@leslietownes Oops...I actually meant loop hole in license verification / requesting...i.e. I can bypass the licensing indefinitely on their official server/website ...and they'll allow me xD

@TedShifrin No....they are just by accident...I dont look...they appear

Sort of like how I can glance at a typed page and see typos immediately, even though the author thought it was error-free.

We are cursed with these talents.

Yeah almost like that

And it is actually a problem for matlab because they might unncessarily fill up their servers with internet garbage....why? They allow verification on temporary mails and allow upto 5GB storage per account

I could literally store my Google Photos on MATLAB for free...xD (Google is discontinuing unlimited storage)

After a few months of fighting trying to learn basic Matlab, I gave up and stuck with Mathematica and Maple. I remember nothing of Matlab.

I believe Matlab was "invented" in the town in which I went to high school. Trivial useless fact.

the matlab language is horrible, but it has become a sort of standard in industry (dsp, etc.).

in the 80's there was nothing else that you could easily do interactive matrix computations on.

@copper.hat idts...I find MATLAB language fairly simple...it's almost like python

or probably they changed their language significantly since then

ummm, not sure i would put python and matlab in the same sentence...

Given a lattice $L$ as a discrete subgroup of $\Bbb C$ and an integer $n\ge4$ we can calculate the Eisenstein series of the lattice: $$G_n(L)= \sum_{\omega \in L,\omega\ne0} \frac{1}{\omega^n}. $$ What does the notation $\omega \in L$ mean?

What it always means.

$\omega$ is an element of the lattice. so is it an integral ordered pair, like (2,3) or something?

(assuming an integer lattice)

Yes, if $\omega_1,\omega_2$ is a $\Bbb Z$-basis for the lattice, then $\omega = m\omega_1+n\omega_2$ for some integers $m,n$.

I shouldn't have used $n$ because you already used it. But you get the point.

ah okay

@copper.hat depends...I used MATLAB for Machine Learning...and used Python with TF too....I found that MATLAB was a bit more versatile and fast and offered good gui...whereas TF/all ML libraries for py are Command line based

i'm a cli person.

uhm..so am I but...GUI didnt mean that it'd be slow....it is a cocktail of GUI and CLI

i have used both extensively, but every time i need to something a little different it is a struggle in matlab whereas in python i can usually find what i need quickly.

Ohh I see

i started using it with clive moler's fortran version.

before any of this namby pamby nan stuff

when divide by zero caused power failures and natural disasters.

and slide rules were so big they had a zero on them.

@copper.hat it's an insult to python

to be fair, python came along much, much later. user interfaces were dirty words back then.

experience i mean, not interface.

If you know Python, you should take a look at SageMath, which is built on Python. You can even use it online, without installing anything. I often use sagecell.sagemath.org to write Python on my phone.

i was very down on matlab.

I found it infuriating that the syntax was that everything — even one-dimensional calculus — had to be matrices.

And Maple was infuriating because you could not easily combine calculus and linear algebra (e.g., to do differential geometry you couldn't make it understand vectors back in the day). So I am firmly a Mathematica devoté. Maple was always better for commutative algebra, etc.

some of matlab's matrix stuff was understandably very fast, relative to other programs (withoout modification/plugins). the only reason why i used it.

@TedShifrin this

the evolutionary pressure on computer languages seems to be one of financial gain or some sort of intellectual challenge.

I'd say minimizing entropy is one first goal

which will never be attained since language changes according to external changes

Are you agreeing with me, @user2103480?

Regarding matlab, yes. I haven't used maple though

matlab's floating point seemed more accurate to more digits for certain matrix operations. i never figured that out but appreciated it. the maple analogue of my code was non deterministic. lots of algorithms depend on choosing random numbers and hence on a choice of seed, but you'd run my code five times for the same matrix and watch everything past the 4th or 5th decimal point change each time.

all of my knowledge and opinions are 15+ years old. i assume maple and mathematica have improved but that matlab still feels like driving a car with bad wheel alignment.

kahan's attention to detail is underappreciated.

oh, does matlab actually comply with the standard?

floating point is a peculiar beast.

i would imagine the underlying libraries are sane, so to speak.

that's funny. i was aware of kahans work at the time but never made the connection. i just thought 'wow, that guy sure hates it when people do floating point the wrong way'

[2 hours later] 'totally unrelated but i wonder why maple is doing this'

i think he was one of my committees, my advisor and himself were pals. both tough nuts.

by that stage i had learned never to make an assertion that i would not back up there & then.

my advisor was less forthright. if i said something questionable he would just say "hrm." i figured out what that meant pretty quickly

he's an interesting fellow with a comprehensive knowledge (in general, not just 'his area') and a unique way of looking at things. i can follow but never emulate.

i was used to sniper fire. luckily i was quick on my feet and sure of myself.

i suspect my accent made them think i was easy meat for some reason.

haha

some accents strike me that way. it's involuntary. i have to manage it.

