serious-discussion

[little vine]

Don't need to think about getting hurt as much

[bright hill]

Even the military?

Aren't they supposed to promote a strong physique or smth ?

[vivid halo]

for good reason yes

likewise a lot of athletes don't squat

[bright hill]

Huh

Why is that?

[vivid halo]

it's kinda prone to back injury or pain compared to other lifts

[little vine]

Squat rack is a great piece of equipment

But you can do lots of lifting on the same group without it

[vivid halo]

yeah

[bright hill]

How expensive is a squat rack?

[vivid halo]

few grand

[bright hill]

Bruh

[vivid halo]

like a grand for a really shitty one

[bright hill]

It's just a hunk of metal

[vivid halo]

actually a grand will get you a nice one

it's the like $500 ones that start to get like

it's not a box anymore just the absolute minimum needed to hold stuff

[vivid halo]

why do weights cost so much

[little vine]

They do

It's insane

[vivid halo]

at least a squat rack is something that has to be machined, it has to be adjustable, bear a lot of load, etc

but plates it's just fucking

a chunk of metal

[little vine]

No you're doing well if you can get one in a home gym

[vivid halo]

make your own plates with concrete

[little vine]

Might as well

[zealous garden]

100% I get scared for my back sometimes when I squat

[eager reef]

@errant ridge

https://cdn.discordapp.com/attachments/991827364352892938/1001565441744969928/unknown.png

[bright hill]

[reef carbon]

alright so

are there any complex-analysis-pilled people here who could help me out w/ some terminology

what do you call a contour that goes around the boundary of the region {0 ≤ |z| ≤ R, 0 ≤ arg(z) ≤ theta}

like this-ish

[next schooner]

That region is a called a sector

I don't know that its boundary has a specific name

[reef carbon]

that i do know of, in retrospect

im talking about like. integrating over the boundary of a sector whose radius goes to infinity

[cold needle]

honestly thats not a bad way to say what it is you’re doing

but maybe theres a funny catchphrase like keyhole contour or whatever

[odd narwhal]

Bruh what

Mine cost like

300$

And it's good. It doesn't move around and can hold upwards of 500kg

I've put >230 on a bar for squats on it so far at home and it was good

[odd narwhal]

I really can't think of any discipline in which athletes weight train that doesn't use squatting to some degree

Now if they're doing them properly is a different story

It's also a very versatile exercise with a lot of variations for different purposes

But military training is usually not heavy on the gym training. It's there but it's also just a lot of cardio, cardio in gear, rucking, etc

[umbral lion]

also somewhat a focus on calisthenics, military men and women love their pullups n pushups after all

i think training strength can be taken for personal tastes but in general will be enough as a monotherapy against the plagues that come from modern living, or in a minor form is a compatible lifestyle choice to running

[vivid halo]

I was looking at the wrong shit lmao

[odd narwhal]

Lol

[umbral lion]

how much do you guys lift?

[little vine]

Not much at all. I'm not super athletic

It depends on the exercise

[umbral lion]

mathcord lifting comp?

[little vine]

HAHHAHha

My chances are better than most other places

Unless you meant to lift math

[fast ivy]

Let's put in this this, I am a fibration

[umbral lion]

I actually like the idea of like endurance lifting but there's a modifier for the number of questions you can answer midset

mathcord strong&smartman lifting competition

[little vine]

That's crazy enough to work

Shit if only I could study and work out

[meager sonnet]

wait lemme find the image

[little vine]

HAHAHAHAHAHA

Yeah that's wassup

It's like the chess boxing

[odd narwhal]

255/165/247.5 are.my.meet prs (kg) but I messed up dl last meet

[umbral lion]

is that DBS or SBD? pretty good numbers regardless

[odd narwhal]

Sbd

Dl.is actually from last meet since this meet I fucked up

This being 2 months ago

Hbu

[little vine]

Yeah idk what that means

[odd narwhal]

Squat/bench/deadlift

[little vine]

Oh that's good

Do you count the bar?

[odd narwhal]

Yea you always count the bar

[little vine]

How much is it

[odd narwhal]

20kg

[little vine]

Ah ok

[odd narwhal]

Standard olympic barbell

[umbral lion]

i don't compete or anything but in kg my prs pre injury were 200x13/125x5/185x3

[little vine]

That's better then hahaha

[odd narwhal]

200x13

Lmao damn

I could probably do that but that sounds awful

[umbral lion]

i've mostly been chasing these numbers since covid started mind you, but i enjoy the craft a lot

[cold needle]

HOMOTOPY LIFTING PROPERY

ah shi chat jumped down

in pain

[umbral lion]

i was going for 220x13 when i got injured lmao i've since stopped doing high rep high weight

[odd narwhal]

Oof

What kinda injury

[umbral lion]

tore my midback, doc said i was lucky nothing was bulging but i was bedridden for a few months

[bright hill]

You do???

[odd narwhal]

Yes..

[odd narwhal]

Oof damn

That sounds rough

[bright hill]

[odd narwhal]

Worse i've had is a strained band in my leg 2.5 years ago, luckily I could still train upper body

[little vine]

Yeah I never want to hurt myself

[umbral lion]

It was pretty funny for the time cause i got accepted for a summer research position the day before and then had to tell the prof i had to work from home

[odd narwhal]

That sounds awful nasty

Oof lmao

[umbral lion]

Yeahh I chuckle about it but that prof still won't talk to me ahahahaha

regardless i think expanding horizons was probably the best thing that happened after that

[odd narwhal]

Not like it was your fault

[umbral lion]

i was told i couldn't touch a barbell for atleast a year and a half so i started doing calisthenics stuff in the mean time and i got pretty far with that the following year

[umbral lion]

oh cmon it totally was, i was being irresponsible

[odd narwhal]

Sure, but it's not like you could have foreseen the injury

[little vine]

I get it though. You really start pursuing something

[umbral lion]

Yeahh, I suppose I didn't, you get so lost in the moment leading up to a PR like that you don't do the long term trajectory on failure, just that you'll do it

[little vine]

I was like that with running

[umbral lion]

regardless i think its a great past time and the risks are only apparent if you're being dumb or if you're at your limits

[umbral lion]

yeah? did you push too hard?

got any tips btw? i'm starting to get into it again

[little vine]

Listen to great music

[eager reef]

Find an enjoyable route

Good views and shit go a long way imo

[little vine]

I got sesamoiditis

[eager reef]

What

[umbral lion]

apologies but that looks like something off an incel forum

[little vine]

(sp)?

