Recent content by n+1

CLRS discusses polynomial multiplication (Chapter 32). They verify that polynomial multiplication using the FFT has complexity n log(n). I guess my confusion stemmed from talk about "the interpolation of polynomials using roots of unity." Every paper I read talks about this. As far as I can...

Multiplying big numbers is a very common application of the FFT, and as such, there are many papers on the subject available online. However, these papers all use sophisticated algorithms where a simple one seems to work. My question is, what's wrong with the simple algorithm: Multiplication...

Short and sweet I am an undergraduate math major attempting to transfer. I am looking for help composing a list of schools to visit. Some Information about Myself I'm not a terribly academically driven guy. While I've come across some success academically, it's mostly been the result of...

Nevermind NEVERMIND Whoops! The product of two non-ideal subrings isn't even well defined! While I don't need to mention property of ideals explicitly in my proof, I'm assuming I, J, K are ideal when using terms like I(J+K). Sorry about bumping the thread just to say that it doesn't...

This is correct. I can't seem to find the "edit" button for my og post, but when I do, I'll fix that typo. Also, bump.

Homework Statement Problem 35, Section 7.3 of Dummit and Foote: Let I, J, and K be ideals of R. (a) Prove that I(J+K) = IJ+IK and IJ+IK = I(J+K). (b) Prove that if J \subseteq I then I \cap (J + K) = J + (I \cap K). 2. Concern/Question Despite the problem statement specifically...

Yep. Because if an = 0, an-1 multiplied by any element in <a> can be rewritten as an*whocares=0. Cool cool.

Hmmm. I'm not quite sure how the ring generated by [[0,0],[0,1]] would satisfy anything, especially since it has an identity. Also, wouldn't <[[0,0],[0,1]]> just be isomorphic to Z? It like the matrix part of all this is no longer important... Which is fine! Because all of this talk about...

Thanks for the response, Dick. So concerning nilpotent matrices, obviously any ring consisting of only nilpotent matrices would satisfy (2). Unfortunately the set of all nxn nilpotent matrices does not form a ring since it's not closed under multiplication (consider...

Homework Statement Is there a finite non-trivial ring such that for some a, b in R, ac = bc for all c in R? Does there exist finite non-trivial rings all of whose elements are zero-divisors or zero? 2. The attempt at a solution Let a, b ≠ 0 in R such that ac=bc for all c in R...

Ah, I see. I was implicitly assuming that (E1 + E2)2-(p1+p2)2 = (E12 - E22) + (p12 - p22) by saying that total invariant mass equals the sum of the individual particles' invariant masses. So naturally my invariant mass was off by (2E1E2 - 2p1p2). Makes sense! Thanks for your help Dale and...

Hello PF community! I'm having trouble with what strikes me as an inconsistency within conservation of energy, conservation of momentum, and the four-momentum invariant equation (E2-p2c2 = m2c4). For the sake of this question, I'll be using non-relativistic mass--i.e. mass is the same in all...