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author committer David A. Madore 2012-03-15 16:13:27 +0100 David A. Madore 2012-03-15 16:13:27 +0100 94e0454a6d6d7491286b2c19ed487936835fc7ec (patch) eb553521987d01b7c886ad59114372c3274eee95 /chapitres 2dec55d27d7a2bc4b141d49cdb26c6da4ca8478a (diff) galois-94e0454a6d6d7491286b2c19ed487936835fc7ec.tar.gzgalois-94e0454a6d6d7491286b2c19ed487936835fc7ec.tar.bz2galois-94e0454a6d6d7491286b2c19ed487936835fc7ec.zip
 diff --git a/chapitres/radicaux.tex b/chapitres/radicaux.texindex 3ba4931..0e5a9c6 100644--- a/chapitres/radicaux.tex+++ b/chapitres/radicaux.tex@@ -725,6 +725,25 @@ vaut $\sqrt{-11}$. On obtient finalement : \end{array} \] +\subsubsection{$n=19$} \XXX++$+\tiny+\begin{array}{rl}+\displaystyle\cos\frac{2\pi}{19}+&\displaystyle=+-\frac{1}{18}++(-\frac{1}{36}+\frac{1}{36}\,\sqrt{-3})\,\root 3\of{\frac{133}{2}-\frac{57}{2}\,\sqrt{-3}}++(-\frac{1}{36}-\frac{1}{36}\,\sqrt{-3})\,\root 3\of{\frac{133}{2}+\frac{57}{2}\,\sqrt{-3}}\\+&\displaystyle +(-\frac{1}{18}\,\root 3\of{\frac{1}{2}-\frac{1}{2}\,\sqrt{-3}}+\frac{1}{18}\,\root 3\of{\frac{9}{2}+\frac{3}{2}\,\sqrt{-3}})\,\root 9\of{\frac{130435}{2}+\frac{144609}{2}\,\sqrt{-3}-214776\,\root 3\of{\frac{1}{2}+\frac{1}{2}\,\sqrt{-3}}-1019502\,\root 3\of{\frac{1}{2}-\frac{1}{2}\,\sqrt{-3}}+599184\,\root 3\of{\frac{9}{2}+\frac{3}{2}\,\sqrt{-3}}+156978\,\root 3\of{\frac{9}{2}-\frac{3}{2}\,\sqrt{-3}}}\\+&\displaystyle +(-\frac{1}{18}\,\root 3\of{\frac{1}{2}-\frac{1}{2}\,\sqrt{-3}}+\frac{1}{18}\,\root 3\of{\frac{9}{2}+\frac{3}{2}\,\sqrt{-3}})\,\root 9\of{\frac{130435}{2}-\frac{144609}{2}\,\sqrt{-3}+778050\,\root 3\of{\frac{1}{2}+\frac{1}{2}\,\sqrt{-3}}+256158\,\root 3\of{\frac{1}{2}-\frac{1}{2}\,\sqrt{-3}}-99180\,\root 3\of{\frac{9}{2}+\frac{3}{2}\,\sqrt{-3}}-178866\,\root 3\of{\frac{9}{2}-\frac{3}{2}\,\sqrt{-3}}}\\+&\displaystyle +\frac{1}{18}\,\root 9\of{\frac{130435}{2}+\frac{144609}{2}\,\sqrt{-3}-41382\,\root 3\of{\frac{1}{2}+\frac{1}{2}\,\sqrt{-3}}+241452\,\root 3\of{\frac{1}{2}-\frac{1}{2}\,\sqrt{-3}}-420318\,\root 3\of{\frac{9}{2}+\frac{3}{2}\,\sqrt{-3}}-57798\,\root 3\of{\frac{9}{2}-\frac{3}{2}\,\sqrt{-3}}}\\+&\displaystyle +\frac{1}{18}\,\root 9\of{\frac{130435}{2}-\frac{144609}{2}\,\sqrt{-3}+241452\,\root 3\of{\frac{1}{2}+\frac{1}{2}\,\sqrt{-3}}-41382\,\root 3\of{\frac{1}{2}-\frac{1}{2}\,\sqrt{-3}}-57798\,\root 3\of{\frac{9}{2}+\frac{3}{2}\,\sqrt{-3}}-420318\,\root 3\of{\frac{9}{2}-\frac{3}{2}\,\sqrt{-3}}}\\+&\displaystyle +(-\frac{1}{18}\,\root 3\of{\frac{1}{2}+\frac{1}{2}\,\sqrt{-3}}+\frac{1}{18}\,\root 3\of{\frac{9}{2}-\frac{3}{2}\,\sqrt{-3}})\,\root 9\of{\frac{130435}{2}+\frac{144609}{2}\,\sqrt{-3}+256158\,\root 3\of{\frac{1}{2}+\frac{1}{2}\,\sqrt{-3}}+778050\,\root 3\of{\frac{1}{2}-\frac{1}{2}\,\sqrt{-3}}-178866\,\root 3\of{\frac{9}{2}+\frac{3}{2}\,\sqrt{-3}}-99180\,\root 3\of{\frac{9}{2}-\frac{3}{2}\,\sqrt{-3}}}\\+&\displaystyle +(-\frac{1}{18}\,\root 3\of{\frac{1}{2}+\frac{1}{2}\,\sqrt{-3}}+\frac{1}{18}\,\root 3\of{\frac{9}{2}-\frac{3}{2}\,\sqrt{-3}})\,\root 9\of{\frac{130435}{2}-\frac{144609}{2}\,\sqrt{-3}-1019502\,\root 3\of{\frac{1}{2}+\frac{1}{2}\,\sqrt{-3}}-214776\,\root 3\of{\frac{1}{2}-\frac{1}{2}\,\sqrt{-3}}+156978\,\root 3\of{\frac{9}{2}+\frac{3}{2}\,\sqrt{-3}}+599184\,\root 3\of{\frac{9}{2}-\frac{3}{2}\,\sqrt{-3}}}+\end{array}+$+ \ifx\danslelivre\undefined