LMAO

Ok you have a joint in your toe that can get overworked

[umbral lion]

true, I live next to a bunch of parks which has been pretty dandy

[umbral lion]

i see that now

[little vine]

And it hurt so much but I'd still tried to run because I was addicted to it

[eager reef]

Parks are Great

You can be that asshole who is condescendingly doing sports while people enjoy themselves there

[little vine]

Really start slow. Find a nice mile and a half route

Make it as fun as possible

[umbral lion]

i am always that guy

[little vine]

Blast good music

[eager reef]

Whats a mile and a half man

Fuck your units

[umbral lion]

i dominate the local public schools doing pull ups and dips with a 40 gallon jug of sand tied to my nuts

[little vine]

Like 2.5 k

[eager reef]

Absolute banger

[umbral lion]

children fear me, their mothers want me, the fish find me

[eager reef]

Mfer tagged modmail

[umbral lion]

i pity the fool who won't

[marble delta]

What’s the point of this channel? We already have a discussion channel

[little vine]

It's where actual discussion happens

Discussion one is shitposting

[open aspen]

It’s for when discussion is moving fast

Overflow

I tend to just talk on top of people

Since it’s text

[lime spindle]

I recently discovered a solution to an optimization issue I've been running into for the past 2 weeks! WOOO!

[storm sage]

yayyyyyyyyy

[barren anchor]

awooooooga

[lime spindle]

Actually.... I seems like I got excited too early. For my problem I've realized that my present solution just moves the issue to another part of my code.... 😢

[dusk basin]

"How are you still single?" - Grandma

[barren anchor]

I'm stuck on some bug

20 minutes with 0 progress. Everything looks fine.

maybe bedtime. Lame though it was shaping up.

it is kind of infuriating because the logical save point is exactly after one small tweak that can easily occur w/ no bug

wow dumb. I moved the files out of the directory and moved them back and now it's all good.

elixir's favorite build tool mix's tracking busted somehow

[stoic zealot]

Guys this is rly hard and I need help

What is

1+1 ?

[ember topaz]

https://youtube.com/shorts/518-lOf6M_s?feature=share

Does this make any sense?

[umbral lion]

just geometric series it

[storm sage]

this is only valid if 0.9999... converges, so it's not really a rigorous proof

but it's a nice informal way of thinking about things yeah

[deep mango]

Not really, in general. The only thing I can think of is that they come up once in a while in complex analysis and analytic number theory, where you have functional equations for special functions.

[burnt dune]

yooooooooo

someone called me and told me all my info is up on doxbin

couldnt find myself tho

[deep mango]

[burnt dune]

i have my number on fb so its not weird how he got my number

he was egyptian whos phone zone was in the USA but he told me he is in canada

is that possible?

[honest veldt]

but it does converge

[bronze wedge]

Doxbin was shut down like 7 years ago lol

[burnt dune]

there are mirrors

on the normal web

not even on the deep web

like .org

i kept searching for me

he told me the postt was like a few hours ago

couldnt find anything

and he kept insisting that he sends me a link

told him okay but then he didnt send shit

u think he is just trying to phish?

[bronze wedge]

Duh

Unless you know the person

Personally

[neat lintel]

the internet is not a substitute for real life

[burnt dune]

no i dont

but he did saay something interesting

[neat lintel]

some of the people that have profiles like instagram, or worse are anonymous but describe themselves and their interests like it's their social life

[burnt dune]

but that something is not in any of my phones

[umbral lion]

sounds like spearphishing

[burnt dune]

he said i have long hair

( all my pfps in any social media have long hair )

and he has my number

but my number is on fb

so wduthik

[neat lintel]

dude dont use ur irl pic for discord

[umbral lion]

probably doesn't take much effort to scan discord profiles for matching faces

well relatively speakin

[neat lintel]

it's easy to get the full res and reverse search or something

[burnt dune]

good point

i just wanna makesure my phone isnt hacked

idc about my info on fb or insta

he can ssuck my dick

[neat lintel]

your phone can't get hacked

[burnt dune]

how do i know that

how do u know

[neat lintel]

because only you have your sim card

if someone can call you, it doesn't mean you've been hacked

[umbral lion]

well unless you're of high enough interest to be worth it its quite unlikely

[burnt dune]

im not

[bronze wedge]

If someone messages you "I have your info pay up" it's best to ignore them

[burnt dune]

how do i know if im not hacked

[umbral lion]

you never will 😎

[neat lintel]

stop being an idiot and do your own research instead of whatever you're doing now

[umbral lion]

hijacking conversation to bitch about linked in not taking down profiles and leaving them indexed in search engines for like a fucking decade

[neat lintel]

yeah someone with security clearance at your provider

even that is illegal

[umbral lion]

goddamn fucking trogolodytes those microsoft fucks

[umbral lion]

well i mean those sorts of people skirt the law how they please so that's not much of a counter

i was talking more like if someone hit your phone with the fuckin whats it called uhh pegasus? spyware

[neat lintel]

he isn't high profile enough

[umbral lion]

thats what i'm saying, but still a little bit of paranoia goes a long way

[neat lintel]

and the people that are use alternative providers

[umbral lion]

you'd be surprised

[neat lintel]

yeah it sounded like shizo adderall comedown

[umbral lion]

most elite rich stay on enterprise plans with public providers

and i want to say a majority have godawful op sec

[neat lintel]

yeah but it just doesn't happen man

[umbral lion]

yeahh

which makes me think i think pulling money is really ineffective with those tools

[neat lintel]

mark zuckerburg doesn't use whatsapp

[umbral lion]

its best for silencing dissidents

[neat lintel]

even though it 'uses the signal protocol'

he uses signal

[umbral lion]

zucc don't but the ceo of atleast 200 fortune 500 companies do

[neat lintel]

deep state appreciator very nice

[stoic tide]

Hello,
Why "Kernel" has so much different meanings in math and computing?
And each of those meaning, seemingly dpn't have similar characteristics
Do they actually have similar meaning?
Thank you

[umbral lion]

beware of the day ultraspyware becomes affordable for crime

[neat lintel]

they've all probably got the zucc on the ropes

[neat lintel]

dude, intel chips have had a backdoor since like 2016

everything is spyware

[umbral lion]

please don't use wikipedia like its an authority about these things, kernel usually has the same intuitive meaning on most things besides the kernel of an operating system

[neat lintel]

and being profited on

[umbral lion]

Management engine was pretty difficult to pull cohesive data from, interruption in the bitstream and your datadump will be annoying as hell to work with

i will agree NSA probably got plenty out of it but outside of actual vulnerabilities due to bad core design accomodating for the ME and PSP it was about the best it'll ever be

[neat lintel]

they say all that as if it's a problem they haven't solved

you know how hush hush the computing algorithms are for submarine sonar?

they've got that shit in the bag

[stoic tide]

in natural language, "kernel" = "core of things"? then why it becomes "mapping function" in math? so "kernel" = "mapping function"?
thank you

[umbral lion]

with upcoming fTPM standards being far more aggressive (pluton specifically) and being able to remotely update without allowing the user to do anything about it its kinda ridiculous how fucked the user is

[neat lintel]

muh sonar can't tell the difference between frozen surface ice and the ocean floor

sure bud

[umbral lion]

go learn some math and build the intuition yourself, nothing to give

[umbral lion]

Well yeah there's been blacked out algorithms for a long time now

[neat lintel]

this isn't etymology class

[umbral lion]

i'd dare say that a large portion of mathematics is swallowed up in the same hole

and what you see in academy is useless scraps

[neat lintel]

might even be extended to physics

[umbral lion]

not to talk shit on academics, there's plenty useful things in there but

[neat lintel]

they've been at a roadblock for basically a century

coincidence?

