Ozymandias

Yeah, that was my first one

Good taste, ha!

That one made me rethink my life

I don't think I'm doing anything differently because of it, but still

Puts you back in perspective

Some politicians should read it

Hello guys

I am an engineer ,and I want to deal with Navier stokes equations but I am not a mathematician, what should I learn to start?

genius sees the answer before the question

put that in your pipe and smoke it

dang it bro whatever you're on I want it

Donald Trump smokes fools

it is very true that after discovering a solution to an old problem, you find other constructions and then ask questions which they answer

well, I see Danu is very intolerant these days

@Danu at you bro

Does anyone know of a program like diffpdf which does not get completely thrown off if the changes move more than a few things to new pages?

A pdf editor?

@TheGreatDuck No, just one that can provide a nice view of the differences between two pdf files

Oh idk

i was going to recommend adobe

:p

@TobiasKildetoft Maybe you can have a look at some posts at Software Recommendations site. Or post a new question, if your inquiry is different from the already existing ones.

@MartinSleziak thanks

Hey people

Trying to figure out something about cryptograpy at crypto.stackexchange.com/questions/37324/… and someone said that my problem is in mathematics without explaining how, can one of you guys take a look?

(I would rather not double post)

@Thijser it should be ported to codereview/SO

Was [x] floor?

Are you trying to find the difference of floors?

@Agawa001 should it? I suspect that my code itself works but that I'm not using the right calculations, unless you can vertify that my math is right on this one?

@Thijser code working vs calculation working is the same thing.

and yes, crypto is applied math

number theiry from what i hear

and also what i apparently jump around without meaning to

Brb

i have to go for a few minutes

But it's interesting to see where the problem lies for various people, @Agawa001 thinks it's in one someone at the question thinks it's in my math, with which I partially agree seeing as how I think it's crypto specific math.

you're a crooked tree, what is that peyote??

@Thijser examplify what you are doing, like with c.remainder(n^2),my java knowlegde is a bit outdated

is this kinda rsa implementation ?

dude

c.remainder(x) means the signed modulo of c by x

so assuming both are positive and a<b it's a%b

mmm ahemmmm ohemmmm olammmm

@ForeverMozart are you ok?

just watching ray donovan

and @Agawa001 it's trying to divide 2 encrypted numbers, the overal idea is that [a] is in some way dependend on g^a so that g^(a+b)=g^(a) *g⁽b)

encryption is done by [a]=g^(a)*r^(n) mod n^2 for a random r, a publicly known g and n and a input a.

The wikipedia article also explains this fairly well en.wikipedia.org/wiki/Paillier_cryptosystem

@Thijser look i am trying to mitigate the way you use arithmetic modulus with big integers

a=b^2+c=b^b+b^d+e where e<b and d<b

a= b(b+d)+e

What does [a] mean?

floor(a)?

[a] means encrypted a

In that case...

for this , you wight just divide by b to get an integer in narrower range, then divide again by b

im out of here

i cannot help :p

then remainder would equal to bd+e

So you are suggesting deviding by b twice might work?

since it is bigintegers problem

c (actually [c]) becomes zero

i would suggest to go to SO people and present it in CS dish tagged with java

so d is zero

what about e ?

c=a.divide(b)

What is e in this example?

ah so a.divide(b) also seems to become [0,1,2] very often

wait a.divide is division ?

hmm

and gives 0 ?

i dont think c is big integer unless n is even bigger than it

guten tag @Huy

Well c can become 0 if [b]>[a] when a/b

guten Tag @ForeverMozart

hey huy

morning @Thijser

what kind of mathematics does @Huy do?

