Message from @YourFundamentalTheorum
Discord ID: 503835445113782352
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?
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
I'll stop there
@YourFundamentalTheorum haha I like the sigma algebra one but don't get the epic one? It's a true statement if f is 1-1 and onto. Not sure what else.
@ThisIsChris epic means an epimorphism
which is literally defined by that equation
so f is epic