[umbral lion]

invention secrecy act guarantees its been in physics since the 50s

i knew a nuclear tech who's an absolute wiz

[neat lintel]

heck they might have a cure for cancer and are just using the hype for income now

[umbral lion]

i think the secret for the military was doing a good job segmenting information

[neat lintel]

we just don't know

[umbral lion]

the nuclear tech had no idea about anything to do with complex analysis but he could pick up on stuff real quick because most of what he understood was just obfuscated

or i guess specialized for the cause

[umbral lion]

well no this was more pharma's doing

[neat lintel]

"oh, i've seen something like that before"

and uses intuition like he's worked in 4d space or what

[umbral lion]

resolving most cancers with permanent preventative treatment requires a lot of what pharma can't profit off of long term

[umbral lion]

he told me he just had a lot of experience with signals n stuff i didn't want to prod

[neat lintel]

it's all sketchy. organ harvesting, the clinits keeping people on meds for the rest of their lives

[umbral lion]

finishing with this though, if you look at most treatments for cancer today they more or less keep the patient indentured for a while after treatment, obviously its a bit of cat and mouse but the problem likely would have been resolved with the billions donated if it weren't for the fact that there was trillions of profit at stake

[neat lintel]

can't say that here

[neat lintel]

yeah exactly

keeping them dependent

[umbral lion]

plus the promotion of lifestyles that keep you indentured, such as hormone treatments or the acceptance of obesity as of the past decade has definitely given me a think bout that

[neat lintel]

careful, consider removing the term

[umbral lion]

i don't care if i get banned lol

[neat lintel]

me neither. but it's a chore

all this and things like democratic procedures

how in control are we as people, really

[umbral lion]

dont get too lost in the doomer talk

there's always 2 choices aside from the ones that railroad you

join em or leave em

[neat lintel]

wasn't trying to go there. just extending it to talk about democracy

[umbral lion]

nothing stopping you from going innawoods and living out your life all ted k like

[neat lintel]

strive to become successful within the system, or to be independent of it

in a way

[neat lintel]

dude

[umbral lion]

i'm serious though, partaking is a choice, although that choice is going away over time

[neat lintel]

going away real fast. most higher-academic institutions basically require willful ignorance to be recognized

[umbral lion]

i'm not talking about that really

[neat lintel]

just look at the man that discovered dna, and got the nobel prize for it

[neat lintel]

all his degrees taken away because he said certain social outcomes were partly the result of genetics

[neat lintel]

in what way?

[umbral lion]

i'm talking about the internet being restricted, and all avenues to access it being vetted, and children having their genetic information held onto for an interminable future right at birth

that's all real things, fuck academia lmao

[neat lintel]

it's probably the biggest meme. a phd is just a club membership

[umbral lion]

i'm not talking about that dude

i'm saying that there will people who's entire lives will be assigned numbers and values and expectations

born in this day and age, evaluated in the dataset of insurance and advertising agencies

completely without the choice to leave that

[neat lintel]

like that, yeah

just variables to maximize for profit in an algorithm

sending certain ads etc.

does that really play out as much as the others?

surely advertisements aren't the cause of the current social contagion

[umbral lion]

the "great reset" is a likely end to the means being justified here

cause evidently insurance and advertising has capped out and has reached the point of recursive degradation

[neat lintel]

and i'm not sure money is their objective

[umbral lion]

nope, don't care to read about it either

too busy learning math

[open aspen]

weird flex but ok

[umbral lion]

thanks

[dim nebula]

Hi!
Does anyone know rational expression

[leaden torrent]

#❓how-to-get-help

[ripe wasp]

what math level would you expect from a motivated top high school student (in the us) entering a prestigious college for a math major?

i’ve heard like most mit admits have already studied basic abstract algebra/analysis + probably some like number theory by they time they enter school

[bright hill]

I've heard there are about 4 students that're at about the same level as moth that enter Harvard each year

[ripe wasp]

i’m not really talking about like outlier kids like imo representatives, but the typical average student entering a good college (obviously not average in the normal sense)

[ripe wasp]

what level is moth?

[bright hill]

Graduate

[ripe wasp]

i see

well i’d still consider those people outliers

[bright hill]

I think most have done the stem AP classes but not much more

AP calc, physics, etc

[ripe wasp]

there’s probably some students who come from very targeted math high schools which cover like calculus at 8th grade and end up at like high undergrad/graduate level by graduation

[ripe wasp]

ah that makes sense

seems pretty realistic

[bright hill]

Yeah

Like

More than that, how on earth are you going to prove your knowledge

[ripe wasp]

that’s true

[bright hill]

I wonder how/if moth did that actually

[ripe wasp]

the best way would probably be just like taking dual enrollment right

[leaden torrent]

i would be very surprised if a dual enrolment situation allows students to take high-level math courses

"high level" meaning upper UG/early grad

[ripe wasp]

hmm good point

i can’t think of any way other than just placing really well in competitions

[bright hill]

Bruh, that's a thing???

I wish we had that here

[ripe wasp]

like even if you put ‘self studied undergraduate level math’ on an application, would the ao’s even look at it a second time without any proof that you did so?

[bright hill]

You should prolly ask in #advanced-lounge

[ripe wasp]

i also don’t have this as an option idk what to do

[bright hill]

This server has really warped my sense of how much HSers take UG courses lmao

[leaden torrent]

well i wouldnt even expect the people processing applications to recognize that, say, hatcher is a big boy math book for example

well it has "topology" in the name so they might

but idk, imagine an applications person looking at this lmao

at a graduate level, the applications committee is in-department (or at least works closely with it)

but at an UG level i dont think thats the case even at top schools

[bright hill]

It is?

My perspective is fucked

[leaden torrent]

big boy relative to the average applicant

[bright hill]

But the prereqs for that is like, a good course in algebra and basic pointset, isn't it?

[leaden torrent]

how many high schoolers do you know have point set

[misty obsidian]

whats pointset

[bright hill]

A handful, and all on this server lmao

[bright hill]

The necessary formalism to do topology, analysis etc

[misty obsidian]

oh ok

[bright hill]

It's super general so it can be applied to any arbitrary set

No matter how abstract

[misty obsidian]

k

[eager reef]

I must say this server has done the same to me

I have gaslighted myself into thinking that I should’ve done like 5-6 additional courses so far

[misty obsidian]

Is differential equation, Matrices, Vector Algebra and Linear programming normal topics for senior year high school students

[bright hill]

NO

Lmfao

Most HSers don't know matrices are a thing

[eager reef]

What

[misty obsidian]

what they are gonna be in my class 12th book lol

[eager reef]

Matrices are very much a HS topic here

[surreal sapphire]

eh, basic matrix algebra is a topic in many highschools

sometimes they arent

its not like adding and multiplying matrices is hard

[eager reef]

But like not in terms of

This defines a linear map

And vector spaces

[surreal sapphire]

and this list is really weird, because "matrices" isnt really a topic you learn

[eager reef]

