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

### NY Lost Funds

 Tarantulafudge |Steve|: so for -6y=x^2 the parabola would be vertical and open upward? thermoplyae downwardnote the negative sign Tarantulafudge thermoplyae: oh right, okay I see parker` I thought matlab could do jacobians... I see a lot of tutorials on the net showing matlab doing jacobians with the function "jacobian()" but my version (the newest) doesn't seem to have this function Raikiri http://freshmeat.net/projects/asy/ A vector graphics language for technical drawing and LaTeX. Tarantulafudge thermoplyae: can the length of the latus be negative? for that same example I'm getting -6 thermoplyae What in the world is a 'latus'And no, length is always positive Tarantulafudge thermoplyae: latus rectum, sorry"The line segment through the focus of a parabola and perpendicular to the axis of symmetry" thermoplyae mmmMy guess is that you're forgetting an absolute value somewhere Tarantulafudge thermoplyae: your right, I found it thermoplyae What luck Tarantulafudge thermoplyae: lol sorrythermoplyae: thank you for all your help thermoplyae np x2 yi Let F = Q(beta) be the splitting field for x^4 + 1 over Q. beta = 8th root of unity. Show that Aut(F/Q) has exactly four elements.any ideas? Cale 8th root? powerfox [Steve]: sorry to trouble you, but may you help me with last integral? yi Cale: beta = sqrt(i) |Steve| The boss integral, if you will? yi Cale: or equivalently beta = (sqrt(2)/2) + (sqrt(2)/2)i powerfox sqrt ( (1+ arctgx)/(1-arctgx) ) * dx/ ( (1+x^2)*(1+arctgx) ) yi I showed that the minimal polynomial for beta over Q is x^4 + 1 Cale oh, I suppose it would be, yes yi since that factors as (x^2+i)(x^2-i) powerfox It is the second in my list, but I mist it for better time like now :) yi err, sorry I meant to say that F = Q(beta) is the splitting field for x^4+1 over Q Cale ah, right, somehow I'd read x^4 + 1 as x^4 - 1 :) powerfox *missed Cale That's why I was confused yi since it factors as (x^2+i)(x^2-i), so x = +/- sqrt(i) |Steve| arctgx is arctan(x)? yi but Q(sqrt(i), -sqrt(i)) = Q(sqrt(i)) Cale right powerfox arc tangent, inverse tangent, sin/cos yi so Aut(F/Q) = Aut(F)