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authorDavid A. Madore <david+git@madore.org>2012-03-09 17:21:23 (GMT)
committerDavid A. Madore <david+git@madore.org>2012-03-09 17:21:23 (GMT)
commitc388cd310d8fbb15833403bbd85590983f034c08 (patch)
tree76a4d5135346d96964ca91184f3f85949ec8135c /divers
parent5add41d25031e5dc02504819ceb25bffc0fad68c (diff)
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sageries: mise à jour des fichiers de calculs de racines n-ièmes de l'unité.
Diffstat (limited to 'divers')
-rw-r--r--divers/sageries/racine-11e-de-121
-rw-r--r--divers/sageries/racine-13e-de-12
2 files changed, 22 insertions, 1 deletions
diff --git a/divers/sageries/racine-11e-de-1 b/divers/sageries/racine-11e-de-1
new file mode 100644
index 0000000..3da7c5e
--- /dev/null
+++ b/divers/sageries/racine-11e-de-1
@@ -0,0 +1,21 @@
+K.<a> = CyclotomicField(220)
+omega = a^20
+zeta = a^44
+zeta10 = -zeta^3
+alpha = [sum([zeta10^(i*j)*omega^(2^i) for i in range(10)]) for j in range(10)]
+powtab = [NN(10/gcd(i,10)) for i in range(10)]
+atab = [alpha[i]^powtab[i] for i in range(10)]
+atab_on_zeta_basis = [(QQ^4)((zeta.coordinates_in_terms_of_powers())(x)) for x in atab]
+sqrt5 = 1+2*(zeta+zeta^-1)
+sqrtm10m2sqrt5 = 2*(zeta-zeta^-1)
+sqrtm10p2sqrt5 = 2*(zeta^2-zeta^-2)
+nice_basis = [1, sqrt5, sqrtm10m2sqrt5, sqrtm10p2sqrt5]
+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(zeta10)+0.5)) for i in range(10)]
+btab = [zeta10^zetab[i] for i in range(10)]
+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(5), sqrt(-10-2*sqrt(5)), sqrt(-10+2*sqrt(5))]
+symbolic_omega = 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(10)])/10
+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(0,10,2)])/10
diff --git a/divers/sageries/racine-13e-de-1 b/divers/sageries/racine-13e-de-1
index e0b40eb..47d5016 100644
--- a/divers/sageries/racine-13e-de-1
+++ b/divers/sageries/racine-13e-de-1
@@ -14,5 +14,5 @@ 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_omega = 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