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author committer David A. Madore 2012-03-08 18:18:06 (GMT) David A. Madore 2012-03-08 18:18:06 (GMT) b4f7969f03c9acc931112ee17b82fc160963db94 (patch) fe1aef8ea3e69ba8b50540264bb83c8112239505 9973d013efb65fdf5e60381d00f1bd88a4fb4300 (diff) galois-b4f7969f03c9acc931112ee17b82fc160963db94.zipgalois-b4f7969f03c9acc931112ee17b82fc160963db94.tar.gzgalois-b4f7969f03c9acc931112ee17b82fc160963db94.tar.bz2
 diff --git a/chapitres/radicaux.tex b/chapitres/radicaux.texindex 89be819..5846065 100644--- a/chapitres/radicaux.tex+++ b/chapitres/radicaux.tex@@ -704,6 +704,17 @@ vaut $\sqrt{-11}$. On obtient finalement : \end{array} \] +\subsubsection{$n=13$} \XXX++$+\begin{array}{rl}+\displaystyle\cos\frac{2\pi}{13}+&\displaystyle= - \frac{1}{12} + \frac{1}{12} \, \sqrt{13} + \frac{1}{24} {\left(-1 + \sqrt{-3}\right)} \, \root3\of{-\frac{65}{2} - \frac{39}{2} \, \sqrt{-3}}+- \frac{1}{24} \, {\left(1 + \sqrt{-3}\right)} \root3\of{-\frac{65}{2} + \frac{39}{2} \, \sqrt{-3}}\\+&\displaystyle + \frac{1}{24} {\left(1 + \sqrt{-3}\right)} \, \root6\of{-\frac{4381}{2} - \frac{195}{2} \, \sqrt{-3}} - \frac{1}{24} \, {\left(-1 + \sqrt{-3}\right)} \root6\of{-\frac{4381}{2} + \frac{195}{2} \, \sqrt{-3}}\\+\end{array}+$+ \ifx\danslelivre\undefineddiff --git a/divers/sageries/racine-13e-de-1 b/divers/sageries/racine-13e-de-1new file mode 100644index 0000000..e0b40eb--- /dev/null+++ b/divers/sageries/racine-13e-de-1@@ -0,0 +1,18 @@+K. = CyclotomicField(156)+omega = a^12+zeta = a^13+alpha = [sum([zeta^(i*j)*omega^(2^i) for i in range(12)]) for j in range(13)]+powtab = [NN(12/gcd(i,12)) for i in range(12)]+atab = [alpha[i]^powtab[i] for i in range(12)]+atab_on_zeta_basis = [(QQ^4)((zeta.coordinates_in_terms_of_powers())(x)) for x in atab]+sqrtm3 = 2*zeta^2-1+nice_basis = [1, sqrtm3, zeta, -zeta*sqrtm3]+m = Matrix(QQ, 4, 4, [(QQ^4)((zeta.coordinates_in_terms_of_powers())(x)) for x in nice_basis])+atab_on_nice_basis = [v * m.inverse() for v in atab_on_zeta_basis]+zetab = [ZZ(floor(arg(CC(N(alpha[i])/N(atab[i]^(1/powtab[i]))))/arg(zeta)+0.5)) for i in range(12)]+btab = [zeta^zetab[i] for i in range(12)]+btab_on_zeta_basis = [(QQ^4)((zeta.coordinates_in_terms_of_powers())(x)) for x in btab]+btab_on_nice_basis = [v * m.inverse() for v in btab_on_zeta_basis] +symbolic_basis = [1, sqrt(-3), sqrt((1/2)*(1+sqrt(-3))), sqrt(-(3/2)*(1+sqrt(-3)))]+symbolic_zeta = sum([sum([btab_on_nice_basis[i][j]*symbolic_basis[j] for j in range(4)])*(sum([atab_on_nice_basis[i][j]*symbolic_basis[j] for j in range(4)]))^(1/powtab[i]) for i in range(12)])/12+symbolic_cos = sum([sum([btab_on_nice_basis[i][j]*symbolic_basis[j] for j in range(4)])*(sum([atab_on_nice_basis[i][j]*symbolic_basis[j] for j in range(4)]))^(1/powtab[i]) for i in range(0,12,2)])/12