So Japan is not on the list there but as far as I can gather it means that in areas that are too far away from where the thing is produced they use a repeater to send the signal across a longer distance.
So from the point of the person who is watching they don't know whether it's a relay or just a normal broadcast.
Hello @all .. I have a question about rate of convergence! if $g'(a) \neq 0$ then the rate of convergence is 1, if $g''(a) \neq 0$ then it's 2 and so on. Am I right?
In my book, it says somewhere what I said above, but somewhere else it says if $h(a) =0$ but $h'(a) \neq 0$ the rate of convergence it's at least two .. I'm confused if it's exactly two or at least two
Would it be possible that we have a fifth degree polynomial for which we are not able to find closed form expressions for the roots in terms of elementary (?) functions, but we are able to solve the Newton-Rhapson recursion to obtain a root?
@JonasTeuwen The recursion is awfully nonlinear. I haven't heard of anybody doing explicit solutions except in the important case of computing nth-roots.
There's a question in the book, asking " suppose a is a root of $m$ multiplicity ( $m \ge 0$) from $f(x)=0$. if $h(x)= \frac {f(x)}{f'(x)}$ , show that $h(a)=0$ but $h'(a) \neq 0$ then get the result that convergence of ${x_n}$ is computed by $$x_n+1 = x_n - \frac {h(x_n)}{h'(x_n)}$$ , the rate of convergence is at least 2. " .. That's why I asked if it's exaclty two, so the question is wrong, right @JM?
@JonasTeuwen Eep, sorry to hear. I'm afraid I don't know newer refs, as I've said. I'll only note that "Riemann theta", "Siegel theta", and "multidimensional theta" are effectively interchangeable terms, if you'll try doing your own searches.
@JM Yes, that would be nice. The cartoon on Wikipedia isn't really understandable. I liked Richmond's construction as given in Stewart's Galois Theory. When I was in High School I drew that using Indian ink.
@ZhenLin It certainly is different. We have "mijn" (mine), and it is pronounced completely different and I'm not even sure how to write that in English. I'll look it up.
@tb Thank you. If it's not 100% right I can't be sure whether people are just assuming that I'm being imprecise while I'm still not 100% clear about it. Earlier you said Johan's comment was correctly pointing out a mistake...
@Jonas Yes, I know that <ij> is usually spelled [ɛi] in IPA, while the English sound is usually spelled [ai]... but does it sound completely different?
@QED All our efforts into trying to convince the OP haven't yet stopped them from boasting. I'm sure they are still proud that they shook the foundations of mathematics, not to mention shaking the math community.
@JM we had this horrible course called "Technisches Zeichnen" (technical drawing) which was all about not spilling ink on a huge sheet of paper with the worst possible tools. Out of boredom I decided to challenge myself...
You guys suck! I should know better than listening to guys on the internet. You were all like, you better return the necklace to your ex, its hers! And I am all like, I do not really want to, but I guess I will. So I placed it in her mailbox, with a short note and a piece of her favourite chocolate. And now she hates me.
Is there a function, like f(n), i insert n and it outputs nth prime number? I have been trying to find a pattern between the prime numbers, 1st differences, 2nd differences, but i can't find it.
I woke up early because my dog had decided that my hair was particularly delicious this morning. Trying to get a third faculty member to show up for my qualifying exam talk. I will probably read a lot of Silverman after that.
@Dylan Given that the book says "multiple integrals", and this whole thing is being developed to justify "a mechanical substitution procedure", I think introducing $\wedge$ would just be confusing...
@MrAnubis Actually, you should factor it, kind-of. This is a standard trick in GCD/HCF: If the GCD is d, then write the numbers as d*x and d*y. Where x and y are relatively prime.
@Victor: There is a very well-developed calculus of differential forms that the book is alluding to there. The motivation is explained on that very page.
@Victor : take Zhen Lin's advice seriously! And if I may ask you a favor: before you ask a question on main please think about it for at least two entire days.
Is there a function, like f(n), i insert n and it outputs nth prime number? I have been trying to find a pattern between the prime numbers, 1st differences, 2nd differences, but i can't find it.
