we know the exact # of elements in F[x]/f1(x)

it's going to be q^n

i'm assuming q is prime btw

Sure since it's irreducible. Otherwise, hm...

If a polynomial has a non-prime degree, to guarantee reducibility you need to allow complex coefficients, right?

i don't think it matters what the degree of the polynomial is

like if it's prime or not

i think what matters are the coefficients

if you don't have prime coefficients, your polynomials stop being a field

the reason why F[x] is a field is because Z_q is a field when q is prime

if q is not prime, Z_q is not a field

and therefore F[x] is not guaranteed to be a field

Why is Z_q not a field when q is, say, 4?

the very basic example is that say if you have Z_4, the polynomial "2" does not have a multiplicative inverse

Ohh

Neat

Z_4 is not a field because 2 does not have a multiplicative inverse

Yeah haha been a while

and since Z_q is a subfield of F_q[x]

yeah I've literally pullen out my abstract alg. book out today

i need some cryptography knowledge from it

i learned all of this again today 😛

That's neat. I enjoyed abstract algebra but mostly only needed the linear algebra part since then (11 years ago). Rotation groups and some other stuff relevant to geometry, but not much more. Cryptography seems interesting, we did cover RSA at some point, I only remember the main idea, that factoring is hard 😁

@ThisIsChris wellyeah, some pajeets found a way to crack RSA with you guessed it, Galois fields

Is that a recent thing?

yeah

like a year or so

it's amazing how irrelevant Abstract Algebra used to be until computers, and now it's hella important

Huh no kidding. Guess I better put 2FA on my bank accounts then

yep

idk about you, my dad make me take applied math

it was "fun" i guess, but I really want to go back to college and get a pure math degree

later

😛

pure math is so much more fun that learning about how to earn money at google

"pure math is fun" I will never understand you types

https://giphy.com/gifs/frog-get-out-U9DiGJDKfbwGY

@Deleted User

@ThisIsChris