We are not a course, of course!

I'ma invent a new MSE called MGE or math.graphexechange.com

That uses Neo4J to connect theorems etc.

*I'm going to

@user76284 hi

Hi

What's cookin?

Nothing atm

You?

I'm coding in Python

What you working on?

Here's the output of a console app:

It parses using TextBlob library the parts of speach

It's work in progress of course

I want to tie to Definitions, the defining conditions or axioms

Then the context (logically speaking) is a list of definitions, theorems, props, etc.

Each algorithm I write to handle the logic will descend into the specification of each definition appropriately

This is vaguely proof theory

Though, I'm not following any of "the rules".

I had something similar in mind once.

That's awesome! Maybe we were meant to collide here

It's a cool idea.

I want to convert it over to a website format. Called MGE or math.graphexchange instead of "stack"

We could use Neo4j (graph database tech.) to link stuff and do complex searches

I probably can't work on it right now :P

But it's an interesting project.

I don't like how there's a huge learning curve to get into coding a proof assistant like Coq say. So here I'm taking a "string-based" approach

I was especially trying to build a graph connecting all the concepts in abstract algebra.

LOL, we are crazy inventor bros

What was the hurdle that eventually caused you to stop working on it?

Ring rig, monoid, semigroup, group, loop, abelian group, monomorphism, epimorphism, commutator, metabelian, action, preorder, partial order, automorphism, bijection, kernel, image, meet, join, regular cardinal, limit cardinal, etc. Lots and lots of concepts.

So you were hardcoding each concept?

No hurdle really, just didn't commit to it. Busy with other stuff.

In a relational way, yeah.

It was a concept graph of sorts.

Nice. That's sort of like SymPy but for proofs

I especially like concise definitions.

I think in website form, the "answers" on the site could be different things, say Macaulay2 code, or SymPy code, demonstrating a concrete example.

What's a partial order? An antisymmetric preorder. What's a monomorphism? A left-cancellative morphism. And so on.

Yes, but to code each thing means you can't just type in English like normal (like we communicate on the web)

My goal is to do that

convert the English into standard formats

You mean NLP?

In math there's only so many language structures used, so I believe the problem is much simpler than general NLP, though I am employng TextBlob as my frontend parser

It breaks up the sentences into parts-of-speech

('ring', 'NN') e.g. a list of these

It doesn't matter how TextBlob treats say a symbolic thing (a,b)

as long as both a, b are there in order and the word tuple appears

or 2-tuple

So with this string based approach. Suppose a, b are two strings each considered as typed as elements of a ring R

then a + "+" + b (python syntax) is also a ring element

where "+" is taken from the ring's tuple (R, +, .) and can change

There's probably a lot of issues with this approach, but it is currently making more sense to me than trying to encode all math in some internal format, which is essentially just an alternative to strings

You might want to look into en.wikipedia.org/wiki/Structure_(mathematical_logic) and en.wikipedia.org/wiki/Signature_(logic)

@user76284 if this interests you and you'd like to code on it occasionally as an open source project, I could host it on github.

Seems like you're trying to find a good representation of these.

My email is fruitfulapproach (gmail)

@user76284 I'm more of a code what I need and only what I need, top-down coder

So I'm not sure if I'd even have a function called getSignature, etc.

It all depends on how it turns out

Might be helpful to look up "mathematical knowledge representation" and see what people have worked on.

But yeah, sounds like a fun project.

I hear that a lot, that we should be looking at what people have worked on. However, a counter argument is they're not writing for us the implementors they're writing to impress a journal audience. So it could take years to disseminate their writings.

When you code an application, you're inventing all the time, without publishing

a literature about the invented code. You just code what was necessary

Certainly one of the best ways to learn is by doing. Especially if you're putting out a website for the world to see/tinker with.

I have little skill with Django / Neo4j ._. time to learn those

My IDE (Wingware) has builtin Django project features

*The ide that I use

I used Django many years ago.

Also Node.

I hear Ruby on Rails is really good though.

Well, if I just do django and make the site phone readable, I should be fine, right?

Phone and desktop, hopefully!

I mean properly formatted for phone browsers

Yes!

^_^

Is there a canonical way to extend local field, induced by an algebraic extension of its residue field?

@ChoMedit yes. you get an unramified extension (because the residue field extension is separable)

probably can be generalized to Dedekind domains

I am pretty sure this is correct

Do you mean $M_n(H)=B(H^n)$ or?

you can identify nxn entries with elements in B(H) by Mn(H^n)

for H hilbert space

Yeah I mean through this identification everything works out

@AlessandroCodenotti do you agree?

@AlessandroCodenotti where r u from btw ?

@Semiclassical Do you got some time for me?

yap

@AbhasKumarSinha How’d ya doing?

@Knight good.

@JackOhara hi

@knight not really, no

it's too late to topologize...it's too laateee, it's too laaateee.

lol

A Mathematician's Topology

Sounds like a good blog name

to topologize, or not to topologize; that is the question

@BalarkaSen should "The Lament" apologize?

Hi, a @balarka, skull, et al.

Hello professor @TedShifrin

Hi @Ted

Has anyone read "A Mathematician's Lament"?

