That sucks.

Happy Pi Day!

Any of you goys into data mining? I've been fiddling around with R a lot recently.

@Attrition in the desert

@ThisIsChris Yeah I structure a lot of unstructured data on the web for economic system research mostly.

Been getting into data science comprehensively lately, I feel like the field is about to blow up.

@Attrition in the desert definitely! What data is it that you are making available and to who?

@ThisIsChris Mostly data on commerce exchanges in SE asia. The place I'm working at now handles a lot of soft/hard currency transactions.

https://www.livescience.com/60476-jellyfish-sleep.html

That's neat. I wonder if it's simultaneously done in all areas of the animal.

Hey guys, I'm Nick, and I'm a ChemE undergraduate from NY, excited to talk with all of you

nic

*nice

@Nicholas1166 - NY roll'd

roll'd?

@Nicholas1166 - NY sorry, role'd not roll'd. I gave you the @`AE` role (academic expert) so you will be alerted when people ping @`AE` with academic questions you may be able to help with.

Ah, OK. Yeah, I'd be glad to lend a hand if I can, although I am just a junior right now

I'm graduated from a university with a degree in math

ask me math questions

if you need halp

I very well might, math is my weakest subject. Thank you for the offer.

I didn't know this sever had a role thing. Can I get a role and be alerted?

@micbwilli done!

@ThisIsChris hey do you have any good explanation on how to find isomorphisms between two polynomial factor groups?

that is an isomorphism phi: F[x]/f1(x) -> F[x]/f2(x) where F[x] is the field of polynomials with coefficients in Z_q and f1(x) and f2(x) are irreducible polynomials in F[x]

@YourFundamentalTheorum by F[x]/f1(x) do you mean a quotient group? If so, what is the group you are doing F[x] modulo with? f1 doesn't generate a group unless I am missing something

@ThisIsChris quotient field

and F[x] is a field of polynomials in x with coefficients in Z_q

@YourFundamentalTheorum thanks. How about for an element of F[x]/f1 called G, take a representative g, phi(G) = the coset of g*f2/f1 . Need to prove that the coset is independent of the choice of representative g

the last part is a given.

On the right hand side I mean g times f2 divided by f1 in the normal sense for poly nomials

F[x]/f1(x) is usually represented by all the polynomials """"less than""""" f1(x)

a lesser degree than f1(x) that is

Hm, what happens in the three cases where f2 is higher, equal, or lesser degree than f1?

assume f1 and f2 are of the same degree

otherwise you don't have the same cardinalities

which means they can't be isomorphic

the Galois fields can't be isomorphic that is

Hm I think you can actually prove it if the degrees mismatch too. Since you assume the rep g has degree strictly less than f1, then g*f2/f1 should have degree strictly less than f2

yes you can prove that

it's quite easy actually