it worked to my advantage. better have folks underestimate you.

i also realised that most folks are afraid to ask simple questions. i have no such fear.

my favorite accents, which i tend not to underestimate, are combination accents. someone grows up speaking X natively, is educated in a place that speaks Y, then moves to the US and speaks english, and you can hear aspects of accents X and Y mixed together. i love that.

i have the misfortune of being the only person on earth without an accent. almost everybody else seemed to get one.

my ability to localise accents has evaporated over the years.

my favorite combination accented english is a from guy who grew up in germany and then worked in ireland for about 15 years. many german accents often sound kind of stern to american ears, while many irish accents sound jovial. the mix is enjoyable to listen to.

unfortunately tv & internet have conspired to dilute accents.

this is true. because a lot of mass entertainment is made in CA, so many people around the world sound exactly like i do. it's so boring.

$$G_n(L)= \sum_{\omega \in L,\omega\ne0} \frac{1}{\omega^n}.$$ Why is $G_n(L)=0$ for $n$ odd?

I can't see it

$(-\omega)^n=(-1)^n\omega^n$

oh okay, and $-\omega=-m\omega_1 - k\omega_2$

and $\omega=m\omega_1+ k\omega_2$

so the first real calculations are $G_4(L)$ and $G_6(L)$

you don't really need a lattice here. just any set that can be written as a disjoint union of S and -S (as long as the elements of S are such that the sums will converge; that's kinda where the lattice stuff is coming in)

calculations that result in 0 are still real calculations, let's be nice to them, but i suppose so.

the degenerate lattices satisfy: $20G_4^3-49G_6^2=0$

I don't understand where the $20$ and $49$ are coming from

I guess they just are the only coefficients that make it zero?

and every degenerate lattice is of the form $t\Bbb Z$ for $t\in \Bbb C$ btw

okay now I would like to show the space of nondegenerate lattices in the plane of unit area is homeomorphic to the complement of the trefoil in $S^3$

that relation seems like it would need actually a little bit of elliptic function theory.

so all I really know is the algebraic equation for $S^3$ in $\Bbb C$

$\{(z,w): |z|^2+|w|^2=1\}$

i am always envious of folks who can work on mathematics without either some 'physical' intuition or historical background.

those things might be coefficients in a differential equation satisfied by the corresponding $\wp$ function of the lattice.

blank slates, we call them. i was one of those. i was envious of people who weren't blank slates. i ended up learning a lot of historical background but i never used it. it just sat there in my mind collecting dust.

i mean i guess learning the history educated me about what not to try, saving time. it didn't affirmatively help me very much but it did help. i had an officemate who was truly a blank slate. he'd say really off the wall and wrong things about lie groups, to the point i was able to detect it. and yet his thesis was about lie groups.

I cannot work without validation.

my experience with matlab derived from wanting information about low dimensional examples of something i hoped to do in non-finite dimensions where obviously none of the code would work. probably mostly irrelevant, but helpful to me. and a lot of people published conjectures in my field without even checking the finite dimensional case beyond maybe scalar, 2x2, 3x3.

i thought that journal editors should have a show your work policy similar to math.SE. if you conjecture something for all matrices, submit output of a program showing that you have at least verified it numerically for 100,000 4x4 examples.

not for publication if you do. it's just to prevent the world from being junked up with another false conjecture.

but no. one, two, three, infinity is more than just the name of a book to a lot of people

i like zero, one, infinity myself :-).

math.SE is mostly, infinity. just do this please, all of the cases. prove that it's true.

i did a project masters in cs before i left ireland. my advisor never made the big time, but he was a super smart, and more importantly a super decent fellow. anyway, it was he who suggested that i do a sanity check with $0,1,\infty$.

i still keep in contact with him and consider him a close friend.

i never published anything that i didn't check hundreds of time over, especially the numerics. a lot of crap or loose work out there.

awesome, managed to write some covered calls to claw back some of this year's losses.

nobody cares about anything numerical. outside of math-intensive fields, you can guarantee that almost any formula in a published paper is wrong, or missing context that would make it true.

and even within math-intensive fields, patent applications and patents never have correct equations or data. typos, ambiguity, wrong stuff. junk numbers. nobody cares. most of the time it's not the focus, but you'd think, why put that in if it's not the focus.

because numbers with decimal points in them are fun to look at, i guess?

i was appalled at how little concern there was for correctness or general reproducibility for both number & non numeric work. i estimated that about 75% of my work was 'wasted' in that sense. not that i would have done it any other way.

i was secretly very chuffed when one of my thesis advisors (ole hald) commented that the work i had put in amounted to 5 theses.

of course, that is why i am still driving my 2003 wrx with bent frame.

ole hald!

i won $5 in one of his classes for a counterexample :-)

i liked him a lot. i never took a class from him. he worked in some general graduate advising capacity, though, so i occasionally had to meet with him. cool guy.

it is sad that that $5 meant more to me that many greater accomplishments. he was a very decent fellow.

