bah, I would read that as sin 2 × π

not as sin(2 × π)

unfortunately it's not really my choice though

Hosch250

There needs to be a jimmy tag. — MilkyWay90 24 hours ago

What do y'all think?

(Got to run now, meetings.)

Nice series of questions, BTW.

DJMcMayhem

I would lean towards no

Erik the Outgolfer

definitely no, trends come and go

Adám

sin 2ab vs sin 2a b

flawr

@Hosch250 just because some guy decided to repeatedly use the name "jimmy" in his challenges?

I think we've even banned the useless backstories a while back...

Adám

Jul 17, 2019 19:55

@Hosch250 Nope. It adds nothing to the site.

John Dvorak

Useless backstories are an integral part of any challenge. Please don't get rid of them!

Erik the Outgolfer

@flawr they've not been completely banned, they just shouldn't be long enough to distract from the challenge

more like discouraged

Adám

If sin²x is (sin x)² and sin⁻¹x is arcsin x, what is sin⁻²x? (arcsin x)²?

flawr

totally unrelated, did you guys know you could eat (some of them) physalis fruits?

they are delicious, I just recently found out that there are actually edible varieties

Adám

@flawr sure, they are common as desert decor.

Erik the Outgolfer

Jul 17, 2019 19:59

@Adám sin ^ (-2) x is a debated topic

dzaima

sin sin2x2 vs sin sinx2 vs sin sin x2. ok that's enough precedence for me

Erik the Outgolfer

the convention that sin ^ a x means (sin(x)) ^ a and not (sin ^ a)(x) is stupid IMHO

flawr

@Adám sin⁻²x = sin⁻⁻¹*² x = (sin⁻¹ x)^2 = (arcsin x)^2

@EriktheOutgolfer it is usually very clear which one it is from the context

Adám

@flawr W⍺ says (sin x)⁻²

Erik the Outgolfer

yeah, "context" shouldn't do the justice in maths, ever

flawr

Jul 17, 2019 20:03

and if you want to be sure that people understand that you mean repeated composition, then prepend a composition circle symbol to the exponent

It is not a very standard thing to do but people will always understand.

Erik the Outgolfer

I'm pretty sure that the composition symbol doesn't take a number as its right operand...

flawr

@EriktheOutgolfer yes but people understand:)

In math so many notations and notions do depend on the context.

Otherwise we would have long run out of symbols

Adám

Whoa, W⍺ splits sin^-1.2 x between 1 and . !!!

Conversation ended Jul 17, 2019 at 20:04.

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