Just kinda

Funny square

[bright hill]

It isn't in my country

[eager reef]

We had them in some probability stuff

[surreal sapphire]

linear programming and differential equations are on the other hand super hard

[eager reef]

Uuh

What was it called

[surreal sapphire]

but then again, knowing what a differential equations is is easy in hs

[eager reef]

Where the sum of the entries is one

[surreal sapphire]

and writing a linear program

so they could be covered i guess?

but the necessary theory not

[eager reef]

Yeah we did intro diff eqs in physics and maths

[bright hill]

Ye

We know what a diff eq is too

[misty obsidian]

Matrices 3.1 Introduction 3.2 Matrix 3.3 Types of Matrices 3.4 Operations on Matrices 3.5 Transpose of a Matrix 3.6 Symmetric and Skew Symmetric Matrices 3.7 Elementary Operation (Transformation) of a Matrix 3.8 Invertible Matrices
Is these stuff common for HS

[eager reef]

Btw darQ how’s that plan going

[leaden torrent]

that is a bit above what i would expect from a north american high school course

[eager reef]

Has the non existent squat rack thrown you off track

[leaden torrent]

but below what i'd expect from a university lin alg or calc 3 course

[eager reef]

Or are you managing

[bright hill]

Hardly going

I did a single day lmao

[eager reef]

Which one

[bright hill]

First

[leaden torrent]

that said, its less that its particularly difficult and more that its simply something high school doesnt bother to cover

[misty obsidian]

ohk i guessed it lol I am gonna study this stuff next year

[leaden torrent]

i would consider most of that list conceptually lighter than e.g. conic sections

[bright hill]

The Bench and stuff

[misty obsidian]

ohk

[surreal sapphire]

its hard to motivate

you can do gaussian elimination i guess

but motivating the transpose takes some work

cant imagine a highschool do it properly

[bright hill]

Btw, my biceps don't recover that fast for some reason

I did close grip chin ups at first 10 reps I think just fine

But when I tried to curl by the end of the workout I couldn't even curl a 10 kg

[leaden torrent]

motivate the transpose by wishing to define the pseudoinverse in order to compute the condition number of matrices

🧠

[bright hill]

[leaden torrent]

this seems very stupid but i genuinely think it might be the easiest motivation

[eager reef]

The chin up can be heavy on the bicep

You can kinda manipulate it to hit more of the lats than the bicep tho

[misty obsidian]

How do you get roles such as Undergrad?

[eager reef]

Which I think is the point in the program

You wouldn’t put two bicep exercises in one day with that plan

[bright hill]

#info

[misty obsidian]

ohk thnx

[bright hill]

The biggest barrier rn is time

I sometimes finish uni at 17.30

[eager reef]

How are you running into time issues with that plan

[bright hill]

And the residence gym closes at 19.0

I also have to dine coz the dorm's restaurant also closes by 19.0

[eager reef]

Oooh

Bruh

Are you in uni or in some kind of youth hostel man

[bright hill]

I dunno, it's dumb

Uni attendance is mandatory so I have basically negative time in the morning

[limber thunder]

mandatory attendance

[limber thunder]

huh it's not atypical for me to end uni at ungodly hours

like I only have class in the morning but I study or attend seminars in the afternoon

[bright hill]

Yeah, I'm really hoping to get it waived

[arctic grove]

[tender tulip]

So i want to be able to check if a number n represented in 63 bits is, infact, a perfect square, WITHOUT using square roots "explicitly"

aka casting to a double, doing the sqrt function, then casting back, due to the loss of like, 10 bits

Is there a way I can do some dyadic bullshit and hensel lifting OR a dyadic newton's method on x^2 - k = 0 to maybe find out if a number is a square, possibly after some bit masking

[eager reef]

Man your uni experience is weird

[bright hill]

Well, uh

Coz it technically isn't a uni

[eager reef]

But?

[bright hill]

It calls itself a "school"

But like

In french

Dunno if the meaning is different haha

[eager reef]

[bright hill]

By the end i don't get a bachelor's degree

I get w/e this is https://en.m.wikipedia.org/wiki/Engineer's_degree

[eager reef]

You’re doing engineering?

[bright hill]

Yes

[eager reef]

Why

[bright hill]

It's a long story

[eager reef]

[surreal sapphire]

use gmp

the short answer is you can for most numbers figure out by checking mod various integers p

the long answer depends on the computer architecture you use

[tender tulip]

gmp?

[surreal sapphire]

gnu multi precision arithmetic library

testing modulo smart chosen values of p is super fast

because you only have to examine a few bits

and this has success rate of 90%+

after a single test almost

so unless you are very unlucky this runs in constant time

[tender tulip]

mmm

[tender tulip]

what do you mean by this

what is "p"

[surreal sapphire]

square in Z implies square in Z/pZ^\times

depending on p there are only a few values that can occur

and if p is related to your architecture in the correct way it can be done by checking the last bit(s)

then only "pseudo-squares" remain

and those are rare

[tender tulip]

So just, quadratic/cubic/quartic... residues

[surreal sapphire]

you asked about squares not cubes etc

[tender tulip]

I was referring to this

[surreal sapphire]

?

[tender tulip]

p prime or just any integer

or pow of 2?

[surreal sapphire]

this only cares about quadratic residues

p can be anything

you start by testing mod 256

this can be tested by only checking the last byte

[tender tulip]

what determines what we should chose for "smart values"

[surreal sapphire]

and there arent that many residues that occur

[tender tulip]

mmm masking

[surreal sapphire]

certainly constantly many

and this already has a success chance of 80%+ to rule out wtv you are testing

then depending on architecture you can do more tests

if you are super unlucky you have to take a squareroot i guess

but thats almost impossible

not sure if its necessary actually, never looked at the details

[surreal sapphire]

oh kinda overread, it depends on the architecture and how easily your processor can access the data iirc

On a 32-bit system similar tests are done mod 9, 5, 7, 13 and 17, for a total 99.25% of inputs identified as non-squares. On a 64-bit system 97 is tested too, for a total 99.62%.

and

Only 44 different values occur for squares mod 256, so 82.8% of inputs can be immediately identified as non-squares.

[tender tulip]

jesus

i wanted to be able to explain the choices I made

[tender tulip]

is this true for polys

[surreal sapphire]

sure?

reduction mod an ideal is a homomorphism

[tender tulip]

is this related in any way to hensel lifting

[surreal sapphire]

no

[tender tulip]

this is for reg 16 bit ints, right

[surreal sapphire]

it doesnt matter

the probabilities change, they depend on the distribution of squares vs non-squares

[tender tulip]

oooooo

[surreal sapphire]

like, if you only test small or only big numbers then you would adjust those tests maybe and do more/less

[tender tulip]

Alrighty

[surreal sapphire]

gmp has arbitrary precision integers though

[tender tulip]

so we just chose ones that have the lowest percentages of quadratic residues

[surreal sapphire]

they are chosen bcs they can be computed fast

[eager reef]

Loch

Do you wanna see a funny prüfungsstatistik

[surreal sapphire]

sure

i think the number of residues vs non-residues depends only on the number of primes in the factorization?

i forgor

[eager reef]

DMs

[tender tulip]

w h y

[surreal sapphire]

architecture reasons

These moduli are chosen because they’re factors of 2^24-1 (or 2^48-1 for 64-bits), and such a remainder can be quickly taken just using additions (see mpn_mod_34lsub1).

