## #math - Sun 22 Apr 2007 between 22:46 and 23:02

### NY Lost Funds

 yi since we know it sends Q->Q(char F = 0)so maybe I need to factor x^4+1 into 4 linear factors |Steve| powerfox: That's moderately awful. Cale It factors as (x - beta) (x - beta^3) (x - beta^5) (x - beta^7) yi Cale: how did you get that? powerfox |Steve|: Yes it is :) brick_ http://www.webassign.net/knight/Ex5-07.gif <-- at T(3) is the acceleration 4 or 0? parker` is anyone here good with matlab? if I define a function how can I get matlab to evaluate that function at values I give? Cale Well, (x^2 + i) has +-sqrt(i), that is beta and beta^5 as roots yi Cale: see, I am confused because Auto(F/Q) is isomorphic to a subgroup of Bij(B) where B is the set of roots |Steve| powerfox: It's really, really ugly. yi Cale: so it's isomorphic to a subgroup of S_n where n is the number of rootswhich is 4 in this case Cale yep yi but why are there only 4 then?that's what I can't wrap my head around Cale It's a degree 4 polynomialSo it has 4 roots yi but S_4 has 4! elements Cale oh, have you worked out which ones are actually automorphisms? powerfox |Steve|: Yeh. But all 6 were not very difficult (some of them you've made). I think that there must be a something simple... Ot something not very difficult in firther integrating* all 7 yi Cale: no i haven't |Steve| % Integrate[Sqrt[(1+ArcTan[x])/(1-ArcTan[x])]/((1+x^2)(1+ArcTan[x])),x] mbot |Steve|: (2*ArcSin[Sqrt[1 + ArcTan[x]]/Sqrt[2]]*Sqrt[1 - ArcTan[x]]*Sqrt[(1 + ArcTan[x])/(1 - ArcTan[x])])/Sqrt[1 + ArcTan[x]] |Steve| The only thing that comes to mind is let u = arctan(x).% D[ArcTan[x],x] mbot |Steve|: (1 + x^2)^(-1) |Steve| That's what I thought. powerfox Stop, it's an answer? Cale Well, conjugation, which corresponds to the permutation (beta beta^7) (beta^3 beta^5) is certainly one. |Steve| So you have sqrt((1+u)/(1-u))du/(1-u) = sqrt((1+u)/(1-u)^3)du. Cale (that's in disjoint cycle notation) yi Cale: ah i see, give me a while to catch up i am still working out the factorization powerfox |Steve|: Thanks. I will try|Steve|: I can't kill it :( What's the way? |Steve| No idea. powerfox Ok. Thanks. You've helped me very much! If you're religious I would say: God bless you! |Steve| I'm not.