@Thijser please can you print an example of c

and n

currently just refreshing my gmail tab and hoping to hear back about the flat I applied for

i dont see how big are integers we are dealing with

I think that qualifies as "applied" maths

@Agawa001 well as I just learned it seems that c can varry between 0, 1 , 2 and probably a bit more but I suspect that I have to increase a so that it's bigger

the BigIntegers we are dealing with can be 0,1,2 or they can be 2^2048

Now trying to multiply a by 2^64

(oh and I picked 128 not 64)

where res = c - 2^128

those are [a] [b] [c] and not encrypted res

Oh and if any of the later joiners are wondering we are discussing crypto.stackexchange.com/questions/37324/…

i dont ret it really, c-2^128 results in a negative value where is the problem figuring ?

well because of integer precision a/b tends to be something like 0,1,2

with p[0]>p[1]>[p2] and probably also a chance of p[3]

So by multiplying by 2^128 we can ensure that a>>>b

so that a/b is accurate

But because we multiply on one hand we have to substract on the other

Does that make sense?

really over my cap, i give up this to someone more versed in pascal paillier cryptosystems

ok thanks

By the way if anyone else wants to have a look I have added a little overview of what we disccused here

@Krijn Jabberwocky.

On a more serious note, I like "Alone" by Poe, not to mention "Raven" but that's too long to memorize :)

You mean one of these things securethumbs.ebay.com/images/g/w8AAAOSwhRxXKO-a/s-l225.jpg ?

By the way is one of the people who just arrived good with number theory or cryptography?

Sillence...

Does anyone know if it is a demand, when transforming between two orthogonal coordinate systems, that the length of the basis vectors in the old and new system are the same? From what I've read, it seems not to be, but when trying to prove it, I get that e1' and e2' both need to have the length 1 expressed in the old coordinate system.

Oh, sorry, I forgot to mention: a demand if the inverse transpose of the transformation matrix should be equal to the transformation matrix

Basically: prntscr.com/blnbkq

lengths are not dependent on a choice of basis unless you for some reason decide to define lengths with respect to that basis

or rather, once you have fixed an inner product, this does not change just because you pick a different basis

the pdf I'm reading uses this as an example. Doesn't it do the "unless"-part of what you're saying? (aka letting it depend on that basis?) prntscr.com/blnc6h

There is no length specified in that picture

oh, length = length of basis vectors?

what?

I'm sorry, let me think of a good way to express myself :P

or well, let me think of a good way to ask the right question that alsl makes sense

in order for vectors to have a length, we need to specify a norm, which is usually done via an inner product (otherwise orthogonal would not make sense anyway)

but if you define e'x = 2ex, doesn't that "change" the length somehow?

or the way you express the length in the new coordinate system

sure, if you want to express the length in terms of the basis, that changes. But the length of a given vector does not change by changing the basis unless you also change the inner product

hmm, but doesn't the length never change in that case?

I mean we're just changing the coordinate axis in a way, not the vector itself

right

what I thought was a demand, was that the length of the unit vectors expressed with the old basis vectors (the ones you transform) should be the same

like, in the case where e'x = 2ex, then that demand isn't fulfilled, while a coordinate rotation does fulfill that demand

what I get in my derivation is:

prntscr.com/blngta

I think I may be expressing myself incorrectly, but that image may make it clear if anything

oh, and in that image, the lambda is supposed to be the transformation matrix, fulfilling e'i = lambda ei

Hello everyone

Is the following true: for a function $f:\mathbb R\to\mathbb R$ differentiable everywhere at the interval $[a,b]$, then if $f'$ is always negative in the same interval, then $f$ must be strictly decreasing in the same interval.

The converse is not necessarily true ($y=x^3$ is a counter-example).

flag as math.stackexchange.com/questions/1841294/…

flag as what?

Flag as primarily opinion-based.

Could anyone please clear my doubt? Thank you very much.

hmm, I tried this transformation: prntscr.com/blnumk Seemed orthogonal to me, but turns out that (lambda^-1)^T isn't equal to lambda, but instead: prntscr.com/blnv6o

it all makes sense to me, but all the documentation makes it sound like (lambda^-1)^T SHOULD be equal to lambda, due to both coordinate systems being orthogonal

this is driving me nuts -_-

@Max What makes you think that (lambda^-1)^T should equal lambda?

well, my PDF says that if both coordinate systems (the one that I transform into and the one being transformed) are orthogonal, then they should be equal

for instance, it says that they should be equal when transforming from a function into its gradient's coordinate system

so I had facebook open while I googled on another tab chain saw and next thing you know facebook is showing me an ad of a chain saw

good lawd I'm officially creeped out

@SoumyoB correlation

does not imply

causation

xD

can you explain to me how that relates to this context

well, maybe you search about chain saw very much

@Max sorry I don't get it

could you provide an example?

not really lol

If a polynomial does not have any real roots,does it imply that it is prime?