In any case each modulus is applied to the mpn_mod_34lsub1 or mpn_mod_1 remainder and a table lookup identifies non-squares. By using a “modexact” style calculation, and suitably permuted tables, just one multiply each is required, see the code for details. Moduli are also combined to save operations, so long as the lookup tables don’t become too big. gen-psqr.c does all the pre-calculations.

[tender tulip]

wtf 48

[surreal sapphire]

by now i pasted most of the documentation

https://gmplib.org/manual/Perfect-Square-Algorithm

[tender tulip]

Why 48 and not 64

[surreal sapphire]

However, not all 64-bit instruction sets support full 64-bit virtual memory addresses; x86-64 and ARMv8, for example, support only 48 bits of virtual address, with the remaining 16 bits of the virtual address required to be all 0's or all 1's, and several 64-bit instruction sets support fewer than 64 bits of physical memory address.

[tender tulip]

… how have I not heard of this

[surreal sapphire]

probably didnt read the first paragraph on wikipedia

[tender tulip]

i’m taking computer science

which is why I am doing this, to optimize something I made for a project

[surreal sapphire]

are you taking a computer architecture class

[tender tulip]

no

[surreal sapphire]

well, then there is your answer

the answer is almost always to use a library for things like this

someone else thought more about this than you ever will

[tender tulip]

I want to comprehend why this works, and that 48 bit fact is SUPER useful

thank you btw

[surreal sapphire]

oh yeah, i shouldve just posted the link earlier

gmp is open source, you can also check the code

[tender tulip]

a lot of this is number theory stuff I also want to learn

[surreal sapphire]

the author should be listed somewhere too

if its really important to you, you can email them

uhh

there is a standard book due to cohen

but i doubt its a lot of fun to read 💀

the only better book i know is german however, so ...

there is a chapter on square detection in it too

Cohen's "A Course in Computational Algebraic Number Theory", chapter 1.7.2

it lists a few alternatives and gives proofs on why they work

they are architecture agnostic though

[tender tulip]

what

[tender tulip]

trying to find this

[surreal sapphire]

its in the link i posted

[surreal sapphire]

^

[tender tulip]

I’m there

alright

[burnt dune]

.

[neat lintel]

Pls fill this out

Its hw

https://docs.google.com/forms/d/e/1FAIpQLSdVgItLXUIlmoO3kTEDaJpWECFAEG45z4YsH88RUXxi6YX_Dg/viewform?usp=sf_link

[dusty wagon]

I wanted to but I need to log in

[next schooner]

Why do you need my email for this lol

No thanks

[umbral lion]

why da kids turning to datamining

what is this world coming to 😔

[short pasture]

My bad bruh

[dusty wagon]

It doesn’t work anyway

But nice try

[short pasture]

good

[proud olive]

What did he do?

[short pasture]

i tried to @everyone

[proud olive]

Oh

Trick is to make some faulty bot do it for you

[short pasture]

Damn

You study pure math in cambridge by any chance

[proud olive]

I study pure math by what kind of brigde now?

[short pasture]

Are you a college student at all

[dusty wagon]

Are you?

[short pasture]

Im applying to math in college this year

hoping someone has some god tier tips

I'm applying cambridge but supposedly it's really hard

[dusty wagon]

Tip 1: No tip can reduce the suffering

[proud olive]

Never ever take the weekend off

There you go

God tier tip

[dusty wagon]

Always take the weekend off

Your brain needs rest

[short pasture]

tbh i take most weekdays off

I don't really know what to do

Like Ive done UCAS and stuff

[umbral lion]

if you can minmax standardized tests, do it

[short pasture]

What you mean by minmax

[umbral lion]

a relatively high percent cheat or pay for grades so learning how to spread high marks over multiple sessions (something you do here in north america for SAT or ACT) and being really good at test taking can be done with a lot of effort

[proud olive]

Figure out a way to solve the problems as fast as possible by using the given options

Can save a lot of time by doing that

[short pasture]

oh true

I had SATs this saturday

[umbral lion]

there's a few very convenient mental shortcuts, such as considering whats first not the answer

[short pasture]

I got 760 in math last time

I want to get higher

[umbral lion]

forget what their out of, is it 900 or 1000?

[short pasture]

800

[proud olive]

760 sounds pretty good

gj

[short pasture]

world is so competitive nowadats

[umbral lion]

you can probably do it but dont neglect the language portion

[proud olive]

Yeah I'm glad I'm done with hs

[short pasture]

Did either of you apply to UK

[umbral lion]

lmfao im 5 years removed from all this and back then test score inflation was already a problem, can only imagine how much worse it is now

[umbral lion]

no

[short pasture]

cause my number one college is cambridge

I was hoping someone here has like

applied here

and got in

[sharp bough]

can someone help me with this

[short pasture]

y is 24 and x is 20

Since it's a right angle the intersect from o will be the midpoint

[solid snow]

#❓how-to-get-help

[open aspen]

And pls don't just give ppl answers

[neat lintel]

How do I ß-reduce something

😔

[weary island]

Is anyone good enough in explicits formula and reccursives formula to help me ? on the help 27 channel.

[open aspen]

The rudest of baits

[manic ginkgo]

So I came across this statement today "One third of all numbers are divisible by 3" and for some reason wanted to delve into it a bit more. So, am I right in saying that it's:

true for integers, false for real / complex numbers, etc. However, is it even possible to assign a meaningful proportion in the case of reals / complex numbers? How would this kind of counting work?

[umbral lion]

the usual manner of counting is by correspondences, however its a bit meaningless in the case of the reals unless you're comparing two uncountable sets of things, in which case i don't think you can make a reasonable assessment of densities that way

[manic ginkgo]

hmm I see, thanks

[umbral lion]

i'm sure there's someone really into analysis around here who could tell you more though

[peak tide]

also worth asking what you mean by divisibility by 3 in the case of real and complex numbers... aren't they all divisible by 3?

[storm sage]

^

[storm sage]

you could think about it in terms of measure theory

idrk how measure theory works though

[proven hornet]

lmao

[manic ginkgo]

Dunno either

[errant arrow]

Yo

Any good books

Or content

For someone looking to learn math

For engineering

[limber thunder]

divisibility only really makes sense for integers, a number x is divisible by 3 if x=3y for some integer y. If you allow x to be real/complex you get that they'd have to be integers anyway, and it's meaningless to allow y to be a non-integer.

