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 roots which 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 polynomial So 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. |