@robjohn I posted a detailed explanation of it here. anon has given a convincing answer already, but I'm looking for " the general selection condition for the factors of the quadratic term, and the corresponding ordering of the factors of the constant term."
@KannappanSampath no, when you look at the front page in the activity mode displaying 50 questions, the question at the bottom is usually 2-3 hours old these days. Today it's seven hours old.
@Skullpatrol Okay, so your question was about the order of the numbers. Well, since $(ax+b)(cx+d)=(cx+d)(ax+b)$, if we switch both $a$ with $c$ and $b$ with $d$, then we get the same thing. We only need to swap one pair.
@Skull: Would I be correct in interpreting your "general selection condition" question as: "we know to fix the order of the quadratic terms, but how do we know which order to fix"? If so, the answer to that is in my answer: it's completely arbitrary.
@KannappanSampath Well, for a moment we can. (I'll have to go soon.) I just wanted to say that what we tried to attack yesterday had been a conjecture for some time. I saw the proof -- it's beyond my grasp.
I still haven't sussed out all of google's redirection rules; but it seems to me that using a google server in Poland from somewhere in Asia isn't the best idea in the world.
@robjohn @anon So it is arbitrary which pair of: a with c or b with d, we swap. But once that choice has been made the other pair of terms must be combined in every possible way?
@DavidWallace There is this button in Google books that is supposed to give you a working link. But what it does is essentially copy the address from the browser navigation bar into some field and highlights it. They could remove all the unneeded clutter and replace the localized version by com, where there is an automatic redirect to your local Google server.
@KannappanSampath Crap. I could see the whole article yesterday except for references. Now I see the first page only, but it doesn't say "those pages are not shown in this preview". It just says "loading..."
@ymar May be, we should ask someone who can access that Elsevier thingy! How sad! Why should we run for reading research papers.... They should be available for free easily!
@SKull: I already told you. If you fix the order of the quadratic terms (e.g. x,14x and 2x,7x, as opposed to 14x,x and 7x,2x), then you let the other pair vary (you have to check both -1,-5 and -5,-1). If, however, you fix the order of the constant terms (e.g. -1,-5 as opposed to -5,-1), then you have to check all of the orderings of quadratic terms: 14,1 and 1,14 and 2,7 and 7,2.
@Skull: Both tables include all possible orderings in my answer. It demonstrates that one half of the table is equivalent to the other half. Each column involves either fixing the quadratic terms one way (first table) or the constant terms one way (second table). You keep asking me things I've already answered.
@anon BTW Thanks for all your help, sometimes when you are struggling to understand something you don't listen to the person telling you the answer and I apologize for that.
@Skullpatrol - there are two taxis parked outside. They are going to provide transport home from the party, to two men and their wives. The men come out first, and it DOESN'T MATTER which man gets into which taxi. A minute later, the women come out. It's really important which woman gets into which taxi; otherwise, they both end up with the wrong man.
@Skullpatrol choose one pair to fix, the other pair must be permuted to give all possible match ups. It doesn't matter which pair you fix, the other pair needs to go through all the orders and choices.
In 3.7 you need "$f^{p-1}(x)\neq 0$ implies that $f^i(x)\neq 0$ for $0\leq i<p-1$ but not conversely." With $\leq$ instead of $<$ as in the text, the converse actually holds. @KannappanSampath
This is real torture. Reminds me in high school there was this chick that insisted that a Ferrari traveling at 100 km/h is faster than a Toyota traveling at 100 km/h.
If a Ferrari and a Toyota are both stationary, and you ask someone which is faster, they'll say the Ferrari. Why should it be any different if they're both going 100km/h?
I was thinking about how incongruous it would be, given that I have written about sheaves and descent in a fairly modern category-theoretic way, to write about cohomology using old-fashioned derived functors.
@BenjaminLim I learned about it at it during my undergrad years, but I started thinking about it seriously only sometime during my thesis and using it was only in 06 or around that time.
@BenjaminLim: It is not quite true that Tor is always the kernel. But it is close. The preface of Cartan and Eilenberg give a very nice sketch of why we might be interested in such things.
@tb: I read an article earlier today which had some amusing comments, like " This motivation is of course what guided the creators of derived categories (principally Verdier, or as he is traditionally known in this context, Grothendieck’s student Verdier) but, equally of course, is not written down."
@anon I see that there is some difference, but I see nothing wrong with yours. I will have to look at the others closer to see where the difference lies.
Neem Buds/Flowers for its bitterness, signifying Sadness
Jaggery and ripe banana pieces for sweetness, signifying Happiness
Green Chilli/Pepper for its hot taste, signifying Anger
Salt for saltiness, signifying Fear
Tamarind Juice for its sourness, signifying Disgust
Unripened Mango for its tang, signifying Surprise
Of course we prepare other sweets that day.....we only eat the Pachchadi as a formality....as the saying goes one must never miss a pinch of it on a Ugadi day
The question is to give a formula in $x$ and $y$ that gives all three sides of an equilateral triangle. The formula should not be true for points that are not part of the perimeter of the triangle.
David Wallace instructed me here to use polar coordinates and floor function describe the perimet...
...I have also iPad but only using to fast reading emails (when on the go), any idea whether it could be used for something else like reading math journals or something like that? (otherwise cannot see it much math related but perhaps I am too conservative)
@Skullpatrol Well so what, I neither if my friend had not bougth it to me. Most of the time paper and pen works better. It was totally useless to me if I had no procmail -etc servers which I have customed to fit my needs on the iPad... but iPad is secondary, there are serious probs with it such as data liberatation etc...
The question is to give a formula in $x$ and $y$ that gives all three sides of an equilateral triangle. The formula should not be true for points that are not part of the perimeter of the triangle.
David Wallace instructed me here to use polar coordinates and floor function describe the perimet...