[limber thunder]

and a way of giving a well-defined notion of "a third of all positive integers" is through the concept of https://en.wikipedia.org/wiki/Natural_density

under which the set of all multiples of 3 is indeed a set with natural density = 1/3

[limber thunder]

as for books I don't think I can rec much more than like, Stewart's calculus which includes a bunch of engi applications

but if you mean like casual content then Zach Star is an engineer that makes videos about math and their applications, sometimes in engineering https://www.youtube.com/c/zachstar/videos

[errant arrow]

I'm looking to learn math in general tho

Like I'm kinda lost

Idk which path to follow in order to get the knowledge I need for calculus algebra and geometry

[limber thunder]

have you tried Khan Academy

they probably have a pre-calculus section

[errant arrow]

Tried till 8th grade and then

Didn't know where to go

[errant arrow]

Will try that one I guess

Not sure if I have what it takes tho

[wooden flax]

TIL people read Lang cover to cover

@teal lion

[limber thunder]

TIL people read Lang

[peak tide]

Lang wrote like 100 books, some of them are actually good

[limber thunder]

sure thing

I'm just shitposting

[neat lintel]

I recommend basic mathematics by lang if you want something that covers high school math but u want proof.

[meager sonnet]

Math! Encounters with High School Students

[neat lintel]

I fr thought your username said the one and only snoop dog

I read it as that at first

[iron osprey]

@meager sonnet cube 2 sauerbraten instagib is only arena fps

[bright hill]

22 45 90 minutes into the lecture (the whole lecture was like that)

The lecture so far her literally been the prof writing definitins and stuff down

And people writing them into their notebooks

Kill me

[neat lintel]

This game is the best game

[fringe needle]

That’s just how lectures are at first but it’s not because you already know some of the material that you’ll stay ahead so don’t let down

[bright hill]

I won't

[wanton pecan]

hi

[random cargo]

Yo

[spiral saffron]

is there a real-life (non theorical) example of application for complex number in polar coordinates?

[storm sage]

Yes

[spiral saffron]

i can't understand what's the damn Im and Re and a and b and z ...

[storm sage]

This is used very often in anything that involves trigonometry, for example

Basically anything that involves oscillation will be modeled by e^it

so like for example a pendulum

or an ac circuit

complex numbers in polar coordinates are used frequently in the solution to how these systems behave

[spiral saffron]

ah ok

[storm sage]

The way you should think about polar coordinates is that it lets you keep track of an amplitude, an angular frequency, and a phase simultaneously which is why we love complex numbers

which are all really important quantities to keep track of if you're working with stuff that oscillates

[spiral saffron]

i googled it but i don't understand anything about complex and ac circuit

[storm sage]

so like

amplitude = how big the oscillation is (for ac circuits, this is like how big the voltage gets at its maximum), angular frequency = how fast the oscillation is (for ac circuits, this is like how many times a second the current switches from clockwise to counterclockwise), phase = what part of the oscillation the system is at (for ac circuits, this is like whether it starts clockwise, whether it starts counterclockwise, whether it starts with zero voltage, etc)

[spiral saffron]

is there a schema somewhere for the application of complex on circuits?

i can't find anything visual ; (

[spiral saffron]

then, is there a link between clocks and how particles behave (quantum physics)?

i heard that shrodinger used complex numbers to manipulate the wave functions (a concept from Broglie, right) right?

[storm sage]

how much math do you already know?

[storm sage]

yes! quantum mechanics models stuff like electrons as "wave functions"

for the same reason

easy way to store both an amplitude and a phase

[spiral saffron]

i just love to learn about how things work by analogies and history

[storm sage]

Lol

Do you know any calculus

[spiral saffron]

yeah

[storm sage]

What about differential equations

There is a good differential equation lecture playlist on mit ocw

That's where I learned diffeqs from

I don't know of any short visual videos that explain why e^it is important, but I'm sure they exist if you look them up

[spiral saffron]

i'm on the level of an undergraduate in maths

but i'm relearning everything from first principles

i need to behave like a 5yo

[spiral saffron]

yeah i learn it from caltech videos

[storm sage]

well one of the reasons we use e^it is because it has nice derivative properties

it's an eigenfunction of the derivative operator

so like d/dt e^it = i e^it

this makes it extremely useful to solve differential equations

[open aspen]

You can highlight text in notability?? Like it snaps to the right shape? Wow TIL

[errant arrow]

how much math do i need to solve this? does anyone know? (the goal is to reduce it to a single transfer function)

[clever lintel]

does anyone mind giving a second opinion on #help-51 we have just gone back and forth and made no progress we both think it is suppose to be done a different way, thanks.

[bronze wedge]

<@&268886789983436800>

[waxen shoal]

is it an easy thing to derive n(n+1)/2

instead of memorizing it

[open aspen]

Derive that from what

Some sorta summation?

[worldly island]

One; lion; lemon; orange; apple; ball

a) tie
b)hydro
c)class
d)juniper

[velvet dagger]

@waxen shoal think about it like this

If I add 1 to n

And double that

That's like

1 + 2 + ... + n
n + (n-1) + ...+ 1

[umbral lion]

habanero

[velvet dagger]

But you'll notice that if you add something from the top row by the corresponding entry in the bottom row

[worldly island]

?

[velvet dagger]

That's n+1

And we have n such terms

So n(n+1) = 2(1+...+n)

[trim sparrow]

Hey guys, i watched tutorial online (math high school) but mostly only teach me how to solve problem in particular topics, any recommended tutorial or book to make me understand those? (Like gilbert strang lecture for linear algebra)

[velvet dagger]

Khan Academy I think is decent

[tender tulip]

I'm wondering if you can like, construct a sheaf of semigroups

why? the answer is why not (also because I'm bored)

let S be a abelian semigroup, then we can consider the collection of all multiplicatively closed subsets, denoted L(S). Well, we can consider the product of two subsets to just be the collection of all the products between them, forming a semigroup structure on L(S). From there, we can define an ideal to be a subset A such that for all subsets B, AB is a subset of A. We can then define the collection of ideals to be I(S). For any A and B in I(S), then AB ⊆ A and AB ⊆ B, so we have a sort of join-semilattice

So by extension, for any ideal C
A ⊆ C OR B ⊆ C => AB ⊆ C

so we can create a collection of prime ideals, where the aforementioned condition is biconditional for all A and B, and now we have a topology

[neat lintel]

If this is signal processing, a decent bit. Most transfer functions are complex functions so you should know some basics of complex analysis, as well as fourier analysis

[tender tulip]

actually, gtg

[placid willow]

Noot Noot

https://tenor.com/view/pingu-entered-the-chat-pingu-irl-real-pingu-face-reveal-gif-20047697

[errant arrow]

Holy

It is lmao

[sacred arch]

I made a hyperbolic geometry visualization out of post its and tape

Semi-related random thought, is there any sort of equivalent to Penrose tiling in hyperbolic space?

Also this thing is probably much cooler in person cause you can actually look at abd play around with it

[waxen shoal]

why isnt law of cosines taught first instead of pythagorean theorem

[ancient flame]

bc students typically learn pythag before trig

[waxen shoal]

i mean i learned pythag before law of sines/cosines but never really had the law of cosines importance emphasized in my school

i remembered law of sines more but it was never said directly to me that pythag is a special case of law of cosines.