I passed along @MichaelAlbanese’s exercise about the tautological bundle on $\tilde G(2,4)$ to a Berkeley grad student (who took Calc Theory from me his last year of high school). He hasn't yet responded.

Hi, Captain.

Sup, Ted

Hi @Ted @Balarka

@TedShifrin Did you see my response to you earlier regarding that conjugacy problem on the sphere

Hi, demonic!

Quotient of a free $\Bbb Z_2$-action on $S^n$ is indeed homotopy equivalent to $\Bbb{RP}^n$ but need not be homeomorphic to $\Bbb{RP}^n$. Mike says he can construct fake $\Bbb{RP}^n$'s, so that'd give you examples, but I don't know how to construct one explicitly.

(That's the summary of the response)

But this is enough to push through the Lefschetz fixed point theorem proof I was writing down

Yes, I did see, thanks, balarka.

Thanks for pointing out the subtlety!

this is an interesting probability problem:

(the way I'm inclined to look at it is to classify the state of each die as a particular integer partition of 6, e.g., 3, 5, 3, 6, 1, 2 -> 2+1+1+1+1=6. each time you re-roll, you transition to another such partition with some probability; however, the number of parts in the partition cannot increase upon re-rolling.)

@CaptainAmerica16 I have.

Oh cool, what did you think of it? I thought it was interesting, although I probably didn't get as much out of it as some people.

sure, it was interesting

anyone up for a number theory question?

One of my teachers "lent" me Godel, Escher, and Bach before they moved to a different job. I want to start it, but I've heard it takes a lot to get through small sections at a time. (I say "lent" because at this point he's never getting it back XD)

@CaptainAmerica16 as you say, it needs mathematical sophistication to really get more out of it

yeah, definitely

Godel, Escher, and Bach is in the same category

Yeah, I can tell. I'm going to just dive in, eventually. Just research as I go along.

I call them "recreational" math reading

Yeah, for fun when I have time

The Man Who Knew Infinity is a good movie to watch for fun.

I was just thinking about watching that the other day! I had randomly come across the trailer.

I enjoyed rewatching

I'm definitely going to check it out

It has so many layers of meaning.

Well, it's a pretty incredible story. I expect to get a lot out of it.

Maybe one day I'll read the book, too

How do I do spherical/hyperbolic trigonometry

I knew the formulas once but forgot them lmao

I think if I have a spherical triangle with side lengths $a, b, c$ and $\alpha$ is the angle between $a$ and $b$ then $\cos(c) = \cos(a)\cos(b) + \sin(a)\sin(b) \cos(\alpha)$

In hyperbolic everything just becomes cosh instead

Yeah ok this is just vector geometry stuff

Oh no in hyperbolic $\cosh(c) = \cosh(a) \cosh(b) - \sinh(a) \sinh(b) \sinh(\alpha)$

Oops, negative of that

So annoying man

Do I have to write down stuff in Poincare metric and bash everything with it to prove this

oeis.org/A309229

are there any measures that are "significantly different" from the Lebesgue measure?

all Haar measures I know are basically Lebesgue with some density function

any discrete or singular continuous measure

atoms are boring, but also the totally discontinuous measures (like the cantor measure) are isomorphic to the Lebesgue measure (in the sense of a measure preserving isomorphism between the measure algebras)

Hi, I have a small question: "for a polynomial p(x) of degree 4 or 5 to be irreducible, it suffices to show that p(x) has no linear or quadratic factors" and "A polynomial p(x) of degree 2 or 3 is irreducible if and only if it does not have linear factors". Now, why for a polynomial p(x) of degree 4 is irreducible only when it siffices to show that p(x) has no linear or quadratic factors, why not saying cubic factors? why not saying all factors that is leas than 4? the same with degree 5

these statements is taken from: math.stackexchange.com/questions/32197/…

@s.harp Do you have any requirement for such measures? Arbitrary things can be very weird

@JackOhara did you figure out that function of monomials yet?

Even reasonable measures can be very weird to be fair, The Dieudonné measure is a nontrivial Borel measure on a locally compact Hausdorff space, but its support is empty

Hi, demonic.

@user777 if you didn’t figure this out, remember that, for example, if a poly if degree 4 has a cubic factor, then the quotient is linear (and of course a factor). Much easier to look for linear factors than for cubics. Etc.

Rehi Ted

Hello Ted

Does anybody here have any good news about the virus?

based upon the numbers I have seen, it is getting worse

We are not flattening the curve

We're way behind and idiocy proliferates.

The politicians and religious leaders are the stupidest and most culpable. /rant

@TedShifrin I was hoping for some good news.

I hope you are feeling better

I need to go

take care

bye

Every one in the bible is rich

doesn't make any sense :D

*was a rich person

This is why I'm a low wage making hermit. There's no point to "working hard".

Cynical times in which we live. I worked pretty hard, but I loved most of what I did.

Food should be free by this point in our technological development. Everything else should be voluntary enterprise. All I wanna do is sit down with a book, not play their money game.

Who's to say that the alternatives of what we do now aren't better / healthier / more advanced technologically.