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

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yisince 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.
CaleIt factors as (x - beta) (x - beta^3) (x - beta^5) (x - beta^7)
yiCale: 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?
CaleWell, (x^2 + i) has +-sqrt(i), that is beta and beta^5 as roots
yiCale: 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.
yiCale: so it's isomorphic to a subgroup of S_n where n is the number of roots
which is 4 in this case
Caleyep
yibut why are there only 4 then?
that's what I can't wrap my head around
CaleIt's a degree 4 polynomial
So it has 4 roots
yibut S_4 has 4! elements
Caleoh, 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
yiCale: 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.
powerfoxStop, it's an answer?
CaleWell, 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)
yiCale: 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.
powerfoxOk. Thanks. You've helped me very much! If you're religious I would say: God bless you!
|Steve|I'm not.

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