[chilly hull]

pythag is understandable without trig

and its also kinda important

[sacred arch]

Youve kind of got a point but I think it comes down to the fact trig is usually taught later

Pythagorean theorem is just a bit easier to teach

[neat lintel]

Should be, the hyperbolic space admits a lot of tilings

[bright hill]

@woven whale unless I made some sort of mistake, the derivative of $||F(x)||$ at $\bar{x}$ is $\frac{1}{||F(\bar{x})||} F(\bar{x})^\text{T}DF(\bar{x})$

[fathom swallow]

DarFuQ
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

DarFuQ

DarFuQ

[plucky seal]

can anyone help me on this 1 problem real quick?

[bright hill]

please see #❓how-to-get-help

[bright hill]

...the directional derivative (the direction being d)...

[dusty wagon]

Pythagoras is trig

[ancient flame]

bruh

[wooden flax]

@light needle dont want to interrupt discussion but what is a good resource for cstar algs

[light needle]

for an intro, pederson for func anal into murphy is p good imo

[wooden flax]

I see

thanks

[little slate]

can anyone explain how -2 modulo 26 is 24

[wooden flax]

-2 = -2+26 mod 26

[little slate]

i understand modulus division is the remainedr but dont understand how it works here

[wooden flax]

sure, so essentially 26 can divide -26

but this has remainder of -2-(-26)=24

does that make sense?

[little slate]

how does 26/-26 have a remainder?

[wooden flax]

lets work with smaller numbers

can 3 properly divide 29?

[little slate]

no

[wooden flax]

what is the quotient/remainder?

[little slate]

r=2

[wooden flax]

correct

what we did was first find the greatest integer less than or equal to 29 that is a multiple of 3

which is 27

then we calculated the quotient to be 27/3=9 and then took the remainder to be 29-27=2

do you follow?

[little slate]

yes

[wooden flax]

so now if we are working mod 26

consider the number 24

the greatest integer less than or equal to 24 that is a multiple of 26 is 0

we have 0/26=0 and 24-0=24

thus the quotient is 0 and r=24 so 24=24 mod 26

do you still follow?

[little slate]

im thinking

[wooden flax]

the greatest integer less than or equal to -2 that is a multiple of 26 is -26

[little slate]

we are doing 26 mod 24 right?

[wooden flax]

correct

[little slate]

makes sense

[wooden flax]

and we have -26/26=-1 and -2-(-26)=24 so r=24

so -2 = 24 mod 26

does this make sense?

in general, you have a = a + kn mod n for k \in Z

if you dont want to work with remainders you can also define a = b mod n if b-a is a multiple of n

then -2=24 mod 26 is obvious as 24-(-2)=26 which is obviously a multiple

let me know if you have any questions

[little slate]

alr thx

[wooden flax]

no problem

[leaden crown]

Is anyone good with math related to audio? Like measuring sine waves based on amplitude, peak-to-peak value, period, wavelength, and frequency? I need some help with some problems related to this.

[azure nymph]

https://dontasktoask.com

Also #❓how-to-get-help

[leaden crown]

@azure nymph Hey buddy, I don't need you to send me links like that. FYI it's difficult finding servers that cover audio-related math so I only asked my question here to check if anyone is familiar with audio math. I was very clear, so need to be that way. Have a good one though...

@azure nymph Sorry if I misunderstood and you were only trying to help. I've just run into some sarcastic, rude people at times.

[rough dirge]

Have you ever felt this mixed feelings of you understand a concept and you don't understand it at the same time? Like for example, you can solve problems that are related to a particular concept, but for some reason it still annoys you as if you don't truly understand the concept, and instead it feels like you memorised it.

[bronze wedge]

Uniform integrability was (for a long time) something I had a hard time intuitively grasping

I hear a lot of people have a hard time with localization

[rough dirge]

thank god, I thought I was the only one
it feels strange isn't it? do I understand it or do I not understand it
Ik I can do problems related to it
but it doesn't feel clicked

[deep grail]

Prerequisites for geometry

[tender tulip]

of rings

Because if so that’s ironic as fuck because that’s what’s confusing my intuition rn lol

[eager reef]

maybe look into what this corresponds to in alg geo

that's what loch suggested at least i think

(if you're talking from a comm alg perspective)

[tender tulip]

yes

i don’t think there is a non-comm analogue that generalizes well

i’m mostly considering integral domains aswell

[eager reef]

no i meant like

if you're learning this because you're reading alg geo it'd be useless to say look into the alg geo perspective

but if you're reading comm alg without knowledge of alg geo it might be helpful to look up the connection occasionally for motivation of the topic

[tender tulip]

isn’t the alg geo perspective like exclusively used for structure sheafs or smth

i’ve heard about it briefly skimming through the alg geo chat

[eager reef]

im just echoing here

so im afraid i cant answer that

[bronze wedge]

lol I'm talking about "localization" in stochastic analysis

Though that applies too

[tender tulip]

[bronze wedge]

Localization (and Sigma localization) are basically ways to generalize "sigma finite/additive/etc measures", but for some reason no one explains it this way

[steep trellis]

hey does anyone have a good resource for understanding or visualizing linear algebra concepts? I'm having difficulty understanding the core of things from Vector spaces/subspaces and after in regards to spans, linear independences and all the theorems that come with it

I guess I'm mainly having difficulty because a lot of the theorems that appear in class seem very random and I can't connect concepts in my brain

[bright hill]

You should definitely check out 3b1b's essence of linear algebra

[eager reef]

Essence of linear algebra

[bright hill]

Snipped

[eager reef]

Who sniped whom

Im first on my Screen

[bright hill]

I'm first on my screen

[eager reef]

We need a third opinion

[storm sage]

darq was first

[bright hill]

YES

[eager reef]

FUCK

[storm sage]

LOL

[bright hill]

WE WIN DEEES

[eager reef]

Win dees nuts are in your mouth

[velvet dagger]

DarQ was first yes

It's okay Timo someone's gotta have the skill issue

[steep trellis]

ok thank you

[eager reef]

I got my revenge

It’s okay

[bright hill]

This is totally normal when you're first exposed to the material btw

Especially in higher level math

Things become much clearer in picture the more you come in contact with the material in the wild, however

And the more you do exercises, etc

[hidden phoenix]

anyone know how to solve this?]

[leaden torrent]

try #discrete-math

but a hint: theres a very naive solution that likely won't be minimal but that does successfully cross the bridge

||have each woman cross with their husband and then return alone. then simply have them cross back in pairs, with a single woman returning each time||

[hidden phoenix]

they cant return alone because theyll be in the presence of a man who is not her husband

[stray kite]

how are proofs by contradiction usually structured in actual papers

do they ever just say "suppose, for contradiction"?

[fervent pebble]

idk fs but i seriously doubt it

i'd bet it's something like: assume blahblahblah. <.....> so we see our assumption was false, and thus <....>

[rain dome]

Try solving the 3 lions and 3 goats or the wolf, goat, cabbage puzzle first to work your way up to the n problem.

