diff options
Diffstat (limited to 'divers/sageries/racine-13e-de-1')
| -rw-r--r-- | divers/sageries/racine-13e-de-1 | 6 |
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 |