@tatan No. For example, $x^4+4$ has no real roots, but $x^4+4 = (x^2-2x+2)(x^2+2x+2)$

@TedShifrin so, looking at your notes, the first thing I'm asking is... Why is the Cousin problem important?

In fact, the roots of $x^4+4$ are: $1+i$, $1-i$, $-1+i$, $-1-i$.

I asked this to some other people before, I think

hi chat

@Semiclassical Could you clear my doubts?

Typo: it should read $y=-x^3$ instead of $y=x^3$.

in what sense is $y=-x^3$ a counterexample?

that it is strictly decreasing but its derivative is not always strictly negative.

ah, of course.

(converse might be valid if one weakens it to 'strictly negative almost everywhere'. but that's besides the point)

Anyways, I think you're right about the forward direction.

Not sure how one proves it, though.

(it's been a while since I could actually prove things in real analysis)

Check this? math.stackexchange.com/questions/1841356/…

@MithleshUpadhyay Might help to list the implications you're using along the way.

@LeakyNun The best example is this: prntscr.com/blp406

My calculation shows that the inverse transpose of the transformation matrix isn't the same, but at the same time, the gradient of a function, which is transformed similarly, is supposed to have the same transpose-inverse-matrix as the transformation matrix

Never mind, I think you should seek help from another person

@Semiclassical ok thanks

@Semiclassical, Thanks, I gave link about review math.stackexchange.com/posts/1841356/revisions

here's what my PDF says: prntscr.com/blp56u

it's fine, thanks for your help anyways :)

no problem

@max what's the question, out of curiousity?

the question is, how can a transformation matrix that transforms between two orthogonal coordinate systems be equal to its inverse transpose, when my example seems to show otherwise

good morning!

@SamuelYusim good evening

and this is the example: prntscr.com/blp6iu

@LeakyNun where are you that it's currently the evening?

I think your point could be summed up as such.

Suppose I were to describe my coordinate system in units of, say, meters.

@SamuelYusim It's 22:24 in Hong Kong

Then I'd measure stuff like volume in units of cubic meters.

wow, that's exactly 12 hours away from me.

Now, suppose I want to change my coordinates to use units of feet.

In that case, I'll also have to change my measurements of things like volume from cubic meters to cubic feet; the specific numbers will all change in a consistent way.

But nevertheless it will still be the case that I'm in an orthogonal coordinate system.

And that would seem to contradict the the transformation matrix be equal to its inverse transpose.

...and I would actually agree with that.

that's a very illustrative example!

made it a lot easier to imagine all of this

If memory serves, the statement about $A^T=A^{-1}$ is confined to pure rotations.

would you say that this is wrong then? or have I interpreted it incorrectly? prntscr.com/blp8si

i.e. you 'keep the same units' but rotate your coordinate system

oh yes, but in rotation the length of the new unit vectors is the same when expressed in terms of the old one

I think the rub here is 'ortho_normal_ basis.'

that's exactly what my conclusion was as well

what do you mean by 'ortho_normal_ basis'? I'm a bit confused

I was intending it to be italicized. not sure it's not showing up that way

ortho normal basis?

oh, now I see

but what do you mean with normal?

that prints right, but isn't quite what I meant visually. anyways

it means that each of the basis vectors should be of unit length as well as be orthogonal to the rest of the vectors.

that does make sense and goes with the conclusion I drew

but one thing still confuses me then

if you start with basis $(1,0)$ and $(0,1)$ then that's orthonormal. so would $(1,1)/\sqrt{2}$ and $(-1,1)/\sqrt{2}$.