[orchid ginkgo]

Okay here's how it should be:
At one time, a couple shall cross the bridge with the torch and the woman shall return back and hand over the torch to another couple.
Like this, after 6 crossings all men will be on the other side and all women (with the torch) will be left to cross.
Now, any one woman will go with another, dropping one to the other side and in the end, everyone will be at par.
Thereby for 3 couples, the minimum amount of crossings will be 9

The same method would apply to 4 couples. Each husband would be dropped by her wife until only all women are left to cross.
The answer will be 13 in this case.

For n couples:
Let's suppose only 1 couple had to cross the bridge.
Thus, only 1 crossing would be needed to cross the bridge.
For 2 couples, at least 5 attempts would be needed to cross the bridge. (Refer to the method above)
If you've noticed *for every couple added, the minimum number of attempts needed to cross the bridge increase by 4. ( For 1 couple-1, for 2 couples-5, for 3 couples-9, for 4 couples-15)
This forms a simple Arithmetic Progression.

Therefore, the minimum number of attempts needed to cross the bridge by n couples is:
=> a + (n-1)d;
where a= the first term of the progression, n= number of couples and d= common difference(here;4)
=> 1 + (n-1)4
=> 1 + 4n-4
=> 4n-3

[orchid ginkgo]

Here's your solution!

[neat lintel]

Give it a shot guys

You will fall in love with the solution!

[tender tulip]

I cannot read your handwriting

[tender tulip]

I am going to punch you for introducing quartics

Symmetric polynomials my hated

[woven whale]

Let x,y,z be real nos such that, x + y + z = 0 and xy + yz + zx = -3. Find the value of |x^3y+y^3+z+z^3x|

[tender tulip]

all of those are sym polys

except the last one ig

(t-x)(t-y)(t-z) = t^3 - t^2(x+y+z) + t(xy + yz + zx) - xyz = t^3 - 3t + xyz

Me trying not to use cardano's

the quartic term of the aforementioned poly is actually x^3y+y^3+z+z^3x

@neat lintel Is this actually solvable?

If we let xyz = w, then x^3y+y^3+z+z^3x = -18w

I can't think of a way to find what w is, I can probably do some poly bullshit though

Actually I can, but it seems like a fuckton of work

[neat lintel]

Yes it is

[neat lintel]

9

[neat lintel]

Correct!!!

How did you do it tho

I plugged in x=0 and y = -z = sqrt 3

[neat lintel]

Ayeee

Don't hate the player, hate the game

[neat lintel]

But there is one more way of getting to the solution

Yeah plug in x = -y = sqrt 3 and z = 0

Nope

That's another way of getting to the solution

Like without plugging

Proper method

Like Solving it

Multiply xy + yz + zx by itself and calculate in the polynomial ring K[x,y,z]/(x+y+z)

[neat lintel]

I dunno if that will work

But its not that

It will

[neat lintel]

I consider these types of solutions to be hit and trial.

Just plugging any value and hoping for the best

[neat lintel]

Would love to see your solution if thats the case.

In fact there must exist a polynomial P such that
(xy+yz+zx)^2 + P(x+y+z) = x^3y + y^3z + z^3x

[tender tulip]

you can see that -18xyz = xy^3 + yz^3 + zx^3x

just finding xyz is what got me stuck

f(t) = (t-x)(t-y)(t-z) = t^3 - 3t - xyz
Knowing f(t)^3’s quartic term is what we are looking for, we can use binomial theorem basically

[neat lintel]

xxyy + 2xyyz + 2xxyz + 2yzzx + yyzz + zzxx
-xxxy -yyyz -zzzx + (x+y+z)(xyz)

Yeah that should work

[tender tulip]

How would I get xyz if I used my method

we are only really given 2 equalities trying to find a solution for 3 variables which seems fucky

[neat lintel]

Why should there be a reasonable form for xyz

[tender tulip]

so how would we solve for the abs value of the quartic term of f(t)^3

[neat lintel]

I don't know

Hint

Just square the -3 term and then for each term in the extended product substitute for y = -x-z and do the same for x and z

The solution pops out

[tender tulip]

Like, if we know x + y =0, we can't really find xy

[neat lintel]

Jesus Christ

[tender tulip]

in this case, if we know x + y + z = 0, and xy +yz + zx = -3 I don't see how we can find xyz

we could use roots though but they get finnicky

[neat lintel]

You guys can

More hints

[tender tulip]

if we use some solution, then yeah, but like otherwise we can't find it afaik

[neat lintel]

\begin{align}
(xy+yz+zx)^2 &= xxyy + xyyz + xxyz + xyyz + yyzz + xyzz + xxyz + xyzz + xxzz\
%\intertext{this is the binomial formula}
&= xxyy + 2xyyz + 2xxyz + yyzz + 2xyzz + xxzz\
&= xx(-x-z)y + \cdots + yyz(-x-y) + \cdots + (-y-z)xzz\
&= -xxxy -xxyz + 2xyyz + 2xxyz -yyyz -xyyz + 2xyzz - xzzz - xyzz\
%\intertext{grouping terms}
&= -xxxy -yyyz -xzzz +xxyz + xyyz + xyzz\
&= -(x^3y+y^3z+z^3x) + (xyz)(x+y+z)
\end{align}

[tender tulip]

Lets assume we know
x + y + z = 0, then z = -(x+y)
xy+yz+zx = -3, let w = xyz, = -xy(x+y)
then f(t) = (t-x)(t-y)(t-z) = t^3 - 3t - xyz
Now, xy^3 + yz^3 + zx^3 is the quartic term of f(t)^3, and by using binomial theorem, we know that it's 8xyz

so |18xyz| = 18|xy(x+y)|

but we cannot say anything else, besides finding the matching z for some pair x,y

and for every (x,y) there is a different xyz

IF we had xyz SET, then we COULD find it

for 3 variables, we'd need 3 equalities to find a unique pair (x,y,z) (with certain conditions ofc)

[neat lintel]

Well in that case you can use one more result

[tender tulip]

I would say, |xy^3 + yz^3 + zx^3| = 18|xyz|

and leave it as that

[neat lintel]

Made you 2 more eqs

[tender tulip]

what did you chose as x, y

or y,z

[neat lintel]

Nothing

[neat lintel]

These are just general identities

[tender tulip]

once again, there shouldn't be only one solution

[neat lintel]

There is not

[fathom swallow]

Brudimann

[neat lintel]

Ok I give up, that's the solution though

[tender tulip]

yes, there is one for every x,y

or yz

[tender tulip]

y,z

However, if you DID specify xyz, or something related, then you CAN solve it

[neat lintel]

Literally just calculate it in the polynomials algebra

[tender tulip]

o N c e A GAIN

it's 18|xyz|

[neat lintel]

I did specify they are real numbers

[tender tulip]

that's not enough

[neat lintel]

But to make things more easy

The solution is 9

Y'all stupid

[tender tulip]

It's NOT

[neat lintel]

Lets say they are integers

[neat lintel]

It is