summaryrefslogtreecommitdiffstats
diff options
context:
space:
mode:
authorDavid A. Madore <david@procyon>2012-03-15 16:44:56 (GMT)
committerDavid A. Madore <david@procyon>2012-03-15 16:44:56 (GMT)
commit2b63d2fe87d077eac73a53abb61ed02f114d03fa (patch)
tree46a4c5fd03b710226bb6ba0c6f9efeb4c4e83181
parentbc75fc0b2d3c4878e79b05e60ededc7f4037d12e (diff)
downloadgalois-2b63d2fe87d077eac73a53abb61ed02f114d03fa.zip
galois-2b63d2fe87d077eac73a53abb61ed02f114d03fa.tar.gz
galois-2b63d2fe87d077eac73a53abb61ed02f114d03fa.tar.bz2
sageries: Changement sans conséquence sur le résultat du calcul.
-rw-r--r--divers/sageries/racine-13e-de-16
1 files changed, 4 insertions, 2 deletions
diff --git a/divers/sageries/racine-13e-de-1 b/divers/sageries/racine-13e-de-1
index 1760e4a..3952c6e 100644
--- a/divers/sageries/racine-13e-de-1
+++ b/divers/sageries/racine-13e-de-1
@@ -6,13 +6,15 @@ 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]
+sqrtm1 = zeta^3
+sqrt3 = -sqrtm3*sqrtm1
+nice_basis = [1, sqrtm3, sqrtm1, sqrt3]
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_basis = [1, sqrt(-3), sqrt(-1), sqrt(3)]
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