but the basis $(2,0)$ and $(0,2)$, while certainly an orthogonal basis, won't be an orthonormal one

yes, A11 squared plus A12 squared would need to be 1, right? if A is the matrix

and A21 squared plus A22 squared

right.

but, the gradient thingy still doesn't make sense, even though all of this does

prntscr.com/blpaih

the factor of two, you mean?

no, I mean

the inverse-transpose-matrix is the same, its said

did you link to the right pic just then? the one you did just now doesn't show any matrices

oh yeah, that figure is associated with the text I sent before

oh my god, the text even says "orthonormal"... how could Ihave missed that+

I didn't understand what it meant and assumed orthogonal

that's what you were saying before, just didn't realize that it was in the text until now

i think the the parenthetical is clearer than the actual text there

since a coordinate system in meters versus feet would both certainly be Cartesian

yeah, exactly

but in that case, how is a gradient's coordinate system orthonormal with respect to its function's coordinate system?

it rescales, right?

i think the point is whether the new basis is orthonormal with respect to the old one

i mean, consider it like this.

suppose i've got my coordinates in units of meters. then when I take $e_1\cdot e_2$, that would literally have units of square meters.

if I then change units to be square centimeters, then that dot product would be 1 square meter = 10^4 square centimeters.

right

which means that, if i don't write units explicitly, the dot product has gone from being 1 to 10000.

hmm, yeah

now, it'll of course be true that $e_1'\cdot e_2'=1$ in units of square centimeters.

but it won't be true for both at the same time.

on the other hand, if you merely rotate your coordinate system, then there's no change of units and therefore $e_1\cdot e_2=1$ and $e_1'\cdot e_2'=1$ at the same time.

I don't know a lot about this topic, but I know that it's possible to smoothly turn a sphere inside out. So I figure it'd be interesting to ask if we know how to do it with $n$-dimensional hyperspheres, for $n > 3$. Is this a thing?

my question is probably poorly worded, so forgive me for that

oh yes, that makes a lot of sense

you can think of the inner product

I mean, is "inside out" even a thing in $>3$ dimensions?

@Danu I think "Can you write down a holomorphic function with prescribed singularities, provided the local data you're given makes sense?" is an interesting question. That's the Cousin problem.

although then I wouldn't say that te gradient's coordinate system is orthonormal, correct?

or maybe I should look into gradients a bit further

@MikeMiller @MikeMiller that makes it sound a lot like a Riemann-Hilbert problem.

I guess it has to be

@SamuelYusim Sure, you're asking whether there's a homotopy between the identity and a reflection map through immersions

alright. so is there?

@Max not sure what you mean by that

Or maybe to -f? I forget what people prefer

I dunno, let me think about it

good luck and godspeed

I mean, is sphere inversion a thing everyone learns about when they study manifolds?

sphere inversion or sphere eversion?

...I don't know the difference

nor I, really. but wikipedia uses the latter term when talking about this stuff.

well then

in that case I'm gonna give it a big who cares

@SamuelYusim there's a detailed-looking answer there, though I'm in no position to assess it

hm

and this MO question has some links re: where to read about it: mathoverflow.net/q/118185/55904

well my first problem is I don't know what $\pi_n$ is for $n > 1$

regardless, the answer is unexpected and cool whether or not understand the argument

yeah

of course, in the higher dimensional case one has little hope of a meaningful 'visualization' as there was for the original sphere eversion

well yeah

I mean, you could project down to a bunch of 3-dimensional cross sections, which would probably be interesting to look at simultaneously

actually that would be really hype

yeah

would probably make my head hurt to watch, though

maybe this is something I can try to animate at some point, not that I have any previous experience with this sort of thing

@SamuelYusim I doubt.

I mean ${6 \choose 3} = 20$ is a fairly large number of cross-sections

@Balarka you doubt what?

That everyone learns the proof of sphere eversion in a manifold course.

ah