is, i suppose

i do like my 2003 wrx and rue the day subaru marketing idiots decided not to manufacture the wrx wagon anymore.

my valentine one radar detector went on the blink last week. i suppose a decade is ok.

i wish someone had given me $5 for something. one time a prof presented one of my counterexamples to the class, with attribution. that meant something, but it didn't buy me coffee.

it saved me thousands i am sad to say, looking back on my irresponsible life.

not a lot of people like subarus, but the people who like them really like them. they are the black licorice of cars.

or the grateful dead of cars.

awesome performer for $24k new. turbo preserves power at altitude (when i was able to ski/backpack) and handles really well in mud & snow.

consumption is dire, but you can't have everything.

but my geo metro xfi was the the best every all rounder.

that's one of the few gas cars that comes close to matching my prius C in mileage. of course it was probably lighter and less safe. but such great mileage.

$6k, 150k miles. skiing, windsurfing, backpacking. even dragged my folks & gf to yosemite in it.

it got a solid 50 mpg.

no unnecessary stuff like aircon or radio. but who needs them.

amazing even now. i remember during the last spike in gas prices the resale market for them was pretty hot.

i donated it unfortunately. bad decision, but we were leaving on a month long trip.

some free career advice: don't leave high paying stable jobs with window offices on high floors in berkeley for the putative enjoyment of a little travel.

too easy. i don't have a window office on a high floor, and i hate travel. i'm totally winning.

i feel like i've accomplished something today just by not satisfying those properties. thank you

don't really care about the office, do like travel and meeting different people.

but my kids liked it as long as i bought arinells pizza

i had a charmed life.

not $$$ wise, just all around.

now i am struggling to help my son with his college mess.

not the $$$ but everything else.

i cannot understand how complicated college is in the usa.

i used to wonder why so many people had college bumper stickers and sweatshirts, now i realise the challenge is figuring out just how to get in.

i can't imagine what it's like now.

i am getting an ulcer as a result.

not because of your imagination :-)

i am wondering if i find some high paid consultant who will magically figure things out?

that was apparently already pretty common (among those who could afford it) when i was applying, although i had no idea at the time. i think it's even more common now.

what do these people even call themslves?

scammers, frauds, ticks, fleas--- no wait, that's what i call them.

i have an idea, my retired patent lawyer neighbour will know...

i am not sure why i find gelfand's formula for the spectral radius so fascinating.

no segue, sry

it's a great result.

i think its weird that it is independent of the specific norm.

i mean i know the analysis, but that does not detract from my fascination

@geocalc33 Eisenstein series are modular forms and this is the case for modular forms

heh

I knew you would be the right one to answer this question

lol tbh the reason is the one you mentioned

@EdwardEvans are you uk based?

hi all

what is the most mysterious form of math ? :)

graph theory has always seemed mysterious to me. but it's also something i've never really studied, even at an elementary level.

categorically category theory

graph theory always seemed to have more application potential that i could ever extract

i hate removed messages

sorry about that, they were noise, you didn't miss anything important, I was just venting my frustration at some OP.

(removed)

(removed)

bold removals

arrgghhhh

my frustrations

sorry, but it always eases my own frustrations when someone else is

glad I could help

BUT HE HAS NOT

sorry caps left on lol

another day on the math grind.............

maybe some of you want to answer that question with a new proof that does not require the UFD ?

ahh, diophantine equations. it doesn't surprise me that there's a clever descent argument. or that it's a famously unsolved problem, or it's FLT. there's nothing in between.

i do not know of an argument and am paywalled out of clicking through.

im against paywalls

like : reallly ? cmon man

i have a payfloor

and a payroof

becoming comedian ?

and my mortage company keeps telling me of the incredible low rates that will not last

"i am not interested"

ok, let me tell you one more think that might interest you...

i got 2 phonecalls from " steve from windows from india " :/

ahh, i've had a few of those. they can be fun...

go f**k yourself i answer

no they are not fun

i love any and all forms of dialogue with representatives of the company that services my mortgage

i meant the windows guys

i usually try to outwit them. they usually go along with outlandish stuff and they end up tripping up.

@mick the articles Kieren referred to have DOIs: 10.1017/S0025557200005283 and 10.1017/S0025557200004034 If only there was a way to break through paywalls with DOIs...

yeah but they still need to be combined

some people are just never going to be happy :)

I agree (both with mick and leslie)

I answered a bounty-question a few minutes ago (was actually pretty easy) but the OP was last seen 2 days ago. What happens to the bounty if he doesn't visit stackexchange when the bounty expires? Is no one getting it or...

the thing is , it not just alot of work , its even unclear how it relates or where to begin.

@vitamind you can get half the bounty if he does not give it too you

@mick Oh okay interesting. Thanks.

@vitamind link ?

@mick math.stackexchange.com/questions/4065004/…

goodnight fellas

Good night :)

@Wolgwang doesn't work either