On Thu, Mar 3, 2011 at 3:04 PM, Bill Gosper <billgosper@gmail.com> wrote:

Axel>I guess you will trash the following (Maple) lame way:

...

sin(Pi/42); convert(%, exp); expand(%);

    -1/2*I*(-1)^(1/42)-1/2*I*(-1)^(41/42)

Yes, that's what happens when you heed Mma's message: "Developer`TrigToRadicals::obs:  Developer`TrigToRadicals has been superseded by ToRadicals, and is now obsolete.  It will not be included in future versions of Mathematica. "

I can't find this interesting (and endangered?) functionality elsewhere in Mma. The Mapleoid answer seems an elegant demonstration that sin pi/n is always expressible in radicals.  How can we articulate our dissatisfaction with it? Simply that the order of the roots is needlessly high, and we'll actually trade greater nesting depth to lower it?  Apparently Developer`TrigToRadicals somehow exploits a theorem(?) that the Galois group of the minimal polynomial of trig(pi/n) is always cyclic. --rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

FWIW, the minpolies of sin(pi/N) for the given N are: N : MIN POLY --------------- 26 : 64x^6 + 32x^5 - 80x^4 - 32x^3 + 24x^2 + 6x - 1 34 : 256x^8 + 128x^7 - 448x^6 - 192x^5 + 240x^4 + 80x^3 - 40x^2 - 8x + 1 42 : 64x^6 - 32x^5 - 96x^4 + 48x^3 + 32x^2 - 16x + 1