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Question: Q-extensions

Question:Q-extensions

loup blanc 50 Maple
evala
February 24 2007
0
Hi, Let P=256*x^8+128*x^7-448*x^6-192*x^5+240*x^4+80*x^3-40*x^2-8*x+1 and Q=x^8-36*x^7+210*x^6-462*x^5+495*x^4-286*x^3+91*x^2-15*x+1. The roots of these 2 irreducible (over Q) polynomials generate the same Q-extension. (P is the minimal polynomial of cos(2*Pi/17)). I'd want to write the Q-roots as algebraic functions of the P-roots; there exist 8 such functions. If I use "evala(Primfield{RootOf(P)}{RootOf(Q)})" I obtain an error message but I see that Maple has the result (in part hidden!!). What can I do ? More generally: let P,Q 2 irreducible polynomials over Q; do they generate the same Q extension ? Does a such test exist